# EvoX Intelligent Evolution System and AI Native Research Practice Course Lecture Notes

Class Hours: 1 · Courseware Pages: 16

## Reading Navigation

- [Lesson 3 | Topic: Real-World Complexity and Multi-Objective Trade-offs](#lecture-lesson-1)

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## Lesson 3 | Topic: Real-World Complexity and Multi-Objective Trade-offs

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### Real-World Complexity and Multi-Objective Trade-offs

*Page 1*

> **Page Objective:** Explore the complex, mutually constraining objectives and constraints in the real physical world, and learn how to use EvoX to generate a set of candidate solutions that embody various trade-off relationships.

> **Page Objective**
>
> This page shifts the perspective from idealized optimization problems to the real physical world, pointing out that engineering objectives are often mutually constraining with sparse feedback, and introduces the idea of using EvoX to generate a set of candidate solutions that reflect different trade-off relationships.

> **Lecture Sequence**
>
> First explain why "objective conflicts" are universal—for example, in airfoil design, lift, drag, structural strength, and noise are difficult to optimize simultaneously; then explain that "sparse feedback" means evaluation costs are high and effective samples are few, making extensive trial-and-error infeasible; finally introduce multi-candidate exploration, where EvoX returns not just a single optimal solution but a set of solutions with advantages in different trade-off directions for subsequent decision-making.

**Key Teaching Points**

- Real systems are constrained by physical laws, manufacturing processes, safety standards, etc., and variables influence each other. Improving one metric often comes at the cost of worsening another, so there is no unique "best"—only compromises under different preferences. Real simulation or experimentation costs are high, feedback is not dense, and algorithms need to utilize existing evaluation information more efficiently. Generating a set of candidate solutions can reveal the trade-off frontier, helping engineers choose based on scenarios rather than being locked into a single solution. This can be used to concretely illustrate how to find multiple feasible designs among objectives such as aerodynamic efficiency, structural reliability, and noise.

**Keyword Coverage**

- Real-world complexity, multi-objective trade-offs, objective conflicts, sparse feedback, multi-candidate exploration, EvoX, airfoil optimization.

**Comprehension Check**

Ask students to give an engineering or everyday example of "improving A sacrifices B," and explain how the decision-making approach would differ if only one solution could be obtained versus a set of candidate solutions.

> **Transition Hint**
>
> After students can distinguish between "single-objective optimum" and "candidate set under multi-objective trade-offs," proceed to the next page on specific methods or case studies.

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### Multi-Objective Conflicts and Real-World Complexity

*Page 2*

> **Page Objective:** Learners should understand the fundamental reality of mutually constraining multiple objectives and nested constraints in the real engineering world.

**Key Teaching Points**

- Real engineering optimization faces the complexity of interwoven multiple objectives, multiple constraints, and expensive feedback. Objectives constrain each other, and there is no single ideal optimum without trade-offs, so the first step is to identify and accept conflicts rather than applying idealized single-objective assumptions. Objectives are not independent—improving one may worsen another; for example, increasing lift often accompanies increased drag or decreased stability.
- Constraints are nested—adjusting local variables affects other subsystems or lifecycle stages, forming coupled feasible regions and implicit boundaries.
- Feedback is expensive—high-fidelity simulation, wind tunnels, flight tests, and other evaluations are costly and cannot support unlimited trial-and-error.
- Objectives that are difficult to quantify, such as safety, stability, cost, regulations, and maintainability, are hard to unify into a single scalar. Improving one metric may worsen another. In aircraft design, increasing lift increases drag and reduces stability.
- If one continues to optimize a certain aerodynamic metric, it may trigger constraints on structural loads, thermal protection, or control complexity. This shows that real problems cannot be simplified into single-objective optimization. The system should not prematurely give a single isolated "optimal answer" but should explore and retain a set of differentiated candidate solutions, allowing experts to weigh benefits and costs.

**Exercise Handling**

The root cause of multi-objective conflicts (objectives constrain each other; improving one may worsen another); the consequence of increasing lift (increased drag, possibly decreased stability); the limitation of expensive feedback (high feedback cost, limited evaluation budget); the correct approach to multi-objective optimization (explore and retain a set of differentiated candidate solutions); the meaning of nested constraints (adjusting local variables affects other subsystems or lifecycle stages). Correct feedback can emphasize: multi-objective conflicts stem from structural trade-offs; lift and drag, stability are classic conflicts; expensive feedback limits trial-and-error; a single optimum often does not exist in real conflicts; nested constraints form coupled feasible regions.

Aircraft multi-objective optimization. The scenario is designing a new UAV that must simultaneously optimize aerodynamic efficiency, structural weight, stability, and manufacturing cost; high-fidelity CFD simulation takes hours, and wind tunnel testing is extremely expensive; objective conflicts such as increasing lift increases drag and structural loads, reducing weight may decrease stability; nested constraints such as aerodynamic shape changes affecting structural loads and thermal protection, which in turn affect control law design. Question 1 requires identifying at least two conflicts and explaining why they cannot be simply merged into a single objective. Reference: lift-drag conflict, weight-stability conflict; they cannot be simply merged because dimensions and priorities differ, merging requires subjective weights that may mask trade-off relationships and cause solutions to degrade in unexpected dimensions.

Question 2 requires describing how to use evolutionary computation to retain differentiated candidate solutions and explaining how experts weigh them. Reference: adopt multi-objective evolutionary algorithms (such as NSGA-II) to maintain a Pareto front, retaining a set of non-dominated solutions, each representing a different trade-off; experts can select appropriate solutions from the Pareto front based on mission requirements, or interactively adjust weights.

**Classroom Activity**

Ask students to retell the content of this page using an example close to their experience, and have them explain the relationship between this example and "first identify conflicts, then model."

**Comprehension Check**

Randomly ask a student to summarize the key points of this page in their own words, and the instructor supplements any missed keywords based on the response.

> **Transition Hint**
>
> After confirming students can articulate the core relationships on this page, proceed to the next page's examples, applications, or summary.

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### Trade-offs and Multi-Objective Exploration in the Real Physical World

*Page 3*

> **Page Objective:** Learners should grasp the core reason why the system cannot prematurely give a single isolated optimal solution.

**Key Teaching Points**

- When seeing any "optimal solution," first ask what it has conceded on which objective. Only when you can clearly explain both benefits and costs simultaneously can you truly understand a multi-objective problem.
- A candidate solution set is not delaying decisions but leaving preference judgments to those who best understand the task. Delivery should include a set of solutions with different emphases and their comparative basis, not a bunch of unranked scattered points.
- Every simulation or experiment incurs real costs. Under limited budgets, prioritize evaluating candidates that are diverse in distribution and cover different trade-off directions, rather than repeatedly fine-tuning around the same point—this yields more complete frontier information.

## Page Objective

Understand why optimization problems in the real physical world typically do not have a "cost-free unique optimal solution," and grasp the core logic and value of retaining differentiated candidate solutions in multi-objective exploration.

## Lecture Sequence

Objectives are difficult to fully quantify, constraints are nested, evaluation feedback is costly, and multiple objectives constrain each other.

2. Use the aircraft design example to illustrate "increasing lift often accompanies increased drag or decreased stability."

3. Using a Pareto front illustration, explain why one should not prematurely converge to a single answer.

Explore and retain a set of differentiated candidate solutions, providing experts with a basis for comparing benefits and costs.

5. Finally, clarify common misconceptions and handle exercises and case studies.

## Key Teaching Points

Three Key Facts**

Objectives can often only be partially quantified (such as "comfort" or "safety margin"), constraints are nested layer upon layer, and each real evaluation (high-fidelity simulation, bench testing, or flight testing) incurs considerable time and money.

Lift and drag, performance and stability, precision and energy consumption often cannot be simultaneously optimal; any improvement must clearly state what cost it incurs.

Unlimited attempts are not possible, so retaining diversity under a limited evaluation budget is more robust than prematurely locking onto a single point.

Why One Cannot Prematurely Converge to a Single Answer**

If the system delivers an isolated "optimal solution" early in exploration, the decision space is compressed: experts cannot see other possibilities and cannot judge what trade-offs this point has made between which two objectives. A more appropriate approach is to retain a set of candidate solutions along non-dominated relationships, each with different emphases on dimensions such as lift, drag, and stability, forming a Pareto front available for trade-offs. Each point on the front represents a legitimate trade-off—improving one objective requires sacrificing another; therefore the value of the front is not "which is best" but presenting the complete relationship between benefits and costs to support subsequent preference judgments and decisions.

Common Misconceptions**

Prematurely "weighted-summing" a multi-objective problem into a scalar objective is equivalent to deciding preference weights for experts before exploration, and trade-off information is lost. Weights should be the last step in the decision phase, not the first assumption in the modeling phase.

## Material Clues

The horizontal axis is Objective A—drag (further left is better), and the vertical axis is Objective B—stability (higher is better). The figure marks three differentiated candidates: Candidate A (low-drag priority), Candidate B (balanced), Candidate C (high-stability priority), all distributed on the non-dominated Pareto front. The figure also marks the dominated region (where improvement space exists), and a "prematurely converged single point" falls within the dominated region. An arrow is labeled "Benefit ⟷ Cost: left to expert trade-off."

