Search Dynamics on Multimodal Multiobjective Problems.

Area of Science:

• Multiobjective Optimization (MO)
• Computational Intelligence
• Heuristics and Optimization

Background:

• Recent work has focused on defining multimodality in multiobjective optimization (MO).
• Existing diversity maintenance approaches are insufficient for complex multimodal MO landscapes.
• There is a need for a test bed and analytical methods that consider landscape topology.

Purpose of the Study:

• To define multimodality in MO and introduce a test bed for multimodal MO problems.
• To analyze the interaction between MO algorithms and problem landscapes, moving beyond performance metrics.
• To extend Exploratory Landscape Analysis (ELA) for MO by incorporating decision space visualization.

Main Methods:

• Definition of multimodality in MO, allowing ellipsoid contours for subproblems.
• Development of a test bed for multimodal MO problems.
• Experimental analysis comparing MO algorithms based on hypervolume gradient approximation and local search.
• Application of visualization techniques in the decision space.

Main Results:

• The study provides a framework for understanding multimodal MO problem landscapes.
• Analysis reveals specific interactions between algorithms and problem characteristics.
• Visualization techniques enhance the understanding of algorithm behavior in the decision space.

Conclusions:

• The proposed approach strengthens the foundations for Exploratory Landscape Analysis (ELA) in MO.
• Focusing on landscape topology and algorithm-interaction offers deeper insights than performance metrics alone.
• This work facilitates the development of more effective algorithms for complex multimodal MO problems.