Vector mirroring algorithm: A metaheuristic method for efficient optimization

Metaheuristic methods are effective in solving complex optimization problems but often require sophisticated iterative strategies that lead to high computational costs, especially in high-dimensional spaces. This paper presents the Vector Mirroring Algorithm (VMA), a simple yet effective metaheuristic method designed for efficient optimization. The core concept of VMA involves using the vertices of the hyperrectangle circumscribed by a hypersphere as candidate solutions in each iteration. This approach maintains diverse search directions while can be efficiently generated through simple sign conventions. Vectors originating from the current solution (i.e., the centroid of the hyperrectangle) and pointing to these vertices migrate towards an improved solution or contract for better precision. This migration and contraction process iterates until the desired accuracy is achieved, following a Markov process that adaptively adjusts vector lengths to fit the size and position of attraction basins, enabling faster convergence. Moreover, the implementation of multi-start and elimination strategies further improves performance in multimodal problems. Benchmark tests show that VMA is averagely 43.3%–94.0% faster and requires 11.6%–87.0% fewer function evaluations on average across 26 widely adopted benchmark functions. The method is further tested on three engineering problems, demonstrating its ability to produce high-quality solutions efficiently in real-world engineering problems.