Q1. The CSS mechanism relies on assessing the consistency of historical predictors. However, there is only one predictor available at t=0.

A1. Thank you for your insightful comment. We actually train multiple predictors at t=0 rather than relying on a single one. These predictors are then used to compute and assess consistency. We will clarify this detail in the revised manuscript.

Q2. It would be interesting to discuss whether using different predictor architectures could lead to significant differences in prediction accuracy.

A2. We have conducted further experiments to validate this. Please refer to A2 in our response to Reviewer 63Rq for more details.

Q3. I recommend that the authors release the annotated EMS design data.

A3. We will release the annotated EMS design dataset upon acceptance.

Q4. The stopping condition in Algorithm 1 is inconsistent with that in Figure 2 ... Furthermore, Algorithm 1 should output the optimal solution found by the search, not a satisfactory solution.

A4. Thank you for your suggestion. We will correct this in our revised version.

Q5. For example, it would be beneficial to explore more thoroughly how much the quadtree-based representation reduces the search space size. What is the specific relationship between the search space size and the parameter $N_{max}$?

A5. The quadtree representation is used to reduce the complexity of the design space. Each leaf node in the quadtree represents a binary decision (either 0 or 1) for its corresponding subregion. Thus, if the current set of leaf nodes is $L$, the total size of the design space is $2^{|L|}$. The parameter $N_{{max}}$ limits the maximum number of leaf nodes, i.e., $|L| \leq N_{{max}}$, so the upper bound of the search space is $2^{N_{{max}}}$. In other words, a smaller $N_{{max}}$ effectively reduces the search space size.

Q6. It would still be beneficial to provide a more detailed computational time including simulations and model-updating—especially since PQS continuously retrains its predictor.

A6. Below, we provide a detailed breakdown of the average computational time for simulation in Table 2 and model-updating in Table 3. Specifically, we measured the model-updating time under both initial and final dataset conditions for each task:

• HGA: 300 samples → 1,000 samples.
• DualFSS: 500 samples → 1,000 samples.

All model updates were consistently performed for 200 epochs.

Table 2: Simulation cost per iteration (seconds).

Table 3: Model updating cost per iteration (seconds).

In both tasks, simulation is the dominant cost. Model updating remains lightweight and efficient throughout the search.

Q7. Since Bayesian optimization is commonly used for optimizing expensive evaluations, I recommend that the authors include a more thorough discussion on this topic.

A7. We will include a more comprehensive discussion of Bayesian optimization in our revised manuscript.

We sincerely appreciate your time and valuable feedback. We acknowledge your concerns and would like to clarify our motivations and technical contributions.

1. Significance of the Task & Motivation

Electromagnetic structure (EMS) design is fundamental to modern antenna/material development, yet faces two critical challenges:

• Vast Design Space: Conventional grid-based representation creates exponentially growing search spaces (e.g., 16×16 layout can contain over $10^{77}$ potential design).
• Expensive Evaluations: Each design must be evaluated via time-consuming electromagnetic simulations (often taking minutes to hours), making large-scale evaluations impractical for industrial timelines.

Existing approaches primarily revolve around two strategies:

• Predictor-Based Methods: Use predictors to approximate the costly electromagnetic simulator. However, such predictors need large amounts of high-quality data to achieve sufficient accuracy, which is infeasible when budgets are tight.
• Generative Approaches: Use generative models to produce promising designs directly. They also require tens of thousands of labeled samples for training.

In short, our motivation is to reduce the reliance on large evaluation costs by introducing a more efficient search mechanism that narrows down the design space in a structured manner.

2. Methodological Innovation

Our proposed Progressive Quadtree-based Search (PQS) addresses these challenges through:

• Quadtree-based Search Strategy:
  • Quadtree-based Representation: To reduce the dimensionality, we encode the layout in a quadtree that recursively subdivides the structure from a coarse resolution to finer details.
  • Progressive Tree Search: To focus the limited budget on the most impactful design decisions, we decompose the high-dimensional search into a tree search from global pattern to local refinement.
• Consistency-based Sample Selection: Rather than requiring a highly accurate predictor, we adopt an adaptive sample selection. Specifically:
  • Ranking-based Reliability: Kendall's Tau is used to measure how consistently the predictors ranks candidate designs across consecutive iterations, which reveals the model's reliability to guide the search effectively.
  • Dynamic Exploitation & Exploration: Based on the consistency, our method dynamically allocates evaluations: high consistency leads to evaluate top-ranked designs, while low consistency leads to an additional exploration to uncover overlooked candidates.

3. Practical Validation

Our proposed approach has already been successfully validated in real-world engineering tasks:

• High-Quality Outcomes: Compared to baseline methods, PQS yields designs with approximately 70% greater improvement in DualFSS design objectives.
• Cost Savings: Achieved 75%-85% cost reduction vs. generative approaches.
• Robust Performance: Repeated experiments showed that PQS exhibited 29%-92% lower variance compared to baseline methods.

