Multi-objective Local Optima Networks based on Decomposition
TL;DR
Mo-LON/D, a decomposition-based local optima network model for multi-objective landscapes, is introduced, indicating that mo-LON/D offers comparable explanatory power (and even higher correlations) with respect to the performance of state-of-the-art algorithms.
Abstract
Fitness landscape analysis provides insights into optimization problems, informing algorithms' design and identifying properties that influence performance. While understanding global landscape structure is critical, tools for analyzing and visualizing multi-objective, high-dimensional optimization problems remain limited. Recent models, such as Pareto local optima solution networks (PLOS-nets), primarily focus on small instances and binary representations, posing challenges for extension to more complex domains. To address this gap, we introduce mo-LON/D, a decomposition-based local optima network model for multi-objective landscapes. This model partitions a multi-objective problem into scalar sub-problems, constructs standard single-objective local optima networks (LONs) for each, and integrates them via a graph union. We validate mo-LON/D on fully enumerated bi-objective ρmnk-landscapes and contrast its structural features against PLOS-nets both visually and quantitatively. Despite the inherent sampling involved in scalarization, our results indicate that mo-LON/D offers comparable explanatory power (and even higher correlations) with respect to the performance of state-of-the-art algorithms. By harnessing established sampling techniques from single-objective research, mo-LON/D could potentially provide a scalable framework for characterizing complex multi-objective landscapes.