Visualizing fitnesses and constraint violations in single-objective optimization

ABSTRACTIn this study, we investigated visualization of search behavior in single-objective optimization function, where the objective function is composed of distinct components, either explicitly (as terms in the objective function or as components of a hybrid function) or implicitly (as constraints). We proposed a visualization method for constrained single-objective optimization in which the constraint violations and the term-by-term values of the polynomial objective function are separately calculated by RadViz and plotted in 3D. The proposed method is superior to the two-dimensional RadViz visualization in that it shows degasement of the fitness and constraint violations over time in the benchmark problem and can display them separately. Similarly, for the hybrid function, which is a benchmark problem consisting of multiple terms with different objective subfunctions, the difference in the timing of the decrease in fitness for each term is visualized by RadViz.