MOLE: Digging Tunnels Through Multimodal Multi-Objective Landscapes

TL;DR

This paper introduces MOLE, a new algorithm designed to effectively explore and exploit locally efficient sets in multimodal multi-objective landscapes, improving upon previous methods like MOGSA through detailed analysis and benchmarking.

Contribution

The paper proposes MOLE, a novel algorithm that models and exploits LE sets in MMMOO problems, addressing limitations of prior algorithms like MOGSA.

Findings

MOLE outperforms MOGSA on various test problems.

Benchmark results show MOLE's efficiency in modeling LE sets.

The approach is practical for bi-objective optimization tasks.

Abstract

Recent advances in the visualization of continuous multimodal multi-objective optimization (MMMOO) landscapes brought a new perspective to their search dynamics. Locally efficient (LE) sets, often considered as traps for local search, are rarely isolated in the decision space. Rather, intersections by superposing attraction basins lead to further solution sets that at least partially contain better solutions. The Multi-Objective Gradient Sliding Algorithm (MOGSA) is an algorithmic concept developed to exploit these superpositions. While it has promising performance on many MMMOO problems with linear LE sets, closer analysis of MOGSA revealed that it does not sufficiently generalize to a wider set of test problems. Based on a detailed analysis of shortcomings of MOGSA, we propose a new algorithm, the Multi-Objective Landscape Explorer (MOLE). It is able to efficiently model and exploit LE sets in MMMOO problems. An implementation of MOLE is presented for the bi-objective case, and the practicality of the approach is shown in a benchmarking experiment on the Bi-Objective BBOB testbed.