Explicitly Multi-Modal Benchmarks for Multi-Objective Optimization
This provides a tool for researchers in optimization to better evaluate solvers by localizing performance on local Pareto fronts, though it is incremental as it builds on existing benchmarking concepts.
The paper tackles the problem of designing multi-objective optimization benchmarks with controlled local Pareto fronts, especially in high-dimensional spaces, by introducing a benchmarking method based on basin connectivity (3BC) that uses basins of attraction to specify multimodal landscapes and accurately represent intended optima.
In multi-objective optimization, designing good benchmark problems is an important issue for improving solvers. Controlling the global location of Pareto optima in existing benchmark problems has been problematic, and it is even more difficult when the design space is high-dimensional since visualization is extremely challenging. As a benchmarking with explicit local Pareto fronts, we introduce a benchmarking based on basin connectivity (3BC) by using basins of attraction. The 3BC allows for the specification of a multimodal landscape through a kind of topological analysis called the basin graph, effectively generating optimization problems from this graph. Various known indicators measure the performance of a solver in searching global Pareto optima, but using 3BC can make us localize them for each local Pareto front by restricting it to its basin. 3BC's mathematical formulation ensures the accurate representation of the specified optimization landscape, guaranteeing the existence of intended local and global Pareto optima.