Visualizing Topological Properties of the Search Landscape of Combinatorial Optimization Problems

Discrete combinatorial optimization problems such as the Traveling Salesman Problem have various applications in science and in everyday life. The complexity of the problem and the effectiveness of search algorithms depend not only on the problem itself but also on the search operator in use. Therefore, investigating search operators and the search landscapes they give rise to is an important field of research. However, a full topological analysis of the landscapes is impossible due to their exponentially growing size. We propose a visualization system that gives a visual intuition about topological properties of the search landscape. We obtain representative samples of the search landscape and its optima by random sampling and by computing the related optima using local search. The distribution and the correlation of this data within the search landscape is visualized with a combination of one and two dimensional visualizations. Using the TSP as an example we illustrate how the visualization supports the understanding and comparison of search landscapes and their complexity.

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