## Exercise Handling

This page contains 5 multiple-choice questions for immediate comprehension checking. Correct answers and feedback points are as follows:

Choose "Objectives are often difficult to quantify, constraints are nested, evaluation feedback is costly, and multiple objectives constrain each other." Feedback: Accurately captures the three characteristics and multi-objective constraints.

This is a typical manifestation of multi-objective conflicts.

Choose "Compresses the decision space and masks true trade-off relationships, making it impossible for experts to judge what trade-offs this point has made." Feedback: A single-point answer compresses multi-dimensional trade-offs into a black-box conclusion.

Choose "Explore and retain a set of differentiated candidate solutions as a basis for experts to weigh benefits and costs." Feedback: The system should not overstep to decide for experts, nor should it prematurely converge.

"To improve one objective, another objective must be sacrificed." Feedback: Non-dominated means there is no solution that can simultaneously improve all objectives without worsening any.

## Case Discussion

The page provides a "Multi-Objective Design of Hypersonic Vehicle Airfoils" case, suggesting classroom discussion:

Objectives are difficult to quantify, constraints are nested, feedback is expensive, and multiple objectives conflict. Reference answers are in the page analysis.

Deliver a set of differentiated candidate solutions (such as low-drag priority, balanced, high-stability priority), providing objective values, constraint satisfaction status, and key trade-off explanations, allowing decision-makers to compare on the benefit-cost curve, with experts making the final selection based on preferences.

## Comprehension Check

Conclude with three key points:

When seeing any "optimal solution," first ask what it has conceded on which objective.

A candidate solution set leaves preference judgments to those who best understand the task; delivery should include a set of solutions with different emphases and their comparative basis.

Under limited budgets, prioritize evaluating candidates that are diverse in distribution and cover different trade-off directions, rather than repeatedly fine-tuning around the same point.

## Keyword Coverage

Candidate solution set, Pareto front, non-dominated, multi-objective trade-offs, evaluation budget, premature convergence.

## Transition Hint

After confirming learners can explain in their own words "why one cannot prematurely converge to a single point" and "how a candidate solution set supports expert trade-offs," proceed to the next page's examples, applications, or summary.

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### Finding Usable Answers and Thought Experiments

*Page 4*

> **Page Objective:** Learners should understand how to transform problems into explorable and verifiable systematic processes when facing real problems.

**Key Teaching Points**

- When encountering a real problem, first write down the four thought experiment questions: What can be changed? How to evaluate? What must be satisfied? How to judge what is better? If these four questions cannot be clearly answered, no matter what algorithm is chosen afterward, it will be difficult to obtain a usable answer.
- Each candidate solution should at least clearly state four items: benefits, costs, applicable conditions, and risks. Solutions that only say "faster, stronger" without stating costs and boundaries will almost certainly be questioned beyond the point of answering at review meetings.
- Weighting multiple objectives into a single score and taking the maximum is equivalent to assuming weights are already determined. If the weights themselves are subjective, this approach hides trade-off decisions inside the score. Retaining differentiated candidates and explicitly comparing them is closer to a "usable answer."

> **Page Objective**
>
> Understand that when facing real engineering problems, the first task is not choosing an algorithm but transforming the problem into an explorable, executable, and verifiable thought experiment; and systematically expanding exploration in different directions, retaining a set of differentiated candidate solutions rather than prematurely converging to some so-called "optimal answer."

> **Lecture Sequence**
>
> 1. First discuss real-world multi-objective constraints. Increasing aircraft lift may alter drag and stability; reducing model latency may harm accuracy; improving system performance may increase energy consumption, cost, and safety risks. Progress on one metric often comes at the cost of regression on another, so a single-point answer that is "best on all metrics" typically does not exist.
>
> What can be changed? How to evaluate after changes? What conditions must be satisfied? How to judge which results are better?
>
> List variable items and decision variables, such as parameters, structures, strategies, scheduling rules, and clearly define fixed conditions.
>
> Determine metrics and evaluation criteria, such as whether to look at timeliness or energy consumption, peak or average, and which data segment to measure.
>
> Clarify hard constraints and boundaries, such as safety thresholds, latency limits, energy and budget caps, regulations and airspace permits; out-of-bounds solutions are directly eliminated.
>
> Define comparison criteria and preferences, explaining which objective is more important in what scenarios and the acceptable cost range.
>
> 3. Discuss output form. Exploration should expand in different directions, outputting a set of differentiated candidate solutions, each annotated with benefits, costs, applicable conditions, and risks, allowing domain experts to compare choices under different preferences.
>
> Executable, evaluable, satisfying hard constraints, capable of explaining trade-offs, and able to support choices under different preferences. A single-point answer that maximizes only one metric typically does not satisfy these criteria.
>
> Horizontal and vertical axes can represent two mutually constraining objectives; curves or point clusters represent the reachable solution domain; outside hard constraints is the out-of-bounds region. Candidates A through D each have trade-offs; the point of the figure is not to find the unique optimal point but to retain differences and explicitly compare them.

> **Exercise Clues**
>
> - Define variable items, evaluation criteria, hard constraints, and comparison criteria. Do not first ask "which algorithm to use" or "collect data first." Question 2 should choose "Progress on one metric often comes at the cost of regression on another, so a unique global optimum typically does not exist." Objective conflicts are the norm in real problems, not a definition error. Question 3 should explain that premature convergence to a single point loses differentiated candidate solutions and weakens the space for experts to choose and decide under different preferences. In Question 4, the item that is NOT a criterion for a "usable answer" is "achieving a global maximum on one single metric while other metrics can be ignored." Question 5 should explain that thought experiments expose objective conflicts, constraint boundaries, and evaluation criteria before execution, establishing a usable problem framework for subsequent multi-objective exploration. Urban UAV delivery scheduling. Students can be guided to transform the scenario into four questions: variable items include routes and altitude layers, speed profiles, takeoff/landing points and transfer points, charging or battery-swap timing, task batching and order consolidation, aircraft assignment, etc.
> - Fixed conditions include weather, airspace permits, and urban geography. Evaluation metrics include average delivery time, energy consumption per package, safety margin, task completion rate and waiting time distribution, and whether to look at peak hours or all-day averages. Hard constraints at minimum include battery safety margin thresholds, no-fly or rescheduling when wind speed exceeds limits, no violation of no-fly zones and airspace permits, and single-load not exceeding aircraft limits. Comparison criteria should state that timeliness is more important during peak hours, safety margin and completion rate are more important in severe weather, and clearly define acceptable cost ranges, avoiding crude weighting into a single score. Customer preferences, weather, and airspace conditions change; a single-point optimum only holds under one set of assumptions.
> - The candidate set covers different benefit-cost combinations; experts can select based on the day's constraints and preferences, and know each solution's applicable boundaries and risks. Each solution should at least annotate benefits, costs, applicable conditions, risks, and differences from other solutions in the same set. First, choosing an algorithm before thinking about the problem.
> - Second, forcibly weighting multiple objectives into a single score and taking the maximum is equivalent to hiding subjective trade-offs inside the score.
> - Third, only writing "faster, stronger" without costs and boundaries makes it difficult to answer at review.

**Comprehension Check**

Ask students to retell the four questions in their own words and give an engineering or everyday example to explain how objectives conflict, how candidates retain differences, and how hard constraints eliminate out-of-bounds solutions. After confirming students can articulate the three things—"problem transformation, candidate set, usable answer criteria"—proceed to the next page on how EvoX carries multi-objective exploration.

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### Problem Transformation: From Choosing Algorithms to the Exploration Process

*Page 5*

> **Page Objective:** Learners should master the variable objects, evaluation criteria, and constraints that need to be clarified when facing real problems.

**Key Teaching Points**

- When receiving any new task, first list the variable objects: which parameters, structures, strategies, or processes are allowed to be adjusted? This list is the skeleton of the search space and encoding. After it is clearly written, then discuss algorithms.
- Don't wait until the final round to discover that a solution is not deployable. Put non-negotiable requirements (such as latency limits, memory limits, deployment compatibility) directly into the generation or evaluation stage for filtering, so that exploration only proceeds in regions that do not violate constraints.
- Retrospective analysis should use the same problem definition: first fix the search space, evaluation method, and constraints, then compare the performance of different algorithms. This way you can determine whether differences come from the algorithm or from the problem definition itself.

Page Objective

When facing real problems, don't immediately ask "DE or PSO?" Instead, first transform the task into an explorable process. Learners need to master three things: what can be changed, how to evaluate after changes, and which constraints absolutely cannot be violated, and understand that algorithm selection is merely a configurable component within this loop.

Lecture Sequence

Picking up a task and first doing algorithm selection only answers "what tool to use for searching," not "what to search, what counts as good, what cannot be violated."

Real problem → Variable objects (parameters · structures · strategies → encoding) → Evaluation method (objective functions, metrics, preferences) → Core constraints (hard constraints and soft preferences) → Exploration process loop (candidate generation → evaluation → feedback → regeneration) → Candidate solution set.

Variable objects, evaluation methods, core constraints, exploration process.

