A heuristic swarm-based optimization method using multi-variate normal distributions with self-adaptive variance matrices

Abstract

In this paper a heuristic swarm-based optimization method developed based on stochastic search and concepts from statistics was presented for optimal design of problems in structural mechanics. Although in recent years many heuristic optimization methods have been developed, none of them can be considered as the most effective method for solving all types of optimization problems. In general, heuristic optimization methods are formulated to follow specific patterns and often include some random parameters. It has been shown that adding stochastic parameters and concepts from statistics to such algorithms can improve their performance and increase the chance of finding global optimal points. Based upon same notion, we have developed a new swarm-based optimization algorithm in which multi-variate normal distributions with self-adaptive variance matrices (MNSV) are used to generate superior solutions in each iteration. The self-adaptive variance matrix in each iteration was calculated using the variance of the best points from solution history. Such a choice improved both exploration and exploitation of the algorithm and led to a trade-off between them from beginning towards the end of the solution. Computational complexity of MNSV algorithm was comparable to that of other swarm-based optimization algorithms and performance of the algorithm was tested through optimal solution of several benchmarks from structural and mechanical engineering. While MNSV algorithm was simple in terms of both formulation and implementation, it was effective in finding optimal solutions and often converged using a smaller number of iterations when compared to other algorithms.