Explicitly Multi-Modal Benchmarks for Multi-Objective Optimization

TL;DR

This paper introduces a novel benchmark framework called 3BC for multi-objective optimization that explicitly models local Pareto fronts using basin connectivity, aiding in better solver evaluation and landscape control.

Contribution

The paper presents 3BC, a topological benchmark method that explicitly generates and localizes multiple Pareto fronts in high-dimensional landscapes using basin graphs.

Findings

3BC accurately represents specified optimization landscapes.

It enables localization of Pareto optima within basins.

The method improves benchmarking by controlling landscape features.

Abstract

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.