Constrained Hybrid Metaheuristic: A Universal Framework for Continuous Optimisation

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.

Figures (3)

• Figure 1: Goldstein-Price function illustration for range $x \epsilon [-2;2]$.
• Figure 2: Illustration of the cHM optimisation behaviour over iterations for different benchmark functions (Ackley02, Price02 and Rastrigin, respectively. Each figure plots 50 experimental runs).
• Figure 3: Comparative visualisation of 28 benchmark objective functions, highlighting characteristic landscape features—modality, ruggedness, anisotropy, and curvature—relevant to analysing and designing global optimisation methods.