Sebastian Volke
ABSTRACT
Combinatorial optimization problems and corresponding (meta-)heuristics have received much attention in the literature. Especially, the structural or topological analysis of search landscapes is important for evaluating the applicability and the performance of search operators for a given problem. However, this analysis is often tedious and usually the focus is on one specific problem and only a few operators. We present a visual analysis method that can be applied to a wide variety of problems and search operators. The method is based on steepest descent walks and shortest distances in the search landscape. The visualization shows the search landscape as seen by the search algorithm. It supports the topological analysis as well as the comparison of search landscapes. We showcase the method by applying it to two different search operators on the TSP, the QAP, and the SMTTP. Our results show how differences between search operators manifest in the search landscapes and how conclusions about the suitability of the search operator for different optimizations can be drawn.
- S. Bin, S. Volke, G. Scheuermann, and M. Middendorf. Comparing the Optimization Behaviour of Heuristics with Topology Based Visualization. In A.-H. Dediu, M. Lozano, and C. Martín-Vide, editors, Theory and Practice of Natural Computing, volume 8890 of Lecture Notes in Computer Science, pages 47--58. Springer, 2014.Google Scholar
Cross Ref
- K. D. Boese. Models for Iterative Global Optimization. PhD thesis, University of California at Los Angeles, CA, USA, 1996. Google ScholarDigital Library
- R. Burkard, S. Karisch, and F. Rendl. QAPLIB -- A Quadratic Assignment Problem Library. Journal of Global Optimization, 10(4):391--403, 1997. Google ScholarDigital Library
- T. Cox and M. Cox. Multidimensional Scaling. CRC Press, 2010.Google Scholar
- G. A. Croes. A method for solving traveling salesman problems. Operations Research, 6:791--812, 1958.Google ScholarDigital Library
- C. Flamm, I. L. Hofacker, P. F. Stadler, and M. T. Wolfinger. Barrier Trees of Degenerate Landscapes. Z. Phys. Chem., 216:1--19, 2002.Google ScholarCross Ref
- C. Fleurent and F. Glover. Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory. INFORMS Journal on Computing, 11(2):198--204, Feb. 1999. Google ScholarDigital Library
- C. Fonlupt, D. Robilliard, P. Preux, and E.-G. Talbi. Fitness Landscapes and Performance of Meta-Heuristics. In Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 257--268. Kluwer, 1999.Google ScholarCross Ref
- M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google ScholarDigital Library
- J. Garnier and L. Kallel. How to Detect All Maxima of a Function. In Theoretical Aspects of Evolutionary Computing, pages 343--370. Springer, 2001. Google ScholarDigital Library
- F. Glover and M. Laguna. Tabu Search. Kluwer, 1997. Google ScholarCross Ref
- G. Grinstein, M. Trutschl, and U. Cvek. High-Dimensional Visualizations. In Proceedings of the VII Data Mining Conference KDD Workshop 2001, pages 7--19. ACM Press, 2001.Google Scholar
- S. Halim, R. H. C. Yap, and H. C. Lau. Viz: A Visual Analysis Suite for Explaining Local Search Behavior. In User Interface Software and Technology, pages 57--66, 2006. Google ScholarDigital Library
- J. Hallam and A. Prügel-Bennett. Large Barrier Trees for Studying Search. IEEE Trans. Evolutionary Computation, 9(4):385--397, 2005. Google ScholarDigital Library
- H. H. Hoos and T. Stützle. Stochastic local search: Foundations & applications. Elsevier, 2004. Google ScholarDigital Library
- D. S. Johnson. Local optimization and the Traveling Salesman Problem. In M. S. Paterson, editor, Automata, Languages and Programming, volume 443 of Lecture Notes in Computer Science, pages 446--461. Springer, 1990. Google ScholarDigital Library
- S. Khor. Search space analysis with Wang-Landau sampling and slow adaptive walks. CoRR, abs/1112.5980, 2011.Google Scholar
- D. E. Knuth. The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms. Addison-Wesley, 1997. Google ScholarDigital Library
- S. Lin and B. W. Kernighan. An Effective Heuristic Algorithm for the Travelling-Salesman Problem. Operations Research, 21:498--516, 1973. Google ScholarDigital Library
- D. M. McCandlish. Visualizing fitness landscapes. Evolution, 65(6):1544--1558, 2011.Google ScholarCross Ref
- E. Pitzer and M. Affenzeller. A Comprehensive Survey on Fitness Landscape Analysis. In J. Fodor, R. Klempous, and C. Suárez Araujo, editors, Recent Advances in Intelligent Engineering Systems, volume 378 of Studies in Computational Intelligence, pages 161--191. Springer, 2012.Google ScholarCross Ref
- P. Preux, D. Robilliard, C. Fonlupt, R. M. Karp, and J. M. Steele. Fitness Landscapes of Combinatorial Problems and the Performance of Search Algorithms, 1997.Google Scholar
- G. Reinelt. TSPLIB--A Traveling Salesman Problem Library. ORSA Journal on Computing, 3(4):376--384, 1991.Google ScholarCross Ref
- T. Schiavinotto and T. Stützle. A Review of Metrics on Permutations for Search Landscape Analysis. Computer and Operations Research, 34(10):3143--3153, October 2007. Google ScholarDigital Library
- B. Stadler and P. Stadler. Combinatorial vector fields and the valley structure of fitness landscapes. Journal of Mathematical Biology, 61(6):877--898, 2010.Google ScholarCross Ref
- P. F. Stadler and W. Schnabl. The landscape of the traveling salesman problem. Physics Letters A, 161(4):337 -- 344, 1992.Google ScholarCross Ref
- S. Volke, S. Bin, D. Zeckzer, M. Middendorf, and G. Scheuermann. Visual analysis of discrete particle swarm optimization using fitness landscapes. In H. Richter and A. Engelbrecht, editors, Recent Advances in the Theory and Application of Fitness Landscapes, volume 6 of Emergence, Complexity and Computation, pages 487--507. Springer, 2014.Google ScholarCross Ref
- S. Volke, M. Middendorf, M. Hlawitschka, J. Kasten, D. Zeckzer, and G. Scheuermann. dPSO-Vis: Topology-based Visualization of Discrete Particle Swarm Optimization. Computer Graphics Forum, 32(3):351--360, 2013.Google Scholar
- S. Volke, D. Zeckzer, M. Middendorf, and G. Scheuermann. Visualizing topological properties of the search landscape of combinatorial optimization problems. Accepted for presentation at phTopology-Based Methods in Visualization 2015 (Annweiler, Germany, May 20. -- 22., 2015). Final version for workshop proceedings currently under review.Google Scholar
- L. Wilkinson. The Grammar of Graphics. Springer, 1999. Google ScholarDigital Library
Index Terms
- A Visual Method for Analysis and Comparison of Search Landscapes
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