A Comparative Study of Fractal-Based Decomposition Optimization

Abstract

In this work, we present a comparative study of 24 different and unique decomposition-based algorithms derived from Fractal Decomposition Algorithm and Simultaneous Optimistic Optimization. These algorithms were built within a generic, flexible and unified algorithmic framework named fractal-based decomposition algorithms. This generic framework is issued from previous works and is succinctly described in this paper. A software, called Zellij, based on this methodology was used to instantiate the 24 algorithms. Under our generic framework, fractal-based decomposition algorithms are made of five independent and well-defined search components: a type of fractal, a tree search algorithm, a scoring method, an exploration, and exploitation strategies. This new family of algorithms, hierarchically decomposes an initial search space using a generic geometrical object, named fractal. The decomposition forms a rooted tree, where fractals are nodes, and the root corresponds to the initial search space. The tree is explored, exploited and expanded using the four other search components. The proposed algorithms were tested and compared to each other on the CEC2020 benchmark. Obtained performances emphasize the impact of each search component, and pointed out the scalability capacity of certain algorithms. Our results strongly suggest that some search components have major impact on FDA and SOO-based algorithms for large-scale problems, whereas others are used to fine tune performances in terms of convergence.