Nearest-Better Network: A Unified Tool for Visualizing the Fitness Landscapes of Continuous and Combinatorial Problems
Black-box optimization problems are common in real-world applications, yet their unknown mathematical forms make it difficult to analyze problem features, understand algorithm behavior, and design efficient algorithms. If these problems could be made more transparent through visualization, algorithm design and selection would become more intuitive. This report presents the Nearest-Better Network (NBN), a novel and powerful framework for fitness landscape analysis (FLA) applicable to both continuous and combinatorial optimization problems. Unlike existing FLA methods that often rely on algorithm-dependent or operator-biased sampling, NBN can be constructed using uniform sampling. In this directed graph, each solution points to its nearest fitter neighbor, thereby preserving essential structural characteristics of the landscape—such as modality, ruggedness, neutrality, and basin-of-attraction organization. We establish a theoretical foundation showing that NBN effectively approximates the maximum transition probability network under simple evolutionary dynamics. Moreover, to overcome the high computational cost of earlier implementations, we propose efficient algorithms with time complexities of O(NlogN) for both continuous and sequence-based problems, enabling large-scale landscape analyses. Comprehensive case studies on benchmark problems—including the OneMax function and the Traveling Salesman Problem (TSP)—demonstrate that NBN can reveal previously hidden landscape properties and diagnose the weaknesses of state-of-the-art algorithms such as EAX, LKH, and NLKH.
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- Function Room 2, 6th Floor, Shenzhen Nanshan Genpla Hotel, No. 3333 Liuxian Avenue, Nanshan District
- Shenzhen, Guangdong
- China
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Yiya Diao
Biography:
Yiya Diao received both her Bachelor’s and Ph.D. degrees from China University of Geosciences (Wuhan) and is currently a postdoctoral researcher at Harbin University of Science and Technology (Shenzhen). She has published several papers in SCI journals and international conferences, including two papers in IEEE Transactions on Evolutionary Computation (a top-tier artificial intelligence journal, CCF-B), as well as papers presented at major international conferences such as GECCO (CCF-C) and IEEE CEC. Her research primarily focuses on modeling and visualizing fitness landscapes for both combinatorial and continuous optimization problems, as well as on the design of optimization algorithms driven by problem feature learning.
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