MO-ELA: Rigorously Expanding Exploratory Landscape Features for Automated Algorithm Selection in Continuous Multi-Objective Optimisation

TL;DR

This paper introduces MO-ELA, a new set of exploratory landscape features for multi-objective optimization, improving automated algorithm selection by better characterizing problem difficulty.

Contribution

The paper proposes MO-ELA, a novel set of features for multi-objective problems, enhancing the ability to distinguish algorithm performance and aiding automated selection.

Findings

Features improve problem hardness estimation

Models closely match the virtual best solver

Proposed features are top contributors after selection

Abstract

Automated Algorithm Selection (AAS) is a popular meta-algorithmic approach and has demonstrated to work well for single-objective optimisation in combination with exploratory landscape features (ELA), i.e., (numerical) descriptive features derived from sampling the black-box (continuous) optimisation problem. In contrast to the abundance of features that describe single-objective optimisation problems, only a few features have been proposed for multi-objective optimisation so far. Building upon recent work on exploratory landscape features for box-constrained continuous multi-objective optimization problems, we propose a novel and complementary set of additional features (MO-ELA). These features are based on a random sample of points considering both the decision and objective space. The features are divided into 5 feature groups depending on how they are being calculated: non-dominated-sorting, descriptive statistics, principal component analysis, graph structures and gradient information. An AAS study conducted on well-established multi-objective benchmarks demonstrates that the proposed features contribute to successfully distinguishing between algorithm performance and thus adequately capture problem hardness resulting in models that come very close to the virtual best solver. After feature selection, the newly proposed features are frequently among the top contributors, underscoring their value in algorithm selection and problem characterisation.