4. Compare the difference between "one-time algorithm selection" and "closed-loop exploration," pointing out that problem definition quality determines the exploration ceiling.

5. Consolidate with multiple-choice questions and a recommendation ranking model case.

Key Teaching Points

Define which parameters, structures, strategies, or processes are allowed to be adjusted, forming the search space and encoding boundaries. Without this, candidate solutions cannot be represented or generated.

Define how to judge quality after changes, including objective functions, evaluation metrics, preference directions, and measures of feasibility and diversity. The evaluation method essentially determines which direction the search will go.

Distinguish between hard constraints that must be satisfied and soft preferences that can be traded off. Mixing hard constraints into the objective function with a "discount" easily produces solutions that appear to score high but cannot actually be deployed.

Formalize the problem into a loop of "candidate generation—evaluation—feedback—regeneration," letting evaluation results in turn influence subsequent generation, rather than fixing the solution approach once and for all.

Sequentially answer: which parameters are adjustable? What metrics or which conflicting metrics to use for evaluation? Which constraints absolutely cannot be violated? After answering these questions, the task has been formalized into a multi-objective problem that can be plugged into an evolutionary solver; at this point, deciding which algorithm to use and with what operator configuration to explore is merely a replaceable engineering decision within the loop. In other words, the algorithm is not the answer itself; it is just a configurable part of the exploration process, and the quality of the problem definition determines the exploration ceiling.

Directly attributing "poor algorithm performance" to the algorithm itself while ignoring vague search space definitions, evaluation metrics disconnected from real business objectives, and missing hard constraints. Fixing the problem definition first before discussing algorithm replacement is often more effective than repeatedly switching algorithms.

Material Clues

The real problem first passes through variable objects, evaluation methods, and core constraints before entering the exploration process loop. The loop highlights four stages: candidate generation, evaluation, feedback, and regeneration, and emphasizes that algorithm selection is merely an internal component of the loop. When explaining, follow the arrows in the diagram to help students see the sequential relationship between "problem definition" and "algorithm execution."

Exercise Handling

The first step should define which parameters, structures, strategies, or processes are allowed to be adjusted, forming the search space and encoding boundaries. Feedback should emphasize: variable objects make candidate solutions representable, and subsequent evaluation and iteration can then proceed.

The evaluation method should define how to judge quality after changes, including objective functions, metrics, preferences, and measures of feasibility and diversity. Feedback should explain that it is not an accessory to the algorithm but the "steering wheel" of the exploration process, and needs to be determined by the task itself.

P99 latency not exceeding 80 milliseconds is a hard constraint that must be satisfied. Feedback should distinguish "must satisfy" from "try to satisfy": non-negotiable requirements are hard constraints, while trade-off tendencies are soft preferences; hard constraints should be filtered upfront in the generation or evaluation stage.

The key difference between a closed loop and one-time selection is that evaluation results in turn change subsequent generation, continuously adjusting the search direction. Feedback should emphasize that the focus is not on speed or algorithm type but on whether evaluation results can flow back to change subsequent generation methods.

The algorithm is not the answer itself because problem definition quality determines the exploration ceiling, and the algorithm is merely a configurable, replaceable component within the exploration process. Feedback should guide students to shift attention from "which algorithm to switch to" toward "is the problem defined clearly enough."

Case Guidance

The recommendation ranking model multi-objective tuning case can be organized as "variable objects—evaluation methods—core constraints." Variable objects include learning rate, regularization coefficient, network layers, attention heads, feature combination strategies; evaluation methods are offline AUC maximization, online P99 inference latency and model parameter count minimization, with candidate diversity possibly added; core constraints are P99 latency not exceeding 80 milliseconds, memory not exceeding 12GB, and ability to deploy directly on the existing inference framework; soft preferences are fewer parameters and lower latency under the premise of satisfying hard constraints.

Candidate generation samples hyperparameters and structural configurations; evaluation computes AUC and measures or estimates latency and memory usage while checking hard constraints; the feedback stage updates the search distribution based on multi-objective quality and preferences, then generates a new generation of candidates. Deployability assurance treats latency, memory, and framework compatibility as hard constraints to directly eliminate infeasible solutions during generation or evaluation; for expensive metrics like latency, surrogate models or small-scale measurements can be used for preliminary screening, followed by full validation of a small number of candidates. The final output is a set of candidate solutions well-distributed across objective trade-offs, handed to engineering and product decision-makers for selection.

Comprehension Check

Problem definition precedes algorithm selection; variable objects determine the search space and encoding; evaluation methods determine search direction; hard constraints must be filtered upfront; algorithms are merely replaceable components within the loop. If students only recite algorithm names, follow up with "At which stage does the algorithm enter? What needs to be determined before it?"

Transition Hint

After confirming students can explain "first define what is variable, how to evaluate, what cannot be violated, then organize the solution into a loop," proceed to the next page's specific methods, applications, or summary.

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### Preference Optimization and Multi-Candidate Solution Sets

*Page 6*

> **Page Objective:** Learners should understand the practical role of retaining a set of diverse candidate solutions in expert decision-making.

> **Page Objective**
>
> Understand that preference optimization does not make final decisions for experts but uses preferences as guiding signals for search and screening, and lets algorithms output a set of candidate solutions that are comparable and interpretable in trade-off structure, leaving the trade-off authority to domain experts.

**Key Teaching Points**

- Do not prematurely compress multiple objectives into a single scalar score.
- Do not deliver just one "optimal solution" but output a set of candidate solutions. Under multi-objective conflicts, there is no naturally unique optimal solution; comparable solutions link together into an ideal trade-off frontier. Prematurely weighted-summing is equivalent to selecting an implicit compromise point for decision-makers.
- Once constraints or preferences change, that solution may immediately lose value. Reference points, objective priorities, weight intervals, interactive feedback. Together they are used to narrow the focus region and improve search efficiency, not to collapse the solution space into a single point prematurely. Value = Differentiation × Interpretability. Effective differences are not random noise, nor are they perturbed copies near the same solution, but are dispersed along the objective trade-off structure, with representatives at the conservative end, the compromise segment, and the aggressive end. Evolution will spontaneously converge toward the current optimal region, so distribution maintenance, crowding control, or archive set strategies are needed; otherwise the candidate set will degenerate into repeated expressions of a single answer.

**Keyword Coverage**

- Preference optimization, candidate solution set, ideal trade-off frontier, differentiation retention, interpretability, crowding control, archive set strategies.

> **Material Clues**
>
> - The horizontal axis is cost (smaller is better), the vertical axis is latency (smaller is better), the curve is the ideal trade-off frontier, preference reference points guide the search direction, and candidate solutions should be dispersed along the frontier.
> - The right side compares traditional weighted summation that gives only a single optimal point versus preference optimization that gives a candidate solution set.

> **Exercise Clues**
>
> - Preference optimization encodes decision-maker preferences into the search and screening process, rather than scoring once after search is complete. Feedback should emphasize "when preferences intervene" and explain that preferences do not eliminate objective conflicts. Effective differences = dispersed distribution on objective trade-offs + each difference explainable by trade-off structure. Hint to students: large quantity and large differences do not equal effective. Preference forms such as reference points or weight intervals are used to narrow the search focus region and improve efficiency, not to prematurely collapse the solution space into a single point. Hint: preferences do not replace objective functions, nor do they automatically guarantee diversity. Without distribution maintenance, crowding control, or archive set strategies, evolution naturally converges to the current optimal region, and the candidate set becomes repeated copies near the same solution. A change in output form means a change in decision authority: the algorithm provides a comparable candidate set, domain experts combine real-world constraints to make the final trade-off, and can use the selection results as feedback for continued iteration. In urban delivery fleet scheduling and routing decisions, preference optimization uses reference points, objective priorities, weight intervals, or interactive feedback as selection and screening signals during iteration.
> - In output form, it changes from a single "optimal schedule" to a candidate solution set along the cost-latency trade-off frontier, such as conservative (cost-priority), balanced (cost-latency balanced), aggressive (latency-priority). If all candidate solutions are very close in cost and latency, one should suspect the absence of differentiation maintenance mechanisms.
> - To judge whether differences are effective, project solutions onto the cost-latency plane and check whether points are clearly dispersed along the frontier, and whether each point's trade-off direction can be explained by the objective trade-off structure.

**Comprehension Check**

Ask students to distinguish "guiding" from "replacing" in their own words, and explain why candidate set value equals differentiation × interpretability. If students only emphasize quantity, follow up: "Can these solutions be interpreted as different compromise patterns on the objective trade-off?"

> **Transition Hint**
>
> After confirming students can explain that preference optimization is for retaining expert trade-off authority, and that the candidate set must be comparable and interpretable, proceed to the next page on application cases or method details.

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### Multi-Objective Practice Background of Supercritical Airfoil Design

*Page 7*

> **Page Objective:** Learners should understand the specific application scenarios and multiple constraints of supercritical airfoil design in aerospace engineering.

> **Page Objective**
>
> Understand the real engineering scenario of supercritical airfoil design, grasp multi-objective conflicts and constraints, and know that the reasonable output is a set of compromise solutions rather than a single optimal solution.

