An Effective Runge-Kutta Optimizer Based on Adaptive Population Size and Search Step Size

Abstract

A newly proposed competent population-based optimization algorithm called RUN, which uses the principle of slope variations calculated by applying the Runge Kutta method as the key search mechanism, has gained wider interest in solving optimization problems. However, in high-dimensional problems, the search capabilities, convergence speed, and runtime of RUN deteriorate. This work aims at filling this gap by proposing an improved variant of the RUN algorithm called the Adaptive-RUN. Population size plays a vital role in both runtime efficiency and optimization effectiveness of metaheuristic algorithms. Unlike the original RUN where population size is fixed throughout the search process, Adaptive-RUN automatically adjusts population size according to two population size adaptation techniques, which are linear staircase reduction and iterative halving, during the search process to achieve a good balance between exploration and exploitation characteristics. In addition, the proposed methodology employs an adaptive search step size technique to determine a better solution in the early stages of evolution to improve the solution quality, fitness, and convergence speed of the original RUN. Adaptive-RUN performance is analyzed over 23 IEEE CEC-2017 benchmark functions for two cases, where the first one applies linear staircase reduction with adaptive search step size (LSRUN), and the second one applies iterative halving with adaptive search step size (HRUN), with the original RUN. To promote green computing, the carbon footprint metric is included in the performance evaluation in addition to runtime and fitness. Simulation results based on the Friedman and Wilcoxon tests revealed that Adaptive-RUN can produce high-quality solutions with lower runtime and carbon footprint values as compared to the original RUN and three recent metaheuristics. Therefore, with its higher computation efficiency, Adaptive-RUN is a much more favorable choice as compared to RUN in time stringent applications.