AN IMPROVED ANT COLONY SYSTEM ALGORITHM FOR THE VEHICLE ROUTING PROBLEM

ABSTRACT The vehicle routing problem (VRP), a well-known combinatorial optimization problem, holds a central place in logistics management. Many meta-heuristic approaches like Simulated Annealing (SA), Genetic Algorithms (GA), Tabu Search (TS), and Ant Colony Optimization (ACO) have been proposed to solve VRP. Ant Algorithm is a distributed meta-heuristic approach that has been applied to various combinatorial optimization problems, including traveling salesman problem, quadratic assignment problem. In this research, we proposed an improved ant colony system (IACS) algorithm that possesses a new state transition rule, a new pheromone updating rule and diverse local search approaches. The computational results on 14 VRP benchmark problems show that our IACS yields better solutions than those of other ant algorithms in the literature and is competitive with other meta-heuristic approaches in terms of solution quality.

[1]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  M. Garey.  Johnson: computers and intractability: a guide to the theory of np- completeness (freeman , 1979 .

[4]  Reginald R. Souleyrette,et al.  Implementing Vehicle Routing Models , 1990 .

[5]  Attahiru Sule Alfa,et al.  A 3-OPT based simulated annealing algorithm for vehicle routing problems , 1991 .

[6]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[7]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[8]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

[9]  Éric D. Taillard,et al.  Parallel iterative search methods for vehicle routing problems , 1993, Networks.

[10]  Marco Dorigo,et al.  Ant system for Job-shop Scheduling , 1994 .

[11]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[12]  Nicos Christofides,et al.  A new exact algorithm for the vehicle routing problem based onq-paths andk-shortest paths relaxations , 1995, Ann. Oper. Res..

[13]  Alex Van Breedam,et al.  Improvement heuristics for the Vehicle Routing Problem based on simulated annealing , 1995 .

[14]  Giovanni Righini,et al.  Heuristics from Nature for Hard Combinatorial Optimization Problems , 1996 .

[15]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[16]  Hassan Ghaziri,et al.  Supervision in the Self-Organizing Feature Map: Application to the Vehicle Routing Problem , 1996 .

[17]  James P. Kelly,et al.  A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem , 1996, Transp. Sci..

[18]  Luca Maria Gambardella,et al.  HAS-SOP: Hybrid Ant System for the Sequential Ordering Problem , 1997 .

[19]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

[20]  B. Bullnheimer,et al.  A NEW RANK BASED VERSION OF THE ANT SYSTEM: A COMPUTATIONAL STUDY , 1997 .

[21]  Alain Hertz,et al.  Ants can colour graphs , 1997 .

[22]  Corso Elvezia,et al.  Ant colonies for the traveling salesman problem , 1997 .

[23]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[24]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[25]  James P. Kelly,et al.  The Impact of Metaheuristics on Solving the Vehicle Routing Problem: Algorithms, Problem Sets, and Computational Results , 1998 .

[26]  É. Taillard,et al.  MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows , 1999 .

[27]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[28]  Thomas Stützle,et al.  ACO algorithms for the quadratic assignment problem , 1999 .

[29]  Richard F. Hartl,et al.  Applying the ANT System to the Vehicle Routing Problem , 1999 .

[30]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[31]  Luca Maria Gambardella,et al.  A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows , 1999 .

[32]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..

[33]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[34]  M Dorigo,et al.  Ant colonies for the quadratic assignment problem , 1999, J. Oper. Res. Soc..

[35]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[36]  Cyril Fonlupt,et al.  Parallel Ant Colonies for the quadratic assignment problem , 2001, Future Gener. Comput. Syst..

[37]  Barrie M. Baker,et al.  A genetic algorithm for the vehicle routing problem , 2003, Comput. Oper. Res..

[38]  Andrzej Jaszkiewicz,et al.  Genetic local search with distance preserving recombination operator for a vehicle routing problem , 2003, Eur. J. Oper. Res..