Abstract
We perform a novel analysis of the fitness landscape of the job-shop scheduling problem (JSP). In contrast to other well-known combinatorial optimization problems, we show that the landscape of the JSP is non-regular, in that the connectivity of solutions is variable. As a consequence, we argue that random walks performed on such a landscape will be biased. We conjecture that such a bias should affect both random walks and local search algorithms, and may provide a partial explanation for the remarkable success of the latter in solving the JSP.
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Adams, J., Balas, E., Zawack, D.: The shifting bottleneck procedure for job shop scheduling. Management Science 34, 391–401 (1988)
Anderson, E.J., Glass, C.A., Potts, C.N.: Applications in machine scheduling. In: Aarts, E.A., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 361–414. John Wiley & Sons, Chichester (1997)
Balas, E., Vazacopoulos, A.: Guided local search with the shifting bottleneck for job shop scheduling. Management Science 44, 262–275 (1998)
Błażewicz, J., Domschke, W., Pesch, E.: The job shop scheduling problem: Conventional and new solution techniques. European Journal of Operational Research 93, 1–33 (1996)
Smutnicki, C., Nowicki, E.: Some new ideas in ts for job-shop scheduling. In: Rego, C., Alidaee, B. (eds.) Adaptive Memory and Evolution. Tabu Search and Scatter Search, Kluwer, Dordrecht (2003)
Fisher, H., Thompson, G.L.: Probabilistic learning combinations of local jobshop scheduling rules. In: Industrial Scheduling, pp. 225–251. Prentice-Hall, Englewood Cliffs (1963)
Hordijk, W.: A measure of landscapes. Evolutionary Computation 4, 335–360 (1997)
Jain, A.S., Meeran, S.: Deterministic job-shop scheduling: Past, present and future. European Journal of Operational Research 113, 390–434 (1999)
Jones, T.: Evolutionary Algorithms, fitness landscapes and search. PhD thesis, University of New Mexico, Albuquerque, NM (1995)
Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proc. of the 6th Int. Conf. on Genetic Algorithms, pp. 184–192. Morgan Kaufmann Publishers, San Francisco (1995)
Kauffman, S.A.: Adaptation on rugged fitness landscapes. In: Stein, D. (ed.) Lectures in the sciences of complexity, pp. 527–618. Addison-Wesley, Reading (1989)
Kirkpatrick, S., Toulouse, G.: Configuration space analysis for traveling salesman problems. Journal de Physique 46, 1277–1292 (1985)
Kolonko, M.: Some new results on simulated annealing applied to the job shop scheduling problem. European Journal of Operational Research 113, 123–136 (1999)
Van Laarhoven, P.J.M., Aarts, E.H.L., Lenstra, J.K.: Job shop scheduling by simulated annealing. Operations Research 40, 113–125 (1992)
Mattfeld, D.C.: Evolutionary Search and the Job Shop. Physica-Verlag, Heidelberg (1996)
Mattfeld, D.C., Bierwirth, C., Kopfer, H.: A search space analysis of the job shop scheduling. Annals of Operations Research 86, 441–453 (1999)
Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Transactions on Evolutionary Computation 4, 337–352 (2000)
Nowicki, E., Smutnicki, S.: A fast tabu search algorithm for the job shop problem. Management Science 42, 797–813 (1996)
Reeves, C.R.: Landscapes, operators and heuristic search. Annals of Operational Research 86, 473–490 (1999)
Reeves, C.R.: Experiments with tunable fitness landscapes. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VI, pp. 139–148 (2000)
Stadler, P.F.: Fitness landscapes. In: Lässig, M., Valleriani, A. (eds.) Biological and Statistical Physics, pp. 187–202. Springer, Heidelberg (2002)
Stadler, P.F., Schnabl, W.: The landscape of the traveling salesman problem. Physics Letters A 161, 337–344 (1992)
Taillard, É.D.: Comparison of iterative searches for the quadratic assignment problem. Location Science 3, 87–105 (1995)
Watson, J.-P., Whitley, L.D., Howe, A.E.: A dynamic model of tabu search for the job-shop scheduling problem. In: Kendall, G., Burke, E., Petrovic, S. (eds.) Proc. of the 1st Multidisciplinary Int. Conf. on Scheduling: Theory and Applications, University of Nottingham, pp. 320–336 (2003)
Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybernetics 63, 325–336 (1990)
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Bierwirth, C., Mattfeld, D.C., Watson, JP. (2004). Landscape Regularity and Random Walks for the Job-Shop Scheduling Problem. In: Gottlieb, J., Raidl, G.R. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2004. Lecture Notes in Computer Science, vol 3004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24652-7_3
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DOI: https://doi.org/10.1007/978-3-540-24652-7_3
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