Exploration of Pareto-preserving Search Space Transformations in Multi-objective Test Functions
2026-04-09 • Neural and Evolutionary Computing
Neural and Evolutionary Computing
AI summaryⓘ
The authors explain that benchmark problems help test optimization algorithms, but if these problems have hidden patterns, algorithms might do well for the wrong reasons. While multi-objective optimization benchmarks focus on the outcomes (objective space), the authors highlight the need to also consider the problem setup (search space). They introduced special transformations to change the search space without messing up the problem's goals, tested them on popular benchmarks, and found that these changes affect how well different algorithms perform. They also explored doing similar transformations on the objective space and compared the effects.
benchmark problemsoptimization algorithmsmulti-objective optimizationsearch spaceobjective spacetransformationsboundary constraintsbijective transformationsperformance evaluation
Authors
Diedeerick Vermetten, Jeroen Rook
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.