An Expedition to Multimodal Multi-objective Optimization Landscapes

摘要

The research in evolutionary multi-objective optimization is largely missing a notion of functional landscapes, which could enable a visual understanding of multimodal multi-objective landscapes and their characteristics by connecting decision and objective space. This consequently leads to the negligence of decision space in most algorithmic approaches and an almost complete lack of Exploratory Landscape Analysis (ELA) tools. This paper dares a first step into this unexplored field based on gradient properties of the multi-objective landscape. For a first time, basins of attraction and superpositions of local optima are visualized and thereby made intuitively accessible. With this work, we hope to highlight the importance of detailed decision space analysis in multi-objective optimization and to stimulate further research in that direction.