A multi-direction guided mutation-driven stable swarm intelligence algorithm with translation and rotation invariance for global optimization.

In recent years, there have been notable advancements in the theoretical research of existing meta-heuristic algorithms and in the development of novel algorithms. However, the research on the definition and construction methods of the so-called "mutation" operator, a concept widely used in existing meta-heuristic algorithms, remains notably insufficient. In addition, how to directly construct a meta-heuristic algorithm under the guidance of stability and invariance analysis continues to pose a challenge that has yet to resolve. This paper carefully investigates and rigorously defines the concepts of "mutation operator" and "mutation-driven meta-heuristic algorithm" as found in the literature. According to 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 carefully designed based on the analysis of translation invariance, rotation invariance, order-1 stability, and order-2 stability. The stability and invariance properties of the M²SITRI algorithm are validated through numerical simulations, and its superior solving performance is demonstrated by benchmarking it against several other well-known existing meta-heuristic algorithms across a variety of test problems. • Mutation operator and mutation-driven meta-heuristic algorithm concepts are defined. • A novel translation and rotationally invariant meta-heuristic algorithm termed M²SITRI is proposed. • The invariance and stability properties and the excellent solving performance of M²SITRI algorithm are verified. [ABSTRACT FROM AUTHOR]