Comparing communities of optima with funnels in combinatorial fitness landscapes

Thomson, Sarah L.; Daolio, Fabio; Ochoa, Gabriela

Abstract

The existence of sub-optimal funnels in combinatorial fitness landscapes has been linked to search difficulty. The exact nature of these structures --- and how commonly they appear --- is not yet fully understood. Improving our understanding of funnels could help with designing effective diversification mechanisms for a 'smoothing' effect, making optimisation easier. We model fitness landscapes as local optima networks. The relationship between communities of local optima found by network clustering algorithms and funnels is explored. Funnels are identified using the notion of monotonic sequences from the study of energy landscapes in theoretical chemistry. NK Landscapes and the Quadratic Assignment Problem are used as case studies. Our results show that communities are linked to funnels. The analysis exhibits relationships between these landscape structures and the performance of trajectory-based metaheuristics such as Simulated Annealing (SA) and Iterated Local Search (ILS). In particular, ILS gets trapped in funnels, and modular communities of optima slow it down. The funnels contribute to lower success for SA. We show that increasing the strength of ILS perturbation helps to 'smooth' the funnels and improves performance in multi-funnel landscapes.

Citation

Thomson, S. L., Daolio, F., & Ochoa, G. (2017, July). Comparing communities of optima with funnels in combinatorial fitness landscapes. Presented at GECCO '17: Genetic and Evolutionary Computation Conference, Berlin, Germany

• Presentation Conference Type: Conference Paper (published)
• Conference Name: GECCO '17: Genetic and Evolutionary Computation Conference
• Start Date: Jul 15, 2017
• End Date: Jul 19, 2017
• Online Publication Date: Jul 1, 2017
• Publication Date: 2017
• Deposit Date: Aug 16, 2023
• Publisher: Association for Computing Machinery (ACM)
• Pages: 377-384
• Book Title: GECCO '17: Proceedings of the Genetic and Evolutionary Computation Conference
• ISBN: 9781450349208
• DOI: https://doi.org/10.1145/3071178.3071211