🤖 AI Summary
Constructing local optima networks (LONs) in continuous optimization is computationally expensive, hindering systematic investigation into the relationship between LON structure and evolutionary algorithm performance. This work addresses this challenge by proposing a non-iterative definition of basins of attraction tailored to the Max-Set of Gaussians fitness landscape, enabling—for the first time—the direct construction of LONs in continuous space. Integrating novelty search, the method efficiently generates a benchmark problem suite with controllable multimodality and diverse graph topologies. The resulting basins of attraction align closely with those obtained via gradient-based methods and effectively predict the success rates of two evolutionary algorithms. This approach provides a high-quality, structurally rich dataset that advances landscape-aware optimization research.
📝 Abstract
Local Optima Networks (LONs) represent the global structure of search spaces as graphs, but their construction requires iterative execution of a search algorithm to find local optima and approximate transitions between Basins of Attraction (BoAs). In continuous optimization, this high computational cost prevents systematic investigation of the relationship between LON features and evolutionary algorithm performance. To address this issue, we propose an alternative definition of BoAs for Max-Set of Gaussians (MSG) landscapes with explicitly tunable multimodality. This bypasses search-based BoA identification, enabling low-cost LON construction. Moreover, we leverage Novelty Search (NS) to explore the parameter space of the MSG landscape generator, producing instances with diverse graph topologies. Our experiments show that the proposed BoAs closely align with gradient-based BoAs, and that NS successfully generates instances with varied search difficulty and connectivity patterns among optima. Finally, over the instances generated by NS, we predict the success rate of two well-established evolutionary algorithms from LON features. While our LON construction is specific to MSG landscapes, the proposed framework provides a dataset that serves as a foundation for landscape-aware optimization.