4. Broader Impact to ICML Community

By bridging the gap between theoretical optimization and industrial constraints, PQS provides:

• A scalable framework for high-dimensional and expensive structural design problems.
• A low-budget solution for EMS design with limited computational resources.

We will revise the manuscript to better emphasize these aspects and would be happy to provide supplementary materials detailing industrial implementation.

Q1. Time-saving estimate (20-48 days) lacks detailed derivations.

A1. Thank you for your valuable feedback. We acknowledge that the original time-saving estimate (20–48 days) lacked detailed derivation. Upon re-evaluating the calculations, we identified an error in rounding and task-specific simulation reductions. Here is the correct derivation:

• DualFSS Task: The average simulation time is 583.7 seconds; The reduction in simulations is 3,000 times; The total time saved is $\frac{583.7 \times 3,000}{3,600 \times 24} \approx 20.27$ days.
• HGA Task: The average simulation time is 558.8 seconds; The reduction in simulations is 6,000 times; The total time saved is $\frac{558.8 \times 6,000}{3,600 \times 24} \approx 38.80$ days.

Thus, the refined time-saving range is 20.27–38.80 days. We apologize for the oversight and have updated the manuscript to reflect this correction. Importantly, the revised values still robustly demonstrate that our method achieves significant efficiency gains compared to generative approaches.

Q1. PQS should be compared with SOTA surrogate-assisted evolutionary algorithms (SAEAs).

A1. Thank you for your constructive suggestion. We compared our method with TS-DDEO[1] and SAHSO[2] in Tables 1-3. PQS outperforms them by 3.14-3.60 and 9.63-10.99 and achieves significantly higher robustness in the aggregation value of objectives, with 15%-19% lower variance. This stems from PQS’s ability to hierarchically explore the design space and adaptively allocate the tight evaluation budget via CSS. This efficiency could significantly benefit real-world applications where evaluation budgets are tight.

Table 1: Comparisons on High-gain Antenna (HGA).

Table 2: Comparisons on Dual-layer Frequency Selective Surface (DualFSS).

Table 3: Robustness comparison results on High-gain Antenna (HGA).

[1] A two-stage surrogate-assisted metaheuristic algorithm..., Soft Comput. 2023.

[2] A surrogate-assisted hybrid swarm optimization..., Swarm Evol. Comput. 2022.

Q2. Only 300 samples may hinder generalization. Authors should examine dataset sizes and classifiers' impact on performance.

A2. We acknowledge dataset size and model choice's importance. However, in EMS design, simulation takes hours to days (e.g., 559-583 seconds per evaluation). To address this, we begin with a small initial dataset (300 samples) and use the remaining evaluation budget iteratively during optimization. This ensures that computational resources are prioritized for optimization rather than data collection.

In Table 4, we evaluated Kendall's Tau (KTau) between predicted and ground truth across dataset sizes (300-1,100) on a fixed 5,800-sample test set (10 trials). We clarify two key observations:

• Expanding the dataset from 300 to 1,100 samples maintains weak KTau correlation (<0.3), showing larger datasets don't proportionally enhance accuracy in our task.
• All models perform poorly, implying that model capacity is not the limiting factor.

These observations suggest that while gathering more data can be helpful, it is not always cost-effective in EMS design. Our PQS is designed to achieve data-efficient optimization, attaining superior performance even with a limited budget.

Table 4: Impact of training sample size and predictor on model performance.

Q3. The observation that RS and Surrogate-RS outperform Surrogate-GA and Surrogate-GW is unexpected.

A3. One possible factor is each method's reliance on the predictor for solutions. Specifically:

• Surrogate-GA and Surrogate-GW rely on the predictor to guide the evolution of new populations. With a limited training set (300 samples), the predictor's accuracy suffers, misleading GA and GW optimizers to suboptimal regions.
• By contrast, RS and Surrogate-RS avoid predictor dependence: they generate candidates via uniform random sampling. This is like our QSS, which also avoids heavy predictor reliance by hierarchical random exploration.

Q4. Why QSS is superior to other dimensionality reduction approaches, such as PCA or AutoML-based search space simplification?

A4. Our QSS excels in search space reduction and dynamic adaptation:

• Explicit space shrinking: Unlike PCA that projects the design space into a continuous latent space, our QSS preserves the discrete, grid-like nature of EMS through its quadtree-based hierarchical representation, ensuring clear shrinking.
• Dynamic adaptation during search: PCA or feature selection methods perform static, global dimensionality reduction. In contrast, our QSS dynamically adjusts the search granularity during optimization. Initially, it explores coarse global patterns and later focuses on locally promising regions, enabling efficient exploration under tight budgets.

Q5. It does not cover recent advances such as deep reinforcement learning or Bayesian optimization.

A5. We will carefully discuss and cite these works in our revised paper.

Q6. Important training details are missing.

A6. We clarify training details: Batch Size: 256, Epochs: 200, Cosine Annealing LR (lr=0.01, T_max=200, η_min=1e-6), Gradient Clipping (Global L2 norm ≤1.0/batch), Optimizer: Adam, resnet_lr=0.01, fc_lr=0.01. These will be added to the manuscript.