Mutual operator patterns in metaheuristics: A review of classical numerical optimization problems

Abstract

Operator landscapes form an essential tool for evaluating the performance, stability, and convergence ability of metaheuristic algorithms in the face of modality, separability, dimensionality, ruggedness, and landscape deception. For this reason, state-of-the-art hybrid metaheuristics are more often than not built based on the use of several search operators. Despite a growing number of scientific works devoted to various aspects of hybrid optimization, there remains a lack of information about the mutual patterns of operator cooperation that have helped achieve optimization results. To address this gap, this paper reviews common patterns of operator cooperation in metaheuristics used for the classical problem of numerical optimization. First, recurring patterns of operator cooperation in the context of numerical optimization problems, which involve both unimodal, multimodal, rotated, shifted, hybrid, composition, and high-dimensional benchmarks, are discussed. Second, common operator types used in modern optimization algorithms are introduced. Lastly, common patterns of operator cooperation involving combinations of operators used for exploration and exploitation of the optimization landscape, diversification and perturbation of solutions, chaos-based search, Lévy-flight diversification, memetic search, operators' adaptation to the current optimization landscape, and simultaneous multi-population optimization are discussed. In particular, operator-oriented taxonomy and analysis of the ways in which operator cooperation depends on the properties of the landscape are proposed. Key areas of further research include operator compatibility, scalability, reproducibility, explainability, and operator autonomy. New trends in the field consist of adaptable operator ecosystems, reinforcement learning-assisted optimization, modular structure of hybrid algorithms, and self-evolution. In conclusion, the significance of operator cooperation in achieving good optimization results is highlighted.