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On the construction of pareto-compliant quality indicators

The performance comparison of multi-objective evolutionary algorithms (MOEAs) has been a broadly studied research area. For almost two decades, quality indicators (QIs) have been employed to quantitatively compare the Pareto front approximations produced by MOEAs. QIs are set-functions that assign a real value, depending on specific preferences, to such approximation sets. Mainly, QIs aim to measure the capacity of MOEAs to generate nondomi-nated solutions, the diversity of such solutions, and their convergence to the true Pareto front. Regarding convergence QIs, the Pareto-compliance property is crucial to properly assess the performance of MOEAs. However, in specialized literature, the only Pareto-compliant QI is the hypervolume indicator. In this paper, we propose a methodology to construct new Pareto-compliant indicators based on the combination of QIs. Our preliminary experimental results show that our proposed framework to construct Pareto-compliant QIs introduce new preferences over the Pareto front approximations.