Formula omitted]-polytope decomposition-based algorithm for continuous optimization

Abstract

This paper presents a new fractal search space decomposition-based algorithm to address the issue of scaling up the divide and conquer approach to deal with large scale problems (up to 50 continuous decision variables). The proposed algorithm, called polyFrac, fractally decomposes the search space using hyper-polytopes. It allows moving throughout different granularity levels by only computing the average of vertices of a hyper-polytope to obtain the coordinates of the centroids. Only the most promising hyper-polytopes are decomposed into child-polytopes. Then, a simple deterministic local search (single solution-based metaheuristic) is used to perform the intensification process to find the best solution within the selected lowest hyper-polytope. The proposed algorithm performance is evaluated on the well-known SOCO 2011, CEC 2013, and CEC 2017 benchmarks and compared with 26 states of the art algorithms. A real-world optimization problem is also used to calibrate its performance. The obtained results show that polyFrac outperforms all the algorithms. Moreover, experimental results and analysis suggest that polyFrac is a highly competitive optimization algorithm for solving large-scale and complex optimization problems.