A majority–minority cellular automata algorithm for global optimization

Abstract

Cellular automata (CA) are discrete dynamical systems that can give rise to complex behaviors under certain conditions. Its operation is based on simple local interactions between its elements. The different dynamical behaviors of CA offer a great diversity of ideas and inspiration to propose new metaheuristics focused on global optimization. One such automata is the one specified by the majority rule, which is capable of implementing logical operations under the right conditions. Taking this rule as inspiration, this work proposes the majority–minority CA algorithm. This algorithm takes different adaptations of the majority rule and its counterpart, the minority rule, to establish different rules that modify vectors of real values in order to achieve a good balance in exploration and exploitation tasks for optimization tasks. The efficiency of the majority–minority CA algorithm is tested with 50 widely used test problems in the literature, using both uni- and multimodals and fixed dimensions. Additionally, 3 engineering applications used in recent literature are also optimized. The numerical results verify the competitiveness of the algorithm compared to other recently published specialized algorithms. The source codes of the proposed algorithm are publicly available at https://github.com/juanseck/MmCAA.git.