Title: Efficient approximation of melting temperature in simulated annealing algorithms applied to Chebyshev travelling salesman problem

Authors: Omar Al-Araidah; Khaleel Abu Shgair; Wafa Batayneh; Ali Diabat

Addresses: Industrial Engineering Department, Jordan University of Science and Technology, Irbid, 22110, Jordan. ' Mechanical Engineering Department, Al-Balqa Applied University, P.O. Box 15008, Amman 11134, Jordan. ' Mechanical Engineering Department, Jordan University of Science and Technology, Irbid, 22110, Jordan. ' Engineering Systems and Management, Masdar Institute of Science and Technology, P.O. Box 54224, Abu Dhabi, UAE

Abstract: Simulated annealing algorithms are widely used for solving NP-hard combinatorial optimisation problems including the travelling salesman problem (TSP). This article presents results of an empirical investigation for estimating the melting temperature for the simulated annealing algorithm based on the objective function value. We limit our search to Chebyshev order-picking systems with unequal horizontal and vertical speeds. The article utilises 90 randomly generated order-picking problems with densities ranging from 10 to 800 stops per tour. For each investigated problem, we utilise different seed values to generate and to solve ten replicates of the problem. Results show that quality melting temperature values can be estimated based on the statistical characteristics of the search space. This study helps to arrive at quality solutions with significantly fewer re-evaluations of the objective function.

Keywords: simulated annealing; melting temperatures; algorithms; heuristics; metaheuristics; Pafnuty Chebyshev; mathematics; mathematical problems; travelling salesman; efficient approximation; combinatorial problems; optimisation problems; NP-hard; non-deterministic hard; polynomial-time hard; objective function values; order-picking systems; unequal speeds; horizontal speeds; vertical speeds; randomly generated problems; seed values; replicates; replicate generation; temperature values; statistical characteristics; search spaces; quality solutions; business performance; SCM; supply chain management; modelling.

DOI: 10.1504/IJBPSCM.2012.048304

International Journal of Business Performance and Supply Chain Modelling, 2012 Vol.4 No.2, pp.145 - 163

Received: 13 Jan 2012
Accepted: 02 May 2012
Published online: 11 Aug 2014 *

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