AN ANT COLONY APPROACH TO THE ORIENTEERING PROBLEM

ABSTRACT This paper develops an ant colony optimization approach to the orienteering problem, a general version of the well-known traveling salesman problem with many relevant applications in industry. Based on mainstream ant colony ideas, an unusual sequenced local search and a distance based penalty function are added which result in a method that is convincingly shown to be the best heuristic published for this problem class. Results on 67 test problems show that the ant colony method performs as well or better than all other methods from the literature in all cases and does so at very modest computational cost. Furthermore, the ant colony method is insensitive to seed, problem instance, problem size and degree of constraint.

[1]  A. M. Bruckstein,et al.  Hamiltonian(t)-an ant-inspired heuristic for recognizing Hamiltonian graphs , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[2]  Gilbert Laporte,et al.  Annals of Operations Research , 1996 .

[3]  Proceedings of the 1999 Congress on Evolutionary Computation CEC99 , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[5]  T. Tsiligirides,et al.  Heuristic Methods Applied to Orienteering , 1984 .

[6]  Mark H. Karwan,et al.  An Optimal Algorithm for the Orienteering Tour Problem , 1992, INFORMS J. Comput..

[7]  Martin Middendorf,et al.  An Island Model Based Ant System with Lookahead for the Shortest Supersequence Problem , 1998, PPSN.

[8]  M. Rosenwein,et al.  Strong linear programming relaxations for the orienteering problem , 1994 .

[9]  Alice E. Smith,et al.  An ant system approach to redundancy allocation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[10]  Alice E. Smith,et al.  A genetic algorithm for the orienteering problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[11]  Matteo Fischetti,et al.  Solving the Orienteering Problem through Branch-and-Cut , 1998, INFORMS J. Comput..

[12]  Ram Ramesh,et al.  An efficient four-phase heuristic for the generalized orienteering problem , 1991, Comput. Oper. Res..

[13]  Hartmut Schmeck,et al.  Information Exchange in Multi Colony Ant Algorithms , 2000, IPDPS Workshops.

[14]  D. Snyers,et al.  New results on an ant-based heuristic for highlighting the organization of large graphs , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[15]  John M. Norman,et al.  Dynamic Programming in Orienteering: Route Choice and the Siting of Controls , 1984 .

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

[17]  Gilbert Laporte,et al.  The selective travelling salesman problem , 1990, Discret. Appl. Math..

[18]  陳香伶,et al.  An Ant Colony Approach for the Vehicle Routing Problem under Distance and Capacity Constraints , 2003 .

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

[20]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[21]  Daniel Merkle,et al.  Bi-Criterion Optimization with Multi Colony Ant Algorithms , 2001, EMO.

[22]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

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

[24]  C. Keller.  Algorithms to solve the orienteering problem: A comparison , 1989 .

[25]  Ian C. Parmee,et al.  The Ant Colony Metaphor for Searching Continuous Design Spaces , 1995, Evolutionary Computing, AISB Workshop.

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

[27]  Daniel Merkle,et al.  A New Approach to Solve Permutation Scheduling Problems with Ant Colony Optimization , 2001, EvoWorkshops.

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

[29]  Luca Maria Gambardella,et al.  MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows , 1999 .

[30]  Luca Maria Gambardella,et al.  Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem , 1995, ICML.

[31]  Marco Dorigo,et al.  An Investigation of some Properties of an "Ant Algorithm" , 1992, PPSN.

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

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

[34]  Richard F. Hartl,et al.  Ant colony optimization applied to the pickup and delivery problem , 2000 .

[35]  R. Vohra,et al.  The Orienteering Problem , 1987 .

[36]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[37]  Z. Michalewicz,et al.  A new version of ant system for subset problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[38]  B. Naudts,et al.  Ant colonies are good at solving constraint satisfaction problems , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[39]  Bruce L. Golden,et al.  A fast and effective heuristic for the orienteering problem , 1996 .

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

[41]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[42]  Matthijs den Besten,et al.  Ant Colony Optimization for the Total Weighted Tardiness Problem , 2000, PPSN.

[43]  Hartmut Schmeck,et al.  Multi Colony Ant Algorithms , 2002, J. Heuristics.

[44]  H. R. Lourenço,et al.  Adaptive Approach Heuristics for The Generalized Assignment Problem , 1998 .

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

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

[47]  Alice E. Smith,et al.  An ant colony optimization algorithm for the redundancy allocation problem (RAP) , 2004, IEEE Transactions on Reliability.

[48]  Anthony Wren,et al.  Computer Scheduling of Vehicles from One or More Depots to a Number of Delivery Points , 1972 .

[49]  B. Golden,et al.  A multifaceted heuristic for the orienteering problem , 1988 .

[50]  C. Mariano,et al.  MOAQ an Ant-Q algorithm for multiple objective optimization problems , 1999 .

[51]  Marco Dorigo,et al.  The ant colony optimization meta-heuristic , 1999 .

[52]  Marco Dorigo,et al.  Ant Colonies for Adaptive Routing in Packet-Switched Communications Networks , 1998, PPSN.

[53]  Luca Maria Gambardella,et al.  An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem , 2000, INFORMS J. Comput..

[54]  Richard F. Hartl,et al.  Cooperative Ant Colonies for Optimizing Resource Allocation in Transportation , 2001, EvoWorkshops.

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

[56]  Martin Middendorf,et al.  Pheromone Modification Strategies for Ant Algorithms Applied to Dynamic TSP , 2001, EvoWorkshops.

[57]  Hartmut Schmeck,et al.  Ant colony optimization for resource-constrained project scheduling , 2000, IEEE Trans. Evol. Comput..

[58]  Qiwen Wang,et al.  Using artificial neural networks to solve the orienteering problem , 1995, Ann. Oper. Res..

[59]  Gabriele Kotsis,et al.  Parallelization strategies for the ant system , 1998 .

[60]  Daniel Merkle,et al.  On solving permutation scheduling problems with ant colony optimization , 2005, Int. J. Syst. Sci..