Structural bias in multi-objective optimisation

Structural bias (SB) refers to systematic preferences of an optimisation algorithm for particular regions of the search space that arise independently of the objective function. While SB has been studied extensively in single-objective optimisation, its role in multi-objective optimisation remains largely unexplored. This is problematic, as dominance relations, diversity preservation and Pareto-based selection mechanisms may introduce or amplify structural effects. In this paper, we extend the concept of structural bias to the multi-objective setting and propose a methodology to study it in isolation from fitness-driven guidance. We introduce a suite of synthetic multi-objective test problems with analytically controlled Pareto fronts and deliberately uninformative objective values. These problems are designed to decouple algorithmic behaviour from problem structure, allowing bias induced purely by algorithmic operators and design choices to be observed. The test suite covers a range of Pareto front shapes, densities and noise levels, enabling systematic analysis of different manifestations of structural bias. We discuss methodological challenges specific to the multi-objective case and outline how existing SB detection approaches can be adapted. This work provides a first step towards behaviour-based benchmarking of multi-objective optimisers, complementing performance-based evaluation and informing more robust algorithm design.

💡 Research Summary

The paper addresses a largely unexplored aspect of multi‑objective optimisation (MOO): structural bias (SB), i.e., systematic preferences of an algorithm for certain regions of the decision space that arise independently of the objective functions. While SB has been extensively studied for single‑objective optimisation, the authors argue that dominance relations, diversity‑preserving mechanisms and Pareto‑based selection in MOO may introduce new forms of bias or amplify existing ones, making its investigation essential for reliable algorithm benchmarking.

First, the authors review the existing SB detection methodology for single‑objective problems, which relies on the random test function f₀ that returns uniformly distributed values regardless of the input. By running an optimiser many times on f₀ and analysing the distribution of the best solutions, any deviation from uniformity can be attributed to algorithmic design. The BIAS toolbox (and its deep‑learning extension Deep‑BIAS) implements an ensemble of 39 statistical tests and a random‑forest classifier to automate this detection.

The core contribution is an extension of this concept to the multi‑objective case. The authors propose a suite of eleven synthetic bi‑objective test problems, each defined as f =