The main challenge in finding the optimal Pareto Front (PF) and Pareto Set (PS) sets for multimodal multi-objective optimization problems (MMOPs) with conflicting objective functions is to exhibit a balanced and susta...
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The main challenge in finding the optimal Pareto Front (PF) and Pareto Set (PS) sets for multimodal multi-objective optimization problems (MMOPs) with conflicting objective functions is to exhibit a balanced and sustainable diversity and exploitation capability in both the objective and decision spaces. This paper introduces dynamic reference spaces based clustering (DRSC) as a new archive handling method to overcome this challenge. DRSC incorporates a niche method called dynamically switched referencespaces and adapts the K-means-based method for clustering non-dominant vectors and handling the archive. The performance of the proposed DRSC is tested on twenty-four benchmark problems. According to the results of non-parametric statistical analysis using data from four different performance metrics, DRSC-MOAGDE designed using the proposed archiving mechanism managed to achieve the best Friedman rank among thirty different competitors. According to the stability analysis results, the average success rates and average computation times of the three best performing algorithms DRSC-MOAGDE, MMODE-ICD and SSMOPSO are (88.69%, 3.01 s), (66.87%, 9.47 s) and (64.29%, 1372.49 s), respectively. It is also observed that the proposed DRSC-MOAGDE outperforms the best cost optimization values in the literature with a minimum of 0.1838 $/h and a maximum of 30.9157 $/h for the multi-objective OPF real-world problem.
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