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

Researchers Kippei Mizuta, Shoichiro Tanaka, Shuhei Tanaka, and Toshiharu Hatanaka have proposed a novel method to generate continuous optimization landscapes with diverse Local Optima Networks (LONs) at a fraction of the usual computational cost. Traditional LON construction requires iterative search algorithms to find local optima and approximate transitions between Basins of Attraction (BoAs), which is prohibitively expensive for continuous optimization. Their alternative definition of BoAs for Max-Set of Gaussians (MSG) landscapes bypasses this search-based identification entirely, enabling low-cost LON construction.

By leveraging Novelty Search (NS) to explore the parameter space of the MSG landscape generator, the team produced instances with diverse graph topologies, varying search difficulty, and different connectivity patterns among optima. Experiments showed their proposed BoAs closely align with gradient-based BoAs. Using the generated instances, they successfully predicted the success rate of two well-established evolutionary algorithms from LON features. While the LON construction is specific to MSG landscapes, the framework provides a dataset foundation for landscape-aware optimization research.