Abstract
One key component of stochastic local search algorithms is the acceptance criterion that determines whether a solution is accepted as the new current solution or it is discarded. One of the most studied local search algorithms is simulated annealing. It often uses the Metropolis condition as acceptance criterion, which always accepts equal or better quality solutions and worse ones with a probability that depends on the amount of worsening and a parameter called temperature. After the introduction of simulated annealing several other acceptance criteria have been introduced to replace the Metropolis condition, some being claimed to be simpler and better performing. In this article, we evaluate various such acceptance criteria from an experimental perspective. We first tune the numerical parameters of the algorithms using automatic algorithm configuration techniques for two test problems, the quadratic assignment problem and a permutation flowshop problem. Our experimental results show that, while results may differ depending on the specific problem, the Metropolis condition and the late acceptance hill climbing rule are among the choices that obtain the best results.
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References
Appleby, J., Blake, D., Newman, E.: Techniques for producing school timetables on a computer and their application to other scheduling problems. Comput. J. 3(4), 237–245 (1961)
Bohachevsky, I.O., Johnson, M.E., Stein, M.L.: Generalized simulated annealing for function optimization. Technometrics 28(3), 209–217 (1986)
Burkard, R.E., Çela, E., Pardalos, P.M., Pitsoulis, L.S.: The quadratic assignment problem. In: Handbook of Combinatorial Optimization, vol. 2, pp. 241–338. Kluwer Academic Publishers (1998)
Burke, E.K., Bykov, Y.: The late acceptance hill-climbing heuristic. Technical report CSM-192, University of Stirling (2012)
Burke, E.K., Bykov, Y.: The late acceptance hill-climbing heuristic. Eur. J. Oper. Res. 258(1), 70–78 (2017)
Chen, R.M., Hsieh, F.R.: An exchange local search heuristic based scheme for permutation flow shop problems. Appl. Math. Inf. Sci. 8(1), 209–215 (2014)
Dueck, G.: New optimization heuristics: the great deluge algorithm and the record-to-record travel. J. Comput. Phys. 104(1), 86–92 (1993)
Dueck, G., Scheuer, T.: Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90(1), 161–175 (1990)
Hoos, H.H., Stützle, T.: Stochastic Local Search-Foundations and Applications. Morgan Kaufmann Publishers, San Francisco (2005)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)
López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Stützle, T., Birattari, M.: The irace package: iterated racing for automatic algorithm configuration. Oper. Res. Perspect. 3, 43–58 (2016)
López-Ibáñez, M., Stützle, T.: Automatically improving the anytime behaviour of optimisation algorithms. Eur. J. Oper. Res. 235(3), 569–582 (2014)
Mascia, F., López-Ibáñez, M., Dubois-Lacoste, J., Stützle, T.: From grammars to parameters: automatic iterated greedy design for the permutation flow-shop problem with weighted tardiness. In: Nicosia, G., Pardalos, P. (eds.) LION 2013. LNCS, vol. 7997, pp. 321–334. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-44973-4_36
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)
Moscato, P., Fontanari, J.F.: Stochastic versus deterministic update in simulated annealing. Phys. Lett. A 146(4), 204–208 (1990)
Nawaz, M., Enscore Jr., E., Ham, I.: A heuristic algorithm for the \(m\)-machine, \(n\)-job flow-shop sequencing problem. Omega 11(1), 91–95 (1983)
Ogbu, F.A., Smith, D.K.: The application of the simulated annealing algorithm to the solution of the n/m/C max flowshop problem. Comput. Oper. Res. 17(3), 243–253 (1990)
Pan, Q.K., Ruiz, R.: Local search methods for the flowshop scheduling problem with flowtime minimization. Eur. J. Oper. Res. 222(1), 31–43 (2012)
Pan, Q.K., Ruiz, R.: A comprehensive review and evaluation of permutation flowshop heuristics to minimize flowtime. Comput. Oper. Res. 40(1), 117–128 (2013)
Stützle, T.: Iterated local search for the quadratic assignment problem. Eur. J. Oper. Res. 174(3), 1519–1539 (2006)
Taillard, É.D.: Benchmarks for basic scheduling problems. Eur. J. Oper. Res. 64(2), 278–285 (1993)
Taillard, É.D.: Comparison of iterative searches for the quadratic assignment problem. Location Sci. 3(2), 87–105 (1995)
Černý, V.: A thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J. Optim. Theory Appl. 45(1), 41–51 (1985)
Acknowledgments
We acknowledge support from the COMEX project (P7/36) within the IAP Programme of the BelSPO. Thomas Stützle acknowledges support from the Belgian F.R.S.-FNRS, of which he is a senior research associate.
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Franzin, A., Stützle, T. (2018). Comparison of Acceptance Criteria in Randomized Local Searches. In: Lutton, E., Legrand, P., Parrend, P., Monmarché, N., Schoenauer, M. (eds) Artificial Evolution. EA 2017. Lecture Notes in Computer Science(), vol 10764. Springer, Cham. https://doi.org/10.1007/978-3-319-78133-4_2
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