**Key Teaching Points**

- 1. Operating conditions and physical sources. During transonic cruise, airflow accelerates to supersonic speed on the upper surface of the airfoil, then decelerates through a shock wave.
- Shock wave position and strength simultaneously affect drag levels and buffet onset boundaries. Therefore, design is not about pushing one metric to the extreme but about having multiple metrics simultaneously fall within acceptable ranges. 2. Triple constraints. The critical buffet lift coefficient provides the safety and usable lift boundary; premature buffet occurrence compresses buffet margin and flight envelope, making it a threshold that cannot be breached.
- Cruise lift-to-drag ratio reflects aerodynamic efficiency and economics, determining range, fuel consumption, and operating costs—it is the main benefit item.
- High-fidelity simulation costs are high, and single evaluation costs are large, limiting the explorable design space and constituting a resource constraint. 3. Sources of conflict. Improving cruise lift-to-drag ratio typically requires a stronger leading-edge suction plateau and a more aft shock wave, but this weakens the buffet boundary.
- To preserve buffet margin by making the airfoil more relaxed, cruise efficiency may be sacrificed. The typical manifestation is "improving one item, worsening another." 4. Solution approach. What engineering really needs is a set of Pareto compromise solutions that hold under different preferences, allowing decision-makers to make interpretable choices among safety, efficiency, and cost. This can be combined with baseline airfoils and perturbation samples for continuous generation and prediction, turning serial screening into parallel multi-objective exploration and outputting diverse candidate solutions. 5. Judgment criteria. Whenever "improving one metric worsens another" occurs and the metric has a hard lower bound, it should be treated as a multi-objective constrained problem—do not seek a single optimal solution that does not exist.

**Keyword Coverage**

- Supercritical airfoil
- Critical buffet lift coefficient
- Cruise lift-to-drag ratio
- High-fidelity simulation cost
- Multi-objective conflicts and trade-offs
- Pareto front
- Feasible compromise region.

> **Material Clues**
>
> - An airfoil cross-section diagram can illustrate the upper surface suction region, shock wave, and lower surface high pressure.
> - A multi-objective trade-off space diagram can illustrate the trade-off between cruise lift-to-drag ratio and buffet margin, the feasible compromise region, the dominated region, and the Pareto front.

**Exercise Handling**

Multiple-choice questions sequentially examine the multi-objective compromise nature, the safety boundary role of the buffet coefficient, the relationship between cruise lift-to-drag ratio and economic efficiency, serial trial-and-error being limited by simulation budget, and the reasonable approach being to retain Pareto compromise solutions. After answering, ask students to state their reasoning; if incorrect, return to the corresponding paragraph to check the three types of information: "objectives, constraints, resources." For the case question, first determine that the objective is to maximize cruise lift-to-drag ratio, constraints are the buffet coefficient safety threshold and simulation budget cap; then explain using baseline airfoil plus perturbation samples for generation and prediction, exploring in parallel under a limited number of evaluations, outputting an interpretable candidate solution set, with evaluation criteria being each solution's specific values on the buffet boundary and cruise lift-to-drag ratio.

**Comprehension Check**

Which item on this page is a benefit objective, which is a threshold that cannot be breached, and why traditional point-by-point trial-and-error is difficult to effective. If students can only recite terms, follow up with "How does improving cruise lift-to-drag ratio affect buffet margin?"

> **Transition Hint**
>
> After confirming students can distinguish objectives from constraints and explain the "one rises, one falls" conflict, proceed to the next page's examples, applications, or summary.

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### Continuous Generation of Baseline Airfoils and Perturbation Samples

*Page 8*

> **Page Objective:** Learners should master how the system combines baseline airfoils with perturbation samples for continuous prediction.

> **Page Objective**
>
> Understand the closed loop of "baseline airfoil—perturbation samples—prediction/evaluation—evolutionary feedback—continuous generation" in airfoil optimization, master how baseline airfoils provide stable anchors, how perturbation samples provide diversity, and how evolutionary feedback makes multi-objective exploration continuous and scalable.

> **Lecture Sequence**
>
> 1. Establish the baseline first. The baseline airfoil must first satisfy task constraints; it defines the parameterization space, perturbation range, and evaluation criteria. Without a baseline, the search space easily drifts disorderly, and candidate airfoils cannot be fairly compared.
>
> 2. Then generate perturbations. Around the baseline airfoil, apply controlled perturbations to thickness distribution, camber, or control point parameters, continuously generating sample families in batches or online. Small perturbations are for local refinement, large perturbations for global coverage; perturbation strength, direction, and sampling distribution should all be controllable.
>
> 3. Batch prediction/evaluation. Send each round of samples into the prediction/evaluation stage, outputting the performance of multiple candidates on objectives. These performances are not the endpoint but the direct basis for subsequent evolutionary selection, updating, and resampling.
>
> 4. Close with feedback. Adjust the next round's perturbation strength, direction, or sampling distribution based on evolutionary feedback, making the loop truly continuous rather than independently repeating sampling each round.

**Key Teaching Points**

- Baseline airfoil selection
- Continuous perturbation sample generation
- Multi-sample prediction combined with evolution
- Continuous closed loop. The baseline airfoil is a stable reference, not the final answer.
- It makes different perturbation samples comparable under the same evaluation criteria. Perturbation samples provide diversity, balancing local and global. If each round only does small perturbations in the same direction, the population easily matures prematurely.
- If completely random large perturbations are used, evaluation budget may be wasted. A more robust approach is to mix local and global perturbations and use feedback to determine the next round's sampling focus. Evolutionary feedback must act on the next round's perturbation generation strategy. If results are only recorded without changing sampling, the loop degenerates into an open-loop process.

**Exercise Handling**

The main role of the baseline airfoil is to serve as a stable anchor for parameterization, perturbation range, and evaluation benchmarks. When correct, emphasize that it anchors the search space, prevents disorderly drift of candidates, and enables fair sample comparison; when incorrect, return to the evidence of "what happens without a baseline."

When continuously generating perturbation samples, perturbation strength, direction, and sampling distribution should be adjusted in batches or online. Single-direction small perturbations limit diversity; completely random large perturbations waste budget; neither is sufficient to balance local refinement and global coverage.

After perturbation samples are batch-fed into prediction/evaluation, the main output is the performance of multiple candidates on objectives, for use in evolutionary selection, updating, and resampling. A hint: prediction/evaluation is the input to the evolutionary process, not hard-coded labels or final answers.

Evolutionary feedback supports "continuous" generation by adjusting perturbation strength, direction, or sampling distribution, then supplementing the next round of samples. If feedback only records without changing sampling, the loop cannot continuously improve.

The approach that best embodies the closed loop is generating an airfoil sample family each round, entering evolution after evaluation/prediction, then supplementing the next round of perturbation samples based on results. Without any of sample generation, evaluation/prediction, evolutionary feedback, or resampling, continuous optimization cannot be formed.

Case Clues:

In supercritical baseline airfoil optimization, the objectives are to maximize lift-to-drag ratio, minimize drag divergence, and maintain structural thickness constraints; each round can generate 256 samples, and evaluation takes a long time. A round of workflow can be designed as: using the baseline airfoil as an anchor, applying controlled perturbations to thickness distribution, camber, or control points to generate a batch of airfoil samples; batch-feeding into prediction/evaluation to obtain lift-to-drag ratio, drag divergence, thickness constraint, and other performances; then entering evolutionary selection, updating, and resampling; finally adjusting the next round's perturbation strength, direction, or sampling distribution based on feedback. The baseline airfoil cannot be arbitrarily replaced because it defines the parameterization space, perturbation range, and evaluation benchmark; replacement would cause search space drift, make candidates incomparable, and cause the loop to lose its stable reference.

If evolution stagnates for several consecutive rounds, feedback can be used to increase perturbation strength or expand the sampling distribution to introduce global diversity; perturbation direction can also be adjusted to conduct targeted exploration of sensitive parameters such as thickness and camber; local fine perturbations and global perturbations can also be mixed, sample batches increased or supplemented online, and diverse candidates on the Pareto front retained to avoid premature population maturation.

Ask students to retell the four stages of the loop in one sentence and explain why the baseline airfoil cannot be replaced by perturbation samples. After confirming students can articulate the relationship of "first set the anchor, then control perturbations, feed evaluation into evolution, adjust the next round with feedback," proceed to the next page's examples, applications, or summary.

<a id="lecture-page-9"></a>

### Application of Surrogate Models in Addressing High Simulation Costs

*Page 9*

> **Page Objective:** Learners should understand how surrogate models effectively overcome the bottleneck of high-fidelity simulation costs.

> **Page Objective**
>
> Understand why surrogate models can effectively address the bottleneck of high-fidelity simulation costs, and master their positioning, intervention approach, and risk control in multi-objective evolutionary optimization.

> **Lecture Sequence**
>
> First point out that directly embedding high-fidelity simulation into the evolutionary loop causes rapid budget depletion; then explain how surrogate models as "cheap approximate evaluators" replace point-by-point evaluation; next use the comparison between direct high-fidelity optimization and surrogate-assisted optimization to elaborate the acceleration mechanism; then focus on the four stages of offline training, online batch prediction, surrogate-assisted point selection, and backfilling correction; finally discuss accuracy-cost trade-offs, out-of-distribution risks, common misconceptions, and self-check lists.

