Hybrid metaheuristics for architectural design optimization under small evaluation and wall-clock budgets

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. RCMAES is evaluated on three benchmark suites (CEC2017, CEC2020, and CEC2022) and compared with state-of-the-art DE algorithms as well as its closely related counterpart, BIPOP-aCMAES. Experimental results show that RCMAES achieves competitive and robust performance across all benchmarks.

Engineering design tools increasingly embed optimizers as ready-made components that users select by algorithm name, while operator settings and bound, integer and duplicate handling stay fixed inside each tool. This study tests whether the name predicts the result. A tool-agnostic harness exposes one deterministic black box, an emulator of a published 22-variable mixed-integer building-performance problem, to the native optimizers of three Grasshopper plug-ins, to canonical NSGA-II, SMS-EMOA and GDE3 from Python libraries, and to the model-based RBFMOpt. Eighteen configurations were run at 5,000 evaluations under three population allocations, with statistics fixed in advance. Four NSGA-II implementations differed by up to 5% in hypervolume, more than three canonical algorithms of different families differed from one another, and their response to population size differed by up to 10 percentage points; for two MOEA/D implementations, by 28. On ZDT test functions the same NSGA-II implementations differed up to 470-fold in IGD. An ablation in one open-source NSGA-II reproduced the behaviour of one tool from its documented settings but not the gaps of the other two, so documented parameters do not identify an implementation. Counting the budget in wall-clock time reversed the ranking of the model-based optimizer, and reporting the final population instead of the archive understated some configurations by up to a third; most differences fell below the surrogate's error. For optimizers embedded in design-support systems, the implementation is part of the method; a reporting checklist is derived: implementation and version, effective settings, budget in time and evaluations, and archive-based indicators.