Standardizing and weighting the evaluation criteria of many-objective optimization competition algorithms based on fuzzy delphi and fuzzy-weighted zero-inconsistency methods

Along with the developments of numerous MaOO algorithms in the last decades, comparing the performance of MaOO algorithms with one another is highly needed. The evaluation criteria of Many Objective Optimization algorithm (MaOO) play a critical role in evaluating the competition MaOO algorithms. Although these criteria have been criticised in literature, they are employed in the evaluation randomly, and the process of selecting them remains unclear. In addition, the weight of importance is critical for evaluating the performance of MaOO algorithms. All evaluation studies for MaOO algorithms have ignored to assign such weight for the target criteria during evaluation process. Thus, the need for standardizing the criteria set became inevitable. Not to mention the role of weight of importance in assessing the performance of MaOO. These challenges (a) the multiple evaluation criteria and (b) criteria importance considered an intricate multi-criteria decision making (MCDM) problem; in such problem, the MCDM methods are recommended. Several studies in MCDM have proposed competitive weighting methods. However, these methods suffer from inconsistency issues arising from the high subjectivity of pairwise comparison. (c) The inconsistency rate increases in an exorbitant manner when the number of criteria increases which considered an issue in the existing superior weighting methods such as AHP and BWM, and the results are affected accordingly. Thus, this research aims to standardize and weigh the evaluation criteria of MaOO competitive algorithms base on fuzzy Delphi and new fuzzy-weighted zero-inconsistency (FWZIC) methods. The proposal exhaustive evaluation methodology has three phases: The first phase, standardizing the MaOO evaluation criteria, Fuzzy Delphi method utilized to analyse the expert consensus on the best set of evaluation criteria and its indicators. In the second phase, the FWZIC method is proposed to compute the unified criteria set's weight coefficients with zero consistency. Lastly, the exhaustive evaluation methodology evaluated to test its validity and efficiency accordingly. The results show that 31 out of 49 got the expert consensus as the most suitable criteria set; and their importance weight results computed accordingly, the main criterion (called Pareto_based) got the higher weight (0.538) in compared to others. Lastly, the proposed unified model of the most suitable criteria set validated by the experts from the field of study and the efficiency of the FWZIC method proved in comparison to F-AHP and F-BWM superior methods those show high inconsistency results which overall exceeded the maximum consistent ratio (i.e., 0.1). On the other hand, FWZIC effectively computes the important weight of the criteria with zero inconsistency. The implications of this study bring benefits to the optimization community, industrial and researchers by providing exhaustive evaluation methodology for evaluating MaOO algorithms, which can be generalized to solve such problem effectively.

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