**Key Teaching Points**

- In problems such as supercritical airfoils and structural strength, a single CFD or finite element simulation takes tens of minutes to hours. Evolutionary algorithms must evaluate the entire population each generation, and evaluation counts and budgets are consumed approximately linearly—the budget will be exhausted by a few generations. Population size and iteration generations are forced to compress, the multi-objective front is difficult to fully explore, and the design space is blockaded by "cannot afford to evaluate."
- Learn input-output mappings from existing simulation samples to rapidly predict candidate solutions' objective values and constraint performance.
- It is not a more accurate simulation but a cheaper approximation. It replaces point-by-point evaluation, not the verification stage. On the left, direct high-fidelity optimization has few candidates, long single evaluation time, few total evaluations, and narrow search coverage.
- On the right, surrogate-assisted optimization has many candidates, extremely low single prediction cost, many total evaluations, broader coverage, with high-fidelity budget concentrated on key candidates, accompanied by uncertainty threshold screening and a small number of high-fidelity verifications. Offline training establishes a preliminary mapping.
- Online batch prediction evaluates all candidates each generation.
- Surrogate-assisted point selection combines predicted values and uncertainty to select high-potential or high-information candidates.
- Backfilling correction writes a small number of high-fidelity results back to the sample library and incrementally updates the surrogate. More complex surrogates are usually more accurate, but training and inference overhead increases. The key constraint is that the surrogate must be significantly faster than high-fidelity simulation while being accurate enough to support selection pressure, otherwise it becomes a new bottleneck or misleads evolution. Surrogates are only reliable near the training distribution. Out-of-distribution predictions may appear reasonable but severely deviate from true values, misleading search. Feasible approaches include outputting uncertainty estimates, setting confidence thresholds, forcing high-fidelity verification for out-of-bounds candidates, and periodically checking surrogate quality with error statistics. Surrogate models do not cancel verification, nor do they solve problems by compressing the population.
- Their value is concentrating scarce high-fidelity budget on the most critical and uncertain candidates.

**Keyword Coverage**

- Surrogate model, high-fidelity simulation, cheap approximate evaluator, offline training, online batch prediction, surrogate-assisted point selection, backfilling correction, uncertainty threshold, out-of-distribution prediction, accuracy-cost trade-off.

> **Exercise Clues**
>
> - Running high-fidelity simulation for every candidate should be changed to surrogate batch approximate screening plus a small number of high-fidelity verifications. Incorrect options often mistakenly believe in canceling verification or compressing the population. Single simulation costs are high, and evaluating the entire population each generation rapidly depletes the budget. The limitation comes from cost, not differentiability or multi-objective capability. More complex models are usually more accurate but slower in training and inference, requiring matching with evolutionary search speed. One cannot assume complexity has no cost or that simpler is more accurate. Predictions may severely deviate from true values and mislead search. Surrogates do not automatically switch to high-fidelity or automatically correct deviations; uncertainty and verification are needed for control. Let the surrogate continuously correct toward the true response surface, reducing subsequent prediction bias. It is not used to reduce candidate count or replace uncertainty estimation. The process can be written as initial sampling, offline training, online batch prediction, screening, high-fidelity verification, backfill updating, loop iteration.
> - Risk control emphasizes uncertainty estimation, confidence thresholds, reserved supplementary sampling budget, error statistic monitoring, and prioritizing high-fidelity budget allocation to candidates near the front.

**Comprehension Check**

Ask students to explain in their own words five things—who replaced whom, at which step the surrogate intervenes, how to screen out unreliable predictions, which candidates the high-fidelity budget is spent on, and how verification results are backfilled to correct the surrogate.

> **Transition Hint**
>
> After confirming students can distinguish "approximate screening" from "true verification," proceed to the next page's applications or summary.

<a id="lecture-page-10"></a>

### Outputting Diverse Candidate Solutions That Balance All Metrics

*Page 10*

> **Page Objective:** Learners should master how the system ultimately outputs a combination of candidate solutions that balance multiple metrics.

> **Page Objective**
>
> Understand that in multi-objective engineering optimization, the system outputs not a single optimal solution but a set of diverse candidate solutions balancing multiple metrics; master the multi-metric evaluation mechanism, the role of surrogate models, Pareto front comparison methods, and reproducibility requirements.

> **Lecture Sequence**
>
> 1. First confirm the output form. In multi-objective problems like airfoil design, the final delivery is a set of candidate solutions, not a single-point answer. It is necessary to observe the trade-off patterns of the entire candidate set on metrics such as critical buffet lift coefficient, cruise lift-to-drag ratio, structural weight control, and disturbance robustness.
>
> 2. Explain why it is not a single-point answer. When objectives conflict—for example, increasing critical buffet lift coefficient often accompanies decreased cruise lift-to-drag ratio—there is no feasible solution that simultaneously dominates on all metrics. If evaluation is dominated by a single metric, search will converge to a compromise solution that is acceptable on average but not outstanding on any key metric, or even lose design directions with clear preferences.
>
> 3. Explain the generation and prediction mechanism clearly. The multi-metric evaluation mechanism incorporates multiple constraints and objectives into the same evaluation space; continuous generation and prediction continuously produce new candidates around baseline airfoils and perturbation samples, using surrogate models to rapidly estimate metrics, thereby alleviating the bottleneck of high-fidelity simulation costs.
>
> 4. Explain output and comparison methods. Candidate solutions cover different metric preferences and trade-off positions. Plot two key metrics as a scatter plot; points on the outer edge that are not simultaneously exceeded by other candidates on all metrics form the Pareto front, while points on the inner side are dominated. Engineering review typically selects solutions from the front first, then returns to high-fidelity simulation for confirmation; different positions on the front correspond to orientations such as buffet suppression priority or cruise efficiency priority.
>
> 5. Emphasize reproducibility. Each candidate should be traceable to the baseline airfoil and perturbation source, evaluation results on these metrics, and its position on the Pareto front. Without any of these, solution comparison is difficult to verify.

**Key Teaching Points**

- Multi-metric evaluation mechanism, continuous generation and prediction, diverse output forms, comparability. Surrogate models are sieves, not final judges; they are responsible for rapid estimation and guided screening and cannot replace high-fidelity simulation verification on key candidates.

> **Material Clues**
>
> - Radar charts use closed curves to represent metric preferences of different candidate airfoils.
> - On scatter plots, further to the upper right indicates better on both metrics simultaneously.
> - Dashed lines mark non-dominated candidates; gray points indicate dominated candidates.

**Exercise Handling**

The exercises on this page revolve around output form, surrogate model responsibilities, value of diversification, reproducibility records, and the relationship between two metrics. Reference directions: The system delivers a set of candidate solutions balancing different trade-offs; surrogate models perform rapid estimation and guide screening, with final high-fidelity verification still needed for key candidates; the value of diversification lies in explicitly retaining trade-off positions between conflicting metrics, supporting comparison and decision-making; the multi-dimensional metric results and generation perturbation sources should be retained for each candidate; critical buffet lift coefficient and cruise lift-to-drag ratio typically trade off on the front. In the case question, high-fidelity simulation is not executed for each candidate because the number of candidates is large and continuously growing, while single simulation costs are high; surrogate models first narrow the scope, and a small number of key solutions are then verified.

If review needs to choose between buffet suppression priority and cruise efficiency priority, the candidate set provides options, the Pareto front marks optimal trade-off positions, and comparable records ensure reproducibility and verifiability.

**Comprehension Check**

Ask students to explain in their own words why the system outputs a candidate solution set rather than a single-point answer, and state at least three records that support reproducibility.

> **Transition Hint**
>
> After confirming students can distinguish the roles of surrogate model screening and high-fidelity simulation confirmation, proceed to the next page.

<a id="lecture-page-11"></a>

### Addressing Objective Conflicts and Sparse Feedback in Complex Engineering

*Page 11*

> **Page Objective:** Learners should understand methods for addressing sparse feedback and objective conflicts in engineering practice.

> **Page Objective**
>
> Understand the normality of objective conflicts and sparse feedback in complex engineering optimization, and master the approach of replacing single-objective optimization with dynamic multi-objective compromise.

**Key Teaching Points**

- Real engineering often simultaneously pursues performance, cost, reliability, energy consumption, and manufacturing constraints, and these metrics constrain each other. For example, in supercritical airfoil design, increasing lift-to-drag ratio may exacerbate drag divergence, while strengthening structure increases weight and manufacturing difficulty. The key is not ranking metrics but identifying which segment of the Pareto front one is currently on and clarifying what can be exchanged. Evaluation methods such as high-fidelity simulation and physical experiments have high costs, long cycles, high noise, and often return failure samples. Effective evaluation signals are few, delayed, and discontinuous, making the evaluation budget a hard constraint. Surrogate model bias is amplified, overfitting and premature convergence risks increase, the balance between exploration and exploitation is easily disrupted, and fixed preferences struggle to adapt to phased discoveries. Use surrogate models and multi-fidelity evaluation to reduce single feedback costs.
- Use active sampling and batch experiments to improve sample efficiency.
- Use multi-objective evolution to maintain multiple non-dominated candidates and preserve Pareto front diversity.
- Dynamically update preferences and constraints with evaluation results, outputting diverse candidate sets for expert evaluation. The goal is not to eliminate conflicts but to make conflicts, risks, and trade-off relationships interpretable without relying on knowing the unique answer in advance.

