Improved spherical search with local distribution induced self-adaptation for hard non-convex optimization with and without constraints

Abstract

Most metaheuristic optimizers rely heavily on precisely setting their control parameters and search operators to perform well. Considering the complexity of real-world problems, it is always preferable to adjust control parameter values automatically rather than clamp-ing them to a fixed value. In recent years, Spherical Search (SS) has emerged as a population-based stochastic optimization method that exploits the concepts of random projection matrices in linear algebra. As a result of the success of SS in solving non -convex, real-parameter optimization problems of various complexity, we have significantly extended SS in this paper by introducing a set of new algorithms, collectively known as Self Adaptive Spherical Search (SASS). Our proposal aims to enhance the performance of SS by using different projection matrix schemes in conjunction with improved search-direction calculations and an adaptive modification of parameter values. In our proposed adaptation scheme, parameters are modified to relevant values by applying a self-adaptive process that does not rely upon prior knowledge of the correlation between the parameter values and characteristics of the problem space. Consequently, we may apply the algorithms to bound and nonlinearly constrained optimization problems. For the benchmark suites derived from the most recent IEEE Congress on Evolutionary Computation (CEC) competi-tions, simulation results indicate that the SASS family of algorithms performs better than or is comparable to state-of-the-art algorithms from the other paradigms concerning robust-ness and convergence.