METAFOR: A Hybrid Metaheuristics Software Framework for Single-Objective Continuous Optimization Problems

TL;DR

METAFOR introduces a modular, component-based framework (PSOmod, CMA-ESmod, DEmod, LSmod) for automatic design of hybrid metaheuristics aimed at single-objective continuous optimization. By coupling with irace, it automatically assembles and configures 17 hybrid implementations, reveals that CMA-ES–driven hybrids offer broad robustness, and demonstrates that automatic design can outperform fixed single-approach configurations across diverse problem classes. The study compares two instance-separation strategies (25OUT and LDOUT) and shows trade-offs between exploring the full design space and exploiting fixed designs, with generalization guiding when each strategy excels. Overall, METAFOR provides a scalable platform to systematically explore hybridization strategies, offering insights into which components and execution modes yield superior performance on unimodal, multimodal, and high-dimensional problems. The work highlights practical implications for building high-performing, problem-adaptive metaheuristics in real-world optimization tasks.

Abstract

Hybrid metaheuristics are powerful techniques for solving difficult optimization problems that exploit the strengths of different approaches in a single implementation. For algorithm designers, however, creating hybrid metaheuristic implementations has become increasingly challenging due to the vast number of design options available in the literature and the fact that they often rely on their knowledge and intuition to come up with new algorithm designs. In this paper, we propose a modular metaheuristic software framework, called METAFOR, that can be coupled with an automatic algorithm configuration tool to automatically design hybrid metaheuristics. METAFOR is specifically designed to hybridize Particle Swarm Optimization, Differential Evolution and Covariance Matrix Adaptation-Evolution Strategy, and includes a local search module that allows their execution to be interleaved with a subordinate local search. We use the configuration tool irace to automatically generate 17 different metaheuristic implementations and evaluate their performance on a diverse set of continuous optimization problems. Our results show that, across all the considered problem classes, automatically generated hybrid implementations are able to outperform configured single-approach implementations, while these latter offer advantages on specific classes of functions. We provide useful insights on the type of hybridization that works best for specific problem classes, the algorithm components that contribute to the performance of the algorithms, and the advantages and disadvantages of two well-known instance separation strategies, creating stratified training set using a fix percentage and leave-one-class-out cross-validation.