A novel framework to construct quality indicators using the linear assignment problem

In multi-objective optimization problems (MOPs), we aim to simultaneously find the maximum or minimum values of two or more (often conflicting) objective functions. MOPs are often found in real-world applications and, consequently, many methods have been proposed to solve them. Multi-Objective Evolutionary Algorithms (MOEAs) are popular techniques to solve MOPs due to their ease of use and their generality. Assessing the performance of MOEAs has become increasingly important due to the high number of MOEAs that have been developed in recent years. This work presents a novel framework for creating quality indicators using the linear assignment problem. In addition, we introduce two novel quality indicators generated using this framework and present examples to validate their performance. Furthermore, we present a novel algorithm called MOEA-kAP that can incorporate any indicator generated using our proposed framework as a density estimator. Our experimental results show that MOEA-kAP outperforms state-of-the-art algorithms.