Influence of probability distribution initialization methods on the performance of advanced arithmetic optimization algorithm with application to unrelated parallel machine scheduling problem

Abstract

The article investigates the influence of several initialization methods on the performance of the newly proposed advanced arithmetic optimization algorithm, also known as the nAOA. The initialization conditions considered include population sizes, diversity of the population, and the number of iterations. We used 23 different probability distributions with different diversity to test the influence of initialization schemes on the convergence and accuracy of the nAOA. The benchmark classical test functions and the functions defined in the CEC 2020 suite having different properties and modalities were used to compare the possible effects of the initialization methods. The numerical results showed that the nAOA is sensitive to population size and the number of iterations, which must be large for optimal performance. Friedman's and correlation tests were used to gain useful insight into the results we obtained. Findings showed that the performance of the nAOA is not particularly sensitive to the different initialization schemes used for most test functions. The implication is that nAOA is relatively stable and robust. However, the variant of beta distribution, b(3,2), recorded the lowest mean rank for most functions. Hence, it is the best performing initialization distribution scheme for the test problems considered. We can also observe from the experimental results that 47.83% and 100% of the classical and CEC2020 test functions used in this article show significant differences for different initialization methods, respectively. We also investigated the applicability of the nAOA to solve the unrelated parallel machine scheduling problem with sequence‐dependent setup times by using the best‐identified set of initialization methods. The performance of the nAOA is evaluated by comparing its solution to seven other well‐known metaheuristic algorithms, and the results reveal that the nAOA can provide promising results in solving all problem instances of the problem under study using the best initialization schemes.