Capacitated Windy Rural Postman Problem with Several Vehicles: A Hybrid Multi-Objective Simulated Annealing Algorithm

This paper presents the capacitated Windy Rural Postman Problem with several vehicles. For this problem, two objectives are considered. One of them is the minimization of the total cost of all vehicle routes expressed by the sum of the total traversing cost and another one is reduction of the maximum cost of vehicle route in order to find a set of equitable tours for the vehicles. Mathematical formulation is provided. The multi-objective simulated annealing (MOSA) algorithm has been modified for solving this bi-objective NP-hard problem. To increase algorithm performance, Taguchi technique is applied to design experiments for tuning parameters of the algorithm. Numerical experiments are proposed to show efficiency of the model. Finally, the results of the MOSA have been compared with MOCS (multi-objective Cuckoo Search algorithm) to validate the performance of the proposed algorithm. The experimental results indicate that the proposed algorithm provides good solutions and performs significantly better than the MOCS.

[1]  Wen Lea Pearn,et al.  Algorithms for the Windy Postman Problem , 1994, Comput. Oper. Res..

[2]  Martin Grötschel,et al.  A cutting plane algorithm for the windy postman problem , 1992, Math. Program..

[3]  David Soler,et al.  The capacitated general windy routing problem with turn penalties , 2011, Oper. Res. Lett..

[4]  Ángel Corberán,et al.  Min‐Max K‐vehicles windy rural postman problem , 2009, Networks.

[5]  Gerhard Reinelt,et al.  A tabu search algorithm for the min-max k-Chinese postman problem , 2006, Comput. Oper. Res..

[6]  Jack Edmonds,et al.  Matching, Euler tours and the Chinese postman , 1973, Math. Program..

[7]  Ángel Corberán,et al.  A metaheuristic for the min–max windy rural postman problem with K vehicles , 2010, Comput. Manag. Sci..

[8]  Ángel Corberán,et al.  New facets and an enhanced branch‐and‐cut for the min–max K‐vehicles windy rural postman problem , 2011, Networks.

[9]  Masoud Rabbani,et al.  Solving a fuzzy multi-objective products and time planning using hybrid meta-heuristic algorithm: Gas refinery case study , 2016 .

[10]  Daniele Vigo,et al.  Lower bounds and heuristics for the Windy Rural Postman Problem , 2007, Eur. J. Oper. Res..

[11]  Masoud Rabbani,et al.  Vehicle Routing with Time Windows and Customer Selection for Perishable Goods , 2015 .

[12]  Peter Brucker.  The Chinese Postman Problem for Mixed Graphs , 1980, WG.

[13]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[14]  Á. Corberán,et al.  A branch & cut algorithm for the windy general routing problem and special cases , 2007 .

[15]  Zaw Win,et al.  On the Windy Postman Problem on eulerian graphs , 1989, Math. Program..

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  Ángel Corberán,et al.  New heuristic algorithms for the windy rural postman problem , 2005, Comput. Oper. Res..

[18]  Christos H. Papadimitriou,et al.  On the complexity of edge traversing , 1976, J. ACM.

[19]  Meigu Guan,et al.  On the windy postman problem , 1984, Discret. Appl. Math..

[20]  Ujjwal Maulik,et al.  A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA , 2008, IEEE Transactions on Evolutionary Computation.

[21]  E. Minieka.  The Chinese Postman Problem for Mixed Networks , 1979 .

[22]  Teruo Mori,et al.  The New Experimental Design: Taguchi's Approach to Quality Engineering , 1993 .

[23]  Hediye Gun,et al.  Polyhedral structure and efficient algorithms for certain classes of the directed rural postman problem , 1993 .

[24]  B. Suman,et al.  A survey of simulated annealing as a tool for single and multiobjective optimization , 2006, J. Oper. Res. Soc..

[25]  Ángel Corberán,et al.  The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra , 2008, SIAM J. Discret. Math..

[26]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

[27]  C. S. Orloff.  A fundamental problem in vehicle routing , 1974, Networks.

[28]  Bruce L. Golden,et al.  Plowing with precedence: A variant of the windy postman problem , 2013, Comput. Oper. Res..

[29]  M. Dror.  Arc Routing : Theory, Solutions and Applications , 2000 .

[30]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[31]  Ángel Corberán,et al.  An algorithm for the Rural Postman problem on a directed graph , 1986 .

[32]  Francisco Javier Zaragoza Martínez.  Series-parallel graphs are windy postman perfect , 2008, Discret. Math..