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

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.

💡 Research Summary

This paper addresses a notable gap in the field of automated algorithm selection (AAS) for continuous multi‑objective optimisation (MOP) – the scarcity of informative, inexpensive instance features. While exploratory landscape analysis (ELA) has become a cornerstone for single‑objective black‑box optimisation, only a handful of multi‑objective (MO) ELA descriptors exist, and most of them either ignore interactions between objectives or are limited to combinatorial settings. Building on the recent continuous MO‑ELA set introduced by Liefooghe et al. (2021), the authors propose a comprehensive new feature suite, dubbed MO‑ELA, that captures both decision‑space and objective‑space characteristics through five distinct groups: (1) non‑dominated sorting (NDS) based features, (2) descriptive statistics, (3) principal component analysis (PCA) descriptors, (4) graph‑structure metrics, and (5) gradient‑information measures.

The methodology starts with a Latin‑Hypercube sampled set X of N points in the bounded decision space. Each point is evaluated, yielding a paired set S = {(x_i, y_i)}. All features are computed after scaling decision variables to