BA Multi-direction Guided Mutation-driven Stable Swarm Intelligence Algorithm with Translation and Rotation invariance for Global Optimization

Although the theoretical studies on the existing meta-heuristic algorithms and the development of novel meta-heuristic algorithms have achieved fruitful results, the studies on the definition and construction methods of the so-called "mutation" operator widely used in existing meta-heuristic algorithms are still not in-depth enough, and how to directly construct a meta-heuristic algorithm based on the properties of mutation operators under the guidance of stability and invariance analysis is still a problem to be solved. In this paper, the concepts of "mutation operator" and "mutation-driven meta-heuristic algorithm" in the existing meta-heuristic algorithm literature are carefully studied and strictly defined. Based on these definitions, a novel meta-heuristic algorithm, called Multi-direction guided Mutation-driven Stable swarm Intelligence algorithm with Translation and Rotation invariance (M2SITRI) is proposed, and the corresponding mutation operator is elaborately designed under the guidance of translation, rotation invariance and order-1, order-2 stability theory analysis. The stability and invariance properties of the proposed M2SITRI algorithm are verified by numerical simulations, and its outstanding performance is verified by comparing with several other well-known existing meta-heuristic algorithms on multiple test problems.