LLM-Assisted Optimization for Simulation-Based Redesign

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

Design Structure Matrix (DSM) modularization, the task of partitioning system elements into cohesive modules, is a fundamental combinatorial challenge in engineering design. Traditional methods treat modularization as a pure graph optimization, without access to the engineering context embedded in the system. Building on prior work on LLM-based combinatorial optimization for DSM sequencing, this paper extends the method to modularization across five cases and three backbone LLMs. Our method achieves near-reference quality within 30 iterations without requiring specialized optimization code. Counterintuitively, domain knowledge, beneficial in sequencing, consistently impairs performance on more complex DSMs. We attribute this to semantic misalignment between the LLM's functional priors and the purely structural optimization objective, and propose the semantic-alignment hypothesis as a testable condition governing knowledge effectiveness with LLMs. Ablation studies identify the most effective input representation, objective formulation, and solution pool design for practical deployment. These findings offer practical guidance for deploying LLMs in engineering design optimization.

Large Language Models (LLMs) can contribute useful engineering knowledge to robot design, but directly generated designs may rely on implicit assumptions and provide no guarantees of feasibility or optimality. These assumptions are critical because different reasonable modeling choices can materially change which designs are predicted to be feasible or optimal. We therefore present a framework that uses LLMs to construct explicit engineering models containing physical relationships, compatibility constraints, and objectives, allowing these modeling choices to be inspected and revised before formal optimization. The model can then be updated with additional engineering, manufacturer, or system-specific information before formal multi-objective optimization provides feasibility and Pareto-optimality guarantees with respect to the finalized model and specified design space. We evaluate the framework on quadcopter and line-following robot component-selection problems. Across 30 direct LLM design trials, none could be verified as feasible under the corresponding finalized model. Comparisons with an independently developed expert model and successive stages of model refinement further showed that changes in modeling assumptions substantially altered the predicted feasible and Pareto-optimal design sets. Together, these results show that using LLMs to construct explicit engineering models makes the underlying design choices available for inspection and revision before those assumptions determine the optimized designs. Explicit modeling therefore provides an interface for combining LLM-generated engineering knowledge, system-specific information, and formal design optimization.