Exploration of Pareto-preserving Search Space Transformations in Multi-objective Test Functions

2026-04-09

AI Summary

Existing multi-objective optimization benchmark problems introduce bias due to poorly designed search space structures, compromising the objectivity of algorithm evaluation. This work proposes a bijective transformation method that preserves Pareto optimality while parametrically reconstructing both the decision and objective spaces of standard test functions. The approach eliminates unintended structural artifacts without altering the intrinsic Pareto front geometry. By systematically applying this method to diverse benchmark problems and evaluating them with state-of-the-art multi-objective optimizers, the study demonstrates that search space structure significantly influences algorithm performance. The findings expose latent deficiencies in current benchmark suites and establish a new paradigm for constructing more robust and unbiased multi-objective test suites.

Abstract

Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective optimization, for example, many problems used to have their optimum in the center of the search domain. To remedy these issues, search space transformations have been widely adopted by benchmark suites, preventing algorithms from exploiting unintended structure. In multi-objective optimization, problem design has focused primarily on the objective space structure. While this focus addresses important aspects of the multi-objective nature of the problems, the search space structures of these problems have received comparatively limited attention. In this work, we re-emphasize the importance of transformations in the search space, and address the challenges inherent in adding transformations to boundary constraints problems without impacting the structure of the objective space. We utilized two parameterized, bijective transformations to create different instantiations of popular benchmark problems, and show how these changes impact the performance of various multi-objective optimization algorithms. In addition to the search space transformations, we show that such parameterized transformations can also be applied to the objective space, and compare their respective performance impacts.

Problem

• multi-objective optimization
• benchmark problems
• search space transformations
• objective space structure
• Pareto-preserving

Innovation

• Pareto-preserving
• search space transformation
• multi-objective optimization
• bijective mapping
• benchmark design