Plotting Impossible? Surveying Visualization Methods for Continuous Multi-Objective Benchmark Problems

Schäpermeier, Lennart; Grimme, Christian; Kerschke, Pascal

Abstract

Traditionally, visualizing benchmark problems is an integral task in the domain of evolutionary algorithms development. Researchers get inspired for new search heuristics by challenges observed in functional landscapes. Moreover, landscape characteristics, features, and even terminology to describe them are derived from visualizations. And most importantly, benchmark designers need visualizations for identifying diverse problems that potentially challenge different aspects of optimization algorithms. As easy as it is to visualize single-objective problems, until recently there were hardly any approaches for gaining similar insights for multi-objective problems. Also, there have been no seamlessly accessible tools to support such visualizations.

This paper presents a comprehensive overview of the available visualization techniques from literature, including two interactive techniques to visualize three-dimensional problems, as well as two novel techniques which are suitable to scale some visualization properties to even higher-dimensional spaces. All presented techniques are integrated into a single tool, the moPLOT-dashboard, which enables users to perform landscape analyses in an interactive manner. Finally, the value of the tool and the visualizations is demonstrated in a series of usage scenarios on well-known benchmark problems.

Keywords
Multi-Objective Optimization; Visualization; Multimodal Optimization; Benchmarks; Theory; Algorithms