Constrained Hybrid Metaheuristic: A Universal Framework for Continuous Optimisation

2026-03-18

AI Summary

This work proposes a constrained hybrid metaheuristic (cHM) framework to address the limitations of existing metaheuristic algorithms, which often struggle with general continuous optimization problems exhibiting complex characteristics such as non-convexity, non-separability, and varying smoothness. The cHM framework employs a modular architecture and a two-phase adaptive mechanism to dynamically coordinate multiple metaheuristic strategies and candidate solutions under black-box optimization settings, enabling efficient optimization of heterogeneous and unknown objective functions. By adaptively adjusting its search behavior according to the optimization stage, the method significantly enhances convergence speed and robustness. Experimental results demonstrate that cHM matches or outperforms state-of-the-art algorithms across 28 benchmark functions and exhibits strong generality and practical utility in real-world feature selection tasks.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper presents the constrained Hybrid Metaheuristic (cHM) algorithm as a general framework for continuous optimisation. Unlike many existing metaheuristics that are tailored to specific function classes or problem domains, cHM is designed to operate across a broad spectrum of objective functions, including those with unknown, heterogeneous, or complex properties such as non-convexity, non-separability, and varying smoothness. We provide a formal description of the algorithm, highlighting its modular structure and two-phase operation, which facilitates dynamic adaptation to the problem's characteristics. A key feature of cHM is its ability to harness synergy between both candidate solutions and component metaheuristic strategies. This property allows the algorithm to apply the most appropriate search behaviour at each stage of the optimisation process, thereby improving convergence and robustness. Our extensive experimental evaluation on 28 benchmark functions demonstrates that cHM consistently matches or outperforms traditional metaheuristics in terms of solution quality and convergence speed. In addition, a practical application of the algorithm is demonstrated for a feature selection problem in the context of data classification. The results underscore its potential as a versatile and effective black-box optimiser suitable for both theoretical research and practical applications.

Problem

• continuous optimisation
• metaheuristics
• non-convexity
• black-box optimisation
• heterogeneous functions

Innovation

• Hybrid Metaheuristic
• Continuous Optimization
• Black-box Optimization
• Adaptive Search
• Modular Framework