Consistencies and contradictions of performance metrics in multiobjective optimization

Area of Science:

• Computational Intelligence
• Operations Research

Background:

• Multiobjective optimization (MOO) relies on performance metrics for algorithm design and evaluation.
• Existing research lacks comprehensive understanding of the relationships between various MOO metrics.

Purpose of the Study:

• To categorize major MOO metrics based on established performance criteria: capacity, convergence, diversity, and convergence-diversity.
• To investigate the interrelationships among key MOO performance metrics.

Main Methods:

• Grouped prominent MOO metrics according to four performance criteria.
• Conducted a comprehensive study on the relationships between generational distance, ϵ-indicator (I(1)ϵ+), spread (∆), generalized spread (∆∗), inverted generational distance, and hypervolume.

Main Results:

• Identified high consistency among the six studied metrics when evaluating convex Pareto fronts (PFs).
• Observed certain contradictions among these metrics when applied to concave PFs.

Conclusions:

• The choice of MOO metric is crucial and context-dependent, particularly concerning the shape of the Pareto front.
• Further research is needed to reconcile metric behavior on non-convex solution spaces.