Title: Nonlinear threshold accepting meta-heuristic for combinatorial optimisation problems

Authors: Nabil Nahas; Mustapha Nourelfath

Addresses: Systems Engineering Department, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, 31261, Kingdom of Saudi Arabia ' Mechanical Engineering Department, Faculty of Science and Engineering, Interuniversity Research Center on Enterprise Networks, Logistics, and Transportation (CIRRELT), Université Laval, Quebec City, QC G1K 7P4, Canada

Abstract: Local search algorithms are a wide class of improvement algorithms that start from a given solution and try to find a better solution in a defined neighbourhood of the current solution. Stochastic hill climbing algorithms, such as threshold accepting algorithms and simulated annealing are optimisation techniques which belong to the family of local search algorithms. The main difference between the existing algorithms resides in the mechanism of accepting or rejecting the candidate solution from the neighbourhood. In this paper, we test a simple but effective modification of the conventional threshold accepting algorithm. In the proposed variant, the acceptance rule is nonlinear. This acceptance rule is inspired from the RC-filter which is a low-pass filter used in electronics to reduce the amplitude of signals with higher frequencies. We apply the newly developed meta-heuristic to difficult instances of four combinatorial optimisation problems, namely quadratic assignment problem, dynamic discrete facility layout problems, flow-shop scheduling and berth allocation. The results presented show that this algorithm performs well for several test problems. Therefore, it can be used as a specialised heuristic for these problems.

Keywords: nonlinear threshold; local search; quadratic assignment; facilities layout; flow shop scheduling; berth allocation; metaheuristics; combinatorial optimisation; threshold accepting algorithm; acceptance rule.

DOI: 10.1504/IJMHEUR.2014.068904

International Journal of Metaheuristics, 2014 Vol.3 No.4, pp.265 - 290

Received: 17 Oct 2013
Accepted: 30 Sep 2014

Published online: 16 Apr 2015 *

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