Evolutionary Rao algorithm

Abstract

Abstract This paper proposes an evolutionary\u202f\u202fRao algorithm (ERA) to enhance three state-of-the-art metaheuristic Rao algorithms (Rao-1, Rao-2, Rao-3) by introducing two new schemes. Firstly, the population is split into two sub-populations based on their qualities: high and low, with a particular portion. The high-quality sub-population searches for an optimum solution in an exploitative manner using a movement scheme used in the Rao-3 algorithm. Meanwhile, the low-quality one does in an explorative fashion using a new random walk. Secondly, two evolutionary operators: crossover and mutation, are incorporated to provide both exploitation and exploration strategies. A fitness-based adaptation is introduced to dynamically tune the three parameters: the portion of high-quality individuals, mutation radius, and mutation rate throughout the evolution, based on the improvement of best-so-far fitness. In contrast, the crossover is implemented using a standard random scheme. Comprehensive examinations using 38 benchmarks: twenty-three classic functions, ten CEC-C06 2019 benchmarks, and five global trajectory optimization problems show that the proposed ERA generally outperforms the four competitors: Rao-1, Rao-2, Rao-3, and firefly algorithm with courtship learning (FA-CL). Detailed investigations indicate that both proposed schemes work very well to make ERA evolves in an exploitative manner, which is created by a high portion of high-quality individuals and the crossover operator, and avoids being trapped on the local optimum solutions in an explorative manner, which is generated by a high portion of low-quality individuals and the mutation operator. Finally, the adaptation scheme effectively controls the exploitation-exploration balance by dynamically tuning the portion, mutation radius, and mutation rate throughout the evolution process.