> **Exercise Clues**
>
> - The 5 multiple-choice questions on this page respectively examine (1) identification of objective conflicts.
> - (2) characteristics of sparse feedback.
> - (3) impact of surrogate model bias under sparse feedback.
> - (4) approaches to improving sample efficiency.
> - (5) reasonable understanding of preference and constraint updating. When answering, grasp keywords such as "few, expensive, slow, noisy, failure samples" and distinguish objective conflicts from sparse feedback. Liquid cooling plate multi-objective design. Objective conflicts manifest as mutual constraints among heat dissipation performance, pressure drop, weight, cost, and manufacturability.
> - Sparse feedback manifests as high-fidelity CFD requiring tens of hours, bench experiments requiring weeks with fluctuations, and process-infeasible samples directly failing. Response: on the evaluation side, use surrogate models and multi-fidelity evaluation, active sampling.
> - On the search side, use multi-objective evolution to maintain diversity.
> - On the preference side, periodically update weights, constraints, and reference points to avoid being locked in by early fixed weights.

**Comprehension Check**

Ask students to summarize in their own words the difference between objective conflicts and sparse feedback, and give an example illustrating the role of any stage in the dynamic adjustment loop.

> **Transition Hint**
>
> After confirming students can articulate the core relationship of "objective conflicts + sparse feedback → dynamic multi-objective compromise," proceed to the next page.

<a id="lecture-page-12"></a>

### The Decision-Making Role of Domain Experts and Solution Evaluation

*Page 12*

> **Page Objective:** Learners should understand the division of responsibilities between human experts and automated systems in multi-objective exploration.

> **Page Objective**
>
> Understand how automated systems and domain experts divide and collaborate in multi-objective exploration workflows, and how experts transform domain experience into reviewable, traceable evaluation and decision logic.

> **Lecture Sequence**
>
> First point out that "the system spreads out possibilities, experts converge possibilities," then explain the responsibility boundaries between the system side and the expert side; next explain why a single-objective optimum does not equal a deliverable solution, introducing the benefit-cost evaluation matrix; then provide the decision sequence of threshold veto, benefit-cost trade-off, and sensitivity analysis; finally discuss verification under sparse feedback, resampling or termination decisions, and how selection rationale flows back to form a responsibility loop.

**Key Teaching Points**

- The system side completes large-scale candidate generation, surrogate model prediction, Pareto front characterization, and diversity maintenance, answering "what possibilities exist."
- The expert side injects objective priorities, hard constraints, and risk tolerance, judges real-scenario suitability, makes final selections and bears responsibility, answering "which one to choose and why." The boundary is: the system provides a comparable candidate set and quantitative predictions but does not decide bottom lines and preferences for experts.
- Experts provide preferences, constraints, and decision criteria but do not personally complete the generation and screening of massive candidates. Solution evaluation should transform performance benefits and engineering costs into interpretable, auditable evidence. In addition to performance benefits, it should also examine computational and manufacturing costs, robustness, maintainability, uncertainty, and the credibility of conclusions under sparse feedback. A single-objective optimum is often not deliverable; multi-dimensional evaluation allows different candidates to reveal their respective applicable scenarios. Express domain experience as explicit preferences, hierarchical evaluation, decision matrices, threshold veto items, and sensitivity analysis. The common sequence is to first use hard constraints to "veto" candidates violating bottom-line requirements, then conduct benefit-cost trade-offs on remaining candidates, and finally use sensitivity analysis to confirm whether conclusions are robust to weight perturbations. Compensating for hard flaws with weighted total scores is the most common misconception. When high-fidelity evaluation is expensive and feedback is sparse, experts should decide whether to verify, resample, or terminate search based on surrogate model confidence, candidate diversity, and observed failure patterns, rather than blindly trusting the "optimal solution" given by the surrogate. Final selection and risk-taking belong to domain experts.
- Selection rationale should flow back as preferences, constraints, or evaluation signals to guide the next evolutionary search, forming a responsibility loop. In supercritical airfoil multi-objective design, the system outputs candidates balancing drag, lift, and stability.
- Experts combine wind tunnel and simulation costs, manufacturing tolerances, and mission profiles to first eliminate those violating hard constraints, then conduct benefit-cost trade-offs on remaining solutions, select a few for high-fidelity verification, and flow this round's rationale back as the next round's preferences and constraints.

**Keyword Coverage**

- Multi-objective exploration, generation and screening, judgment and decision-making, Pareto front, benefit-cost evaluation matrix, threshold veto, sensitivity analysis, sparse feedback, responsibility loop.

> **Exercise Clues**
>
> - 1. The system side is responsible for large-scale candidate generation, surrogate model prediction, and Pareto front characterization.
> - If hard constraint judgment, objective priorities, or risk-taking are selected, remind that these belong to the expert side. 2. Should comprehensively consider performance benefits, computational and manufacturing costs, robustness, maintainability, and uncertainty.
> - A single-objective optimum does not equal deliverable. 3. Under sparse feedback, decide whether to verify, resample, or terminate based on surrogate model confidence, candidate diversity, and failure patterns. 4. Threshold veto items are used to first veto candidates violating hard constraints, then weigh remaining candidates—not unified weighted scoring. 5. The purpose of selection rationale flowing back is to transform selection rationale into preferences, constraints, or evaluation signals to guide the next evolutionary search. First explain the boundary between system-side "generation and screening" and expert-side "judgment and decision-making."
> - Then follow "threshold veto → benefit-cost matrix → sensitivity analysis" to determine which candidates enter high-fidelity verification.
> - If confidence is insufficient or diversity is low, choose resampling or verification.
> - Finally explicitly record this round's rationale as preferences, constraints, or evaluation signals and input them into the next round of search.

**Comprehension Check**

Ask students to distinguish "expanding options" from "converging options" in their own words, and give an example illustrating the respective actions of the system side and expert side in an engineering decision. If students attribute final decisions, risk-taking, or hard constraint judgment to the system side, return to the responsibility division for re-analysis.

> **Transition Hint**
>
> After confirming students can clearly explain the closed-loop relationship of "generation—evaluation—selection—feedback," proceed to the next page's examples, applications, or summary.

<a id="lecture-page-13"></a>

### Classroom Activity: Multi-Objective Parameter Optimization Evaluation Scheme Design

*Page 13*

> **Page Objective:** Learners should design a parameter optimization evaluation scheme that includes lift and drag trade-offs through practice.

**Key Teaching Points**

- Lift and drag are the original conflicting objectives; composite metrics like lift-to-drag ratio can only be used for explanation and presentation. Self-check method: Remove the composite metric—can the scheme still compare the trade-offs of two candidates? If not, the original objectives have been masked.
- Engineering constraints such as thickness and pitching moment—once violated, the solution is unusable; do not use weighting to soften them into scores that can offset each other. When writing the scheme, annotate each item: is this a hard constraint or a soft preference, and report constraint satisfaction in the results.
- The passing line for evaluation results is: a set of candidates covering different lift-drag trade-offs + metric evidence + constraint satisfaction + uncertainty description + records (seed, budget, elimination rationale). Delivering only one "optimal solution" typically means you have already made the trade-offs for experts.

Page Objective

This page is a classroom activity design; the task is to transform the mutually pulling "lift-drag" objectives into a reproducible, comparable multi-objective parameter optimization evaluation scheme that can be handed to experts for decision-making. The focus of the activity is not to have the model directly give an optimal answer but to design an evaluation mechanism that can be repeatedly tested: who participates in evaluation, what metrics to use, under what constraints and budget, and by what rules candidates are retained. Ultimately, "conflicts" should be written as "executable review rules."

Lecture Sequence

Generate candidates → Enter evaluation → Compare benefits, costs, and constraints based on feedback → Retain effective solutions → Record and enter the next round.

Objectives and constraints, six-step evaluation loop, output candidate set and decision interface, reproducible records.

Lift and drag are the original conflicting objectives; composite metrics like lift-to-drag ratio are only for explanation and presentation.

Candidates should cover different lift-drag trade-off regions; screening results should not retain only one highest score.

5. Provide a deliverable template and conclude with common misconceptions.

Key Teaching Points

Objective A is to maximize lift coefficient, Objective B is to minimize drag coefficient; the two must be independent columns. Do not replace them with lift-to-drag ratio, otherwise trade-offs will be prematurely "flattened" by a single ratio.

Parameter boundaries, relative thickness, pitching moment range, etc. are typically set as hard constraints—violation means elimination; cost, engineering manufacturability, etc. are set as soft preferences for ranking. When writing the scheme, annotate each item as "hard constraint" or "soft preference," and report constraint satisfaction in the results.

