Modified archive update mechanism of multi-objective particle swarm optimization in fuzzy classification and clustering

Evolutionary algorithms have been extensively used to resolve problems associated with multiple and often conflicting objectives. The objective of a multi-objective optimization algorithm is to define the collection of best trade-offs between objectives. Among multi-objective evolutionary algorithms proposed in the literature, particle swarm optimization (PSO)-based multi-objective (MOPSO) algorithm has been cited to be the most representative. One characteristic of MOPSO with Pareto optimality scheme is associated with selection mechanism for archive update. However, the PSO algorithm produces a group of non-dominated solutions which makes the choice of a “suitable” Pareto optimal or non-dominated solution more difficult. According to the literature, crowding distance as one of the most efficient algorithms was developed based on density measures to treat the problem of selection mechanism for archive update. Issues arising from these methods are not conducive to balancing diversity and convergence performances. The present study proposed a modified selection mechanism for archive updates in MOPSO (MOPSO-CD). The approach of the proposed mechanism was based on dominance concept and crowding distances to obviate falling in local optima instead of global optima as well as to have a balance between diversity and convergence by using the Pareto dominance concept after calculating the value of the crowding degree for each solution. For optimum results in performance analysis, the optimal value of the MOPSO-CD was evaluated using (ZDT), (WFG), and (DTLZ) with two or three objectives over D2MOPSO, AgMOPSO, MMOPSO, and EMOSO algorithms. Results showed that MOPSO-CD had better performance and a strong superiority in the IGD with the lowest mean of 9.50E-4, while the HV showed the lowest mean of 9.40E-1 compared to other algorithms. Ten datasets sourced from KEEL repository were used to measure the performance of Fuzzy MOPSO-CD with a modified archive update mechanism (FMOPSO-CD). The FMOPSO-CD was compared with multi-objectives evolutionary algorithms (D-MOFARC, GRBCs), and PSO (FMOPSO, FMOPSO-SA). The FMOPSO-CD's accuracy consistently outperformed other algorithms in all datasets where the best performance accuracy was 99%. Moreover, interpretability also recorded better results on testing problems, where most of the number of rules were fewer than 33. A clustering algorithm based on MOPSO-CD with a modified archive update mechanism (MCPSO-CD) was used to estimate the optimal number of clusters. For optimum results in performance analyses, the technique was evaluated using nine datasets: five datasets were artificially generated, while four were real-world datasets sourced from KEEL over MCPSO and IMCPSO algorithms. The study recorded that the procedure exemplified a state-of-the-art method with significant differences observed in most of the datasets examined. For Shape cluster datasets, the proposed MCPSO-CD method with value of above 7.0 performed better in most datasets in terms of mean ARI. It was superior to the clustering algorithm methods in most real-world datasets with means ARI of over 0.35. MOPSO-CD was proposed as an improvement in multi-objective fuzzy classification in terms of interpretability and accuracy as well as improvement in multi-objective clustering technique in terms of the optimal number of clusters.

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