TRACE-EA: Adaptive Trajectory Observation for Automatic Operator Design in Multi-Objective Combinatorial Optimization

Large Language Models (LLMs) have enabled automatic heuristic design (AHD) for multi-objective combinatorial optimization problems (MOCOPs), but execution feedback used to guide heuristic revision remains centered on aggregate performance measures. Such summaries provide limited information about how progress and stagnation are distributed across trade-off regions or how previously attained coverage is lost during search. We present TRACE-EA, an LLM-driven AHD method that couples heuristic evolution with selective trajectory observation and observation-policy adaptation. An LLM observer selects tools and query arguments to examine trajectories recorded during candidate evaluation within a fixed multi-objective evolutionary solver. The retrieved evidence supports a diagnosis that guides the selection and generation of heuristic variations. A second feedback loop uses the history of observations, variation actions, and candidate outcomes to adapt the observation policy's temporal window, query-round allowance, and tool priors. Policy updates are retained or reverted based on subsequent candidate outcomes. Experiments across 18 multi-objective settings show that TRACE-EA achieves competitive performance, with advantages that carry over to unseen instances and larger problem scales.