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Fitness Landscape Analysis in Data-Driven Optimization: An Investigation of Clustering Problems

Data-driven optimization problems such as clustering provide a real-world representative source of instances for benchmarking continuous metaheuristic optimization algorithms. Although many metaheurstics and other algorithms have been applied to clustering problems, relatively little research has attempted to explore the structure of the problem space and/or fitness landscape for these problems. In contrast, problem-specific analysis and insights for several classes of combinatorial problems have been developed. This paper investigates the structure of the fitness landscapes of clustering problems, focusing on the fundamental parameters that define problem instances (the dimensionality, number and distribution of the data points and the number of clusters). The paper also provides a general method for active, targeted generation of problem instances based on real-world datasets. The results provide a number of new insights into this family of continuous optimization problems as well as methods and guidelines intended to facilitate better experimental evaluation and comparison of continuous optimization algorithms.