Clearly state simulation or surrogate model invocation counts, time, and compute limits, and distinguish between "surrogate evaluation" and "high-fidelity verification" quotas; otherwise different schemes cannot be fairly compared.

Parameter representation → Candidate generation → Evaluation computation → Metric summary → Scheme comparison → Record archiving.

Initial sampling spreads globally; perturbation, crossover, and mutation perform local refinement; preference guidance densifies in expert focus regions; require candidates to be distributed in different lift-drag trade-off regions, avoiding entire generations collapsing to a single direction of "high lift" or "low drag."

Pareto non-dominated, weighted sum, threshold filtering, reference points, or preference ranking can be used; but the output should be a set of candidates covering different trade-offs, accompanied by metric evidence, constraint satisfaction, candidate differences, and uncertainty ranges for expert judgment.

Combining lift and drag into a single total score and taking the maximum appears simplifying but actually uses weight selection to make trade-offs for experts in advance and also loses candidate diversity. The correct approach is to retain multiple candidate sets and leave the judgment of "which one to choose" after the evaluation interface.

A one-page evaluation scheme template, including metric tables (original objectives and auxiliary metrics), six-step flowchart, candidate generation rules, screening rules, output candidate set, risk and uncertainty description; also record parameters, metric definitions, evaluation budget, random seeds, screening basis, and elimination rationale.

Classroom Activity

Ask learners to design a brief multi-objective evaluation scheme for a parameterized object (such as airfoil parameters), which must make the lift-drag trade-off explicitly visible. Fill in four blocks: ① Objectives and constraints; ② Six-step evaluation loop; ③ Output candidate set and decision interface; ④ Reproducible records. After completion, have groups peer-review: Remove the composite metric—can the scheme still compare the trade-offs of two candidates? Are hard constraints mistakenly treated as scores that can be weighted and offset? Is the output only one "optimal solution"?

Exercise Handling

Basic judgments can be reviewed around the following points:

Maximize lift coefficient, minimize drag coefficient; the correct option emphasizes that the two are independent and lift-to-drag ratio can only assist explanation.

2. Thickness and pitching moment range should be set as hard constraints—violation means elimination; the budget should pre-specify invocation counts, time, and compute limits, and hard constraints cannot be relaxed due to budget constraints.

3. Candidate generation should include initial global sampling, combined with perturbation, crossover-mutation, and preference guidance, so that candidates are distributed across multiple trade-off regions.

4. Scheme comparison should output a set of non-dominated candidates covering different lift-drag trade-offs, with disagreements and basis attached; retaining only the highest weighted sum score or listing only a long ranking does not meet activity requirements.

5. Record archiving should at minimum include parameter representation and boundaries, metric definitions, evaluation budget, random seeds, screening basis, and elimination rationale, so that the next round can determine whether result changes come from scheme changes or evaluation condition changes.

Case Review

In the supercritical airfoil scheme, if the team ranks by weighted sum and retains only the first place, the problem is prematurely dissolving the lift-drag conflict, losing Pareto diversity, and experts cannot see trade-off intervals. Modification direction: Switch to Pareto non-dominated screening, retaining several candidates covering different trade-off regions on the front; if retaining weighted sum, provide multiple weight sets or reference points and record the basis. To let the second round inherit this round's results, also supplement parameter and boundary, metric units, hard constraint/soft preference division, budget and actual invocation counts, surrogate model version, random seeds, screening basis, and elimination rationale; each candidate should be accompanied by metric evidence, constraint satisfaction, uncertainty range, and candidate difference descriptions, and provide an expert trade-off interface.

Comprehension Check

Why can't lift-to-drag ratio replace lift and drag as independent objectives? Why can't hard constraints participate in weighted offsetting? Why is a candidate set more suitable for experts than a single optimal solution? Answers that connect metrics, constraints, budget, candidate diversity, and recording requirements are sufficient.

Transition Hint

After confirming learners can clearly explain the main line of "original conflicting objectives—hard constraints/soft preferences—candidate generation—diversified output—reproducible records," proceed to the next page's examples, applications, or summary.

<a id="lecture-page-14"></a>

### Classroom Activity Review: Reasonableness Verification of Trade-off Schemes

*Page 14*

> **Page Objective:** Learners should understand how to verify and reflect on whether the designed trade-off evaluation scheme is scientifically effective.

> **Page Objective**
>
> This page is a review of the classroom activity "Multi-Objective Parameter Optimization Evaluation Scheme Design," with the core being to verify whether the designed trade-off evaluation scheme is reasonable. Learners should be able to identify omitted key metrics and objective conflicts, and clarify the adjustment direction for parameter configurations, making the scheme closer to real engineering decision needs.

> **Lecture Sequence**
>
> It is recommended to first clarify that the first-principles question of the review is "Does the scheme characterize real decisions?" then expand along seven dimensions: ① Objective coverage ② Conflicts and redundancy ③ Constraints and preferences ④ Parameter configuration ⑤ Surrogate models ⑥ Candidate diversity ⑦ Expert support; next derive adjustment directions from the review diagnosis; finally use three criteria—comparability, trade-off capability, and reproducibility—to judge whether the scheme is qualified.

**Key Teaching Points**

- When objectives, constraints, and preferences are incomplete, any parameter tuning is merely refining on the wrong model. Are all quantities that decision-makers truly care about (performance, cost, reliability, manufacturability) included in the scheme? Are hard limits written as constraints? Are preferences explicitly expressed as weights or reference points? Trade-offs are conflicts and should be retained as multi-objectives, with weights or reference points expressing preferences.
- Same-direction changes with overlapping information are redundancy and should be merged or one deleted, avoiding the same demand being double-counted. Judgment mnemonic: Look at direction, and also check whether weights are double-counted. Also check whether any constraint is mistakenly treated as an objective. Does population size and candidate count cover trade-off intervals?
- Does iteration budget match surrogate model accuracy?
- Do mutation, crossover, and selection pressure balance exploration and exploitation?
- Does the sampling strategy direct simulation budget to high-information regions? Any mismatch will manifest as "results exist but are unusable." Insufficient diversity → expand population size and candidate output set.
- Too-fast convergence → reduce selection pressure, increase mutation strength, relax elite retention.
- Excessive evaluation cost → improve surrogate model accuracy, optimize point-adding and sampling strategies.
- Preference deviation → correct weights or move reference points.
- Missing metrics or conflicts → supplement metrics, retain trade-off relationships as multi-objective structure. Comparable—domain experts can clearly see trade-offs between candidates.
- Trade-off capable—can select solutions from the front based on preferences.
- Reproducible—parameters, random seeds, and process records are complete. The final output should be diverse candidates balancing all metrics, not a single "optimal solution." Supercritical airfoil design review. If only lift-to-drag ratio is focused on while structural strength or manufacturing cost is omitted, first supplement metrics and explicitly retain conflicts as multi-objectives.
- Then include evaluation budget, population size, and candidate output count in the parameter adjustment list.
- Finally use "Is the front wider? Can experts compare trade-offs? Are results reproducible?" to verify whether adjustments are effective.

**Keyword Coverage**

- Coverage check, objective coverage, conflicts and redundancy, multi-objective retention, weights/reference points, population size, selection pressure, mutation strength, surrogate models, sampling strategies, trade-off front, comparable, trade-off capable, reproducible.

> **Exercise Clues**
>
> - Check whether objectives, constraints, and preferences are complete, prioritizing discovery of omitted key metrics. Analysis: Metric omission systematically distorts all subsequent trade-offs; coverage check must be done first before discussing parameter adjustments. Two metrics change in the same direction with highly overlapping information—how to handle? Answer: This is redundant measurement; merge or delete one to avoid weights being repeatedly amplified. Analysis: Conflicts are trade-offs; redundancy is same-direction with overlapping information.
> - Redundancy causes the same demand to be double-counted. Optimization converges within very few iterations with highly similar candidates—what parameter adjustment best matches? Answer: Expand population size and candidate output set, increase mutation strength, and reduce selection pressure. Analysis: Too-fast convergence is usually caused by excessive selection pressure and insufficient mutation leading to diversity collapse. How should real conflicts like lift-to-drag ratio and structural strength be handled? Answer: Retain as multi-objectives, use weights or reference points to reflect preferences, and output a trade-off front for expert trade-offs. Analysis: Real conflicts should not be masked by single-objectivization; retaining multi-objectives and explicitly expressing preferences supports decision-making. High-fidelity simulation evaluation costs are too high and iteration budget is insufficient—what is the most reasonable adjustment? Answer: Improve surrogate model accuracy and optimize sampling strategy, concentrating budget on high-information regions. Analysis: Surrogate models and sampling strategies should bear the evaluation cost, rather than sacrificing exploration scale or rewriting the problem definition. Supercritical airfoil design review. Question 1: Point out problems in objective coverage—conflicts/redundancy—constraints and preferences. Reference points: Metric omission (structural strength, manufacturing cost).
> - Conflicts not explicitly handled (lift-to-drag ratio vs. structural strength).
> - Constraints and preferences not made explicit (geometry, processes, safety margins).
> - Expand population size to over 100, candidate output 20–50.
> - Reduce selection pressure, increase mutation strength.
> - Improve surrogate accuracy, improve sampling (e.g., uncertainty-based point addition).
> - Correct weights or move reference points.
> - Candidates cover wider, crowding decreases, front coverage and distribution quality improve, surrogate error decreases, experts can clearly compare trade-offs, results are reproducible.

