Novelty-Based Generation of Continuous Landscapes with Diverse Local Optima Networks

TL;DR

This paper introduces a low-cost method for constructing Local Optima Networks in continuous landscapes using explicit basin definitions, enabling analysis of landscape features and algorithm performance.

Contribution

It proposes an alternative, search-free approach to build LONs for MSG landscapes and uses Novelty Search to generate diverse landscape instances with varying difficulty.

Findings

LON features closely match gradient-based basins.

NS effectively produces landscapes with diverse topologies.

Success rates of algorithms can be predicted from LON features.

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.