Improving Performance and Robustness with Two Strategies in Self-Adaptive Differential Evolution Algorithms for Planning Sustainable Multi-Agent Cyber–Physical Production Systems

In the real world, forming a team of two or more people to solve a problem collaboratively is common to take advantage of the complementarity of the values and skills of team members. This idea can be used to develop more effective hybrid solution algorithms for solving problems by combining different solution strategies. In the realm of metaheuristic optimization, many hybrid metaheuristic algorithms have been developed based on combining different metaheuristic solution approaches. An interesting question is to study whether arbitrarily combining two different strategies can lead to a more effective solution approach to tackle complex problems. To evaluate whether a hybrid solution algorithm created by combining two different strategies to solve a problem is effective, we studied whether the hybrid solution algorithm can improve the performance and robustness by comparing the results of the solutions obtained by the hybrid solution algorithm with those obtained by the corresponding two original single-strategy solution algorithms. More specifically, we studied whether arbitrarily combining two different DE strategies selected from four standard DE strategies can lead to a more effective solution approach for planning sustainable Cyber–Physical Production Systems (CPPSs) modeled with multi-agent systems (MASs) in terms of performance and robustness. Ten cases for testing the algorithms for planning sustainable processes in CPPSs, with up to 20 operations and up to 40 resources, were used in the experiments. We conducted experiments by applying 13 algorithms, including 6 hybrid DE algorithms and 7 existing algorithms (4 standard DE, NSDE algorithms, PSO, SaNADE), to find the solutions for 10 discrete optimization planning problems with various types of constraints. The results of the experiments show that each self-adaptive hybrid DE algorithm either outperforms or performs as well as the four standard DE algorithms, NSDE algorithm, and PSO algorithm in most test cases in terms of performance and robustness for population sizes of 30 and 50. The rankings generated through the Friedman test based on the results of the experiments also show that the rankings of the six hybrid DE algorithms created based on hybridization are better than most of the others seven existing algorithms, with only one exception. The rankings generated via the Friedman test indicate that the top 3 among the 13 algorithms are the hybrid DE algorithms. The results of this study provide a simple rule to develop a more effective hybrid DE algorithm by combining two DE strategies.