**Comprehension Check**

Randomly ask students to summarize the key points of this page in their own words, and the instructor supplements any missed keywords based on the response. Follow up: "If the objective set itself is incomplete, what happens to subsequent parameter tuning?" Guide students to say "it is merely optimizing on the wrong model."

> **Transition Hint**
>
> After confirming students can explain "coverage check first, then parameter adjustment" and "conflicts retained as multi-objectives, redundancy merged or deleted," proceed to the next page's examples, applications, or summary.

> **Material Clues**
>
> - This page features a "Scheme Reasonableness Verification Checklist" diagram, with seven verification dimensions listed on the left, corresponding adjustment directions on the right, and expected verification evidence at the bottom. When explaining, unfold step by step according to the diagram.

<a id="lecture-page-15"></a>

### Core Concept Review of This Lesson

*Page 15*

> **Page Objective:** Learners should systematically review the multi-objective trade-offs, surrogate models, and supercritical airfoil case covered in this lesson.

> **Page Objective**
>
> Help learners systematically review the three core concepts of this lesson—multi-objective trade-offs, surrogate model cost reduction, and supercritical airfoil multi-objective practice—and connect the main line of "conflicts—non-dominated candidates—preference decisions."

> **Lecture Sequence**
>
> First point out that this page is a concluding page; the main line of this lesson is that evolutionary computation provides a solution path that does not pre-specify a unique answer, relying on parallel generation of population candidates and diversity to address objective conflicts and complex constraints. Then review along three main lines: first, objective conflicts and Pareto trade-offs; second, surrogate model cost reduction and verification; third, multi-candidate solution sets and expert decisions. Finally, use cases and memory chains to ground knowledge in the engineering loop.

**Key Teaching Points**

- In real engineering, cruise efficiency, structural thickness, and handling stability constraints often constrain each other. Do not prematurely weight-compress into a single objective, otherwise conflicts will be hidden, preferences solidified, and trade-off information lost. Retaining Pareto candidates gives subsequent decisions room to maneuver. When high-fidelity CFD, wind tunnel, or experiments have high single evaluation costs while search requires many evaluations, surrogate models trade accuracy for speed, accelerating search, screening, and sensitivity analysis. But their credibility comes from independent verification samples, error evaluation, and uncertainty quantification.
- Training set fitting accuracy cannot directly prove generalization reliability. Baseline airfoil perturbation → surrogate-assisted search → diverse candidate output → expert evaluation decision forms a closed loop. The focus is not a unique answer but producing a comparable, interpretable, decision-ready solution set. Experts make trade-offs based on mission preferences and constraints, and new samples are fed back to update the surrogate model. If only lift-to-drag ratio is optimized, solutions with unacceptable drag divergence characteristics or pitching moment may be obtained.
- After retaining the candidate set, trade-offs can be made between cruise efficiency, structural thickness, and handling stability constraints according to mission preferences, also facilitating response to preference changes, robustness comparison, and decision traceability. Samples/simulation → surrogate model → multi-objective search → candidate evaluation → preference decision → new sample feedback. Students can be asked to retell each step and add one sentence about "why it is necessary."

**Exercise Handling**

The multiple-choice questions on this page can be used for quick checking. Question 1 should choose "Premature compression hides conflicts between objectives and narrows the trade-off design space," emphasizing that multi-objective methods explicitly retain non-dominated relationships; Question 2 should choose "When high-fidelity simulation or wind tunnel single evaluation costs are high while search requires many evaluations," emphasizing that the value of surrogate models depends on evaluation cost and count; Question 3 should choose "Use independent verification samples to evaluate prediction error, and quantify and monitor prediction uncertainty," emphasizing generalization and credibility; Question 4 should choose "Baseline airfoil perturbation → surrogate-assisted search → diverse candidate output → expert evaluation decision," emphasizing the closed-loop output of a solution set;

Question 5 should choose "Supports preference changes, robustness comparison, and decision traceability, reducing the risk of single-path lock-in," emphasizing that the candidate set retains trade-off space.

First, instead of directly doing single weighted high-fidelity optimization, first build a surrogate model and retain the Pareto candidate set—the reasons are "cost reduction" and "retaining trade-off space"; second, if the surrogate model has large local deviations, first use independent verification samples to locate high-error or high-uncertainty regions, then supplement high-fidelity verification for selected candidates, with adaptive sampling if necessary, and finally check whether the Pareto front still maintains non-dominated relationships under verification data.

**Comprehension Check**

Ask students to explain in their own words "why retain a candidate set rather than only one optimal solution," and explain why surrogate models must be verified. If students can only recite terms, follow up with "the role of each step in 'conflicts → non-dominated candidates → preference decisions.'"

> **Transition Hint**
>
> After confirming students can articulate the three main lines of this page and their closed-loop relationships, proceed to the next page's summary, applications, or new topics.

<a id="lecture-page-16"></a>

### Summary and Outlook: Research Value in the Real Complex World

*Page 16*

> **Page Objective:** Learners should appreciate the profound research value of retaining diverse usable solutions in addressing real-world complexity.

> **Page Objective**
>
> The research value in real engineering and the physical world is not about using a single algorithm to rapidly converge to an "optimal answer," but about transforming multi-objective conflicts, physical constraints, and sparse feedback into a sustainable exploration process. The core idea of EvoX and AI Native practice is to provide space for subsequent trade-offs, decisions, and methodological evolution by generating and retaining diverse usable solutions.

> **Lecture Sequence**
>
> 1. Start from the "real complex world" on the left, explaining that multi-objective conflicts, physical constraints, and sparse feedback are the norm, not the exception.
>
> 2. Explain why single-objective optimization loses key information. Supercritical airfoil design can be used as an example: lift-to-drag ratio, drag divergence characteristics, structural thickness, and other objectives constrain each other; improving lift-to-drag ratio may sacrifice drag divergence performance or increase structural thickness. If only pursuing single-objective optimization, trade-off relationships are lost, and there is no room for adjustment when facing new constraints or preference changes.
>
> The output should not be a single solution but a candidate solution set containing multiple trade-off relationships. With EvoX, large numbers of candidate airfoils can be generated in parallel, and surrogate models can assist evaluation when simulation costs are high, covering different preferences and constraints.
>
> Support domain expert decision-making; reduce early erroneous convergence risk; preserve possibilities for subsequent problem restructuring and continuous evolution.
>
> The direction of AI Native research is to advance from "choosing algorithms to find answers" to "designing reusable, verifiable, inheritable exploration processes," making real complexity a source of methodological innovation.

**Key Teaching Points**

- In real problems, objectives often constrain each other; do not habitually seek a unique optimal solution but first ask: Have I overlooked certain trade-off relationships? Evolutionary exploration should output a set of candidate solutions containing different trade-off relationships. Diverse solution sets can cover more preferences and constraints, preserving space for expert decisions and subsequent evolution. The left side is the real complex world, the middle is EvoX-driven exploration, and the right side is research value.
- At the bottom there is also a "continuous evolutionary feedback" loop, reflecting that the exploration process does not end once but is accumulable and inheritable. The research value in the real complex world lies in transforming multi-objective conflicts, physical constraints, and sparse feedback into a sustainable exploration process.
- EvoX and AI Native practice provide space for subsequent trade-offs, decisions, and methodological evolution by generating and retaining diverse usable solutions. Exercise Clues and Handling: Multiple-choice questions revolve around "core concepts," "research exploration value demonstrated by airfoil design," and "long-term significance of retaining diverse usable solutions." Correct answers should point to: Retaining diverse usable solutions has profound research value in addressing real-world complexity. If students answer incorrectly, guide them back to this page's explanation to find key evidence or examples before judging.
- If correct, affirm that they can connect to this page's concepts and explain the basis. Question 1: Multi-objective conflicts manifest in conflicts among lift-to-drag ratio, drag divergence characteristics, structural thickness, and other objectives—for example, improving lift-to-drag ratio may come at the cost of increasing structural thickness or sacrificing drag divergence performance. Question 2: Diverse candidate solution sets cover different preferences and constraints, facilitating expert evaluation of trade-offs while reducing early erroneous convergence risk, and preserving inheritable exploration space for subsequent problem restructuring, constraint changes, or methodological evolution. When correct, you can say "This answer connects to this page's concepts and explains the basis."
- When incomplete, you can say "Please return to this page's explanation, find key evidence or examples, and then judge."

**Comprehension Check**

Why is retaining diverse usable solutions more valuable for research than outputting only a single optimal solution? Require connecting at least one example from this page (supercritical airfoil design) and one long-term significance (supporting expert decisions or continuous evolution). If students can only recite terminology, follow up on whether they can give an example illustrating the relationship between "multi-objective conflicts" and "candidate solution sets."

> **Transition Hint**
>
> After confirming students can articulate the relationship of "multi-objective conflicts—candidate solution sets—research value," proceed to the next page or course summary.