Year: 2026
Type: article
Abstract: Understanding the structure of multi-objective optimisation problems (MOPs) is essential for analysing search difficulty and supporting informed decision-making. In single-objective optimisation, fitness landscapes offer a spatial view of a problem, but extending such visualisations to MOPs is challenging due to the vector-valued nature of objectives. In this work, we introduce Pareto landscape, a fitness landscape visualisation technique for multi-objective optimisation on the basis of the Pareto dominance relation. We illustrate the main characteristics of a Pareto landscape, relate it to the classical fitness landscape, and examine its behaviour across benchmark suites, constrained problems, multimodal problems and real-world cases. We also show how it captures problem landscape structures relevant to optimisation difficulty. A comparison with gradient field heatmaps, PLOT, cost landscape, and constrained cost landscape further demonstrates that Pareto landscape offers complementary insight by highlighting structural patterns not visible with existing visualisation methods. Overall, the results indicate that the Pareto landscape provides a consistent way to observe problem structure across different classes of multi-objective optimisation problems.
DOI: 10.3390/mca31030067
Authors: Zhiji Cui, Zimin Liang, Miqing Li
Institution: University of Birmingham
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,689
OpenAlex ID: W7159800600