On the Performance Metrics of Multiobjective Optimization

Multiobjective Optimization (MOO) refers to optimization problems that involve two or more objectives. Unlike in the single objective optimization, a set of solutions representing the tradeoff among the different objects rather than an unique optimal solution is sought in MOO. How to measure the goodness of solutions and the performance of algorithms is important in MOO. In this paper, we first review the performance metrics of multiobjective optimization and then classify variants of performance metrics into three categories: set based metrics, reference point based metrics, and the true Pareto front/set based metrics. The properties and drawbacks of different metrics are discussed and analyzed. From the analysis of different metrics, an algorithm's properties can be revealed and more effective algorithms can be designed to solve MOO problems.