Toward enhancing metaheuristic optimization algorithms using center-based sampling strategies for solving single- and multi- objective large-scale problems

Abstract

Over the last decade, metaheuristic algorithms have become well-established approaches utilized for solving complex real-world optimization problems. Most metaheuristic algorithms have used stochastic strategies in their initialization as well as during the new candidate solution generation process where there is no a priori knowledge about the solution, which is a common assumption for any black-box optimization problem. In recent years, researchers have introduced a new concept called center-based sampling that can be used in any search component of the optimization process, but so far, it has mainly been utilized for population initialization. This concept clarifies that in a search space, the center point has a higher probability value to be closer to an unknown solution compared to a uniformly generated random point, especially when the dimension increases. Thus, this novel concept helps the optimizer to find a better solution efficiently. In this thesis, a comprehensive study has been conducted on the effect of center-based sampling to solve an optimization problem using three different levels of investigation. These levels are as follows: 1) no specific algorithm and no specific landscape (i.e., Monte-Carlo-based simulation); 2) a specific landscape but no specific algorithm (random search vs. center-based random search), and finally, 3) a specific algorithm and specific landscape (proposing three different schemes for using center-based sampling for solving Large-scale Global Optimization (LSGO) problems). Also, a center-based sampling for multi-objective optimization is proposed. Furthermore, in this thesis, I seek to investigate the properties and capabilities of center-based sampling during optimization, which can be extended to utilize it in machine learning techniques, as well. The proposed methods are evaluated on discrete and continuous Large-scale Global Optimization (LSGO) benchmark functions. The experimental results confirm that center based sampling has a crucial impact on improving the convergence rate of optimization/search algorithms when solving high-dimensional optimization problems.