A new randomness approach based on sine waves to improve performance in metaheuristic algorithms

The main goal of this paper is to outline a new approach to represent the randomness that we can find in different metaheuristics as a stochastic process which helps in the performance of the analyzed metaheuristic. This new way of viewing randomness is based on the behavior of sine waves that we can find in many situations in nature or in physics laws. In this paper, we evaluate this proposed randomness with three metaheuristics: the grey wolf optimizer, firefly algorithm and flower pollination algorithm, with the goal of studying the performance of the proposed randomness method in different types of metaheuristics. A set of standard benchmark functions were used to test the proposed randomness method, which are classified as unimodal and multimodal benchmark functions. In addition, the benchmark functions of the CEC 2015 Competition are used. Finally, we present tests with functions that were presented in the CEC 2017 competition for constrained real-parameter optimization. We also present a comparative study of the analyzed metaheuristics, and this comparison is between their original randomness method and the proposed randomness method for each algorithm. Finally, we present the performance and results of the methods with different number of dimensions to complete the study.