An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem

We present a new local optimizer called SOP-3-exchange for the sequential ordering problem that extends a local search for the traveling salesman problem to handle multiple constraints directly without increasing computational complexity. An algorithm that combines the SOP-3-exchange with an Ant Colony Optimization algorithm is described, and we present experimental evidence that the resulting algorithm is more effective than existing methods for the problem. The best-known results for many of a standard test set of 22 problems are improved using the SOP-3-exchange with our Ant Colony Optimization algorithm or in combination with the MPO/AI algorithm (Chen and Smith 1996).

[1]  Egon Balas,et al.  The precedence-constrained asymmetric traveling salesman polytope , 1995, Math. Program..

[2]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[3]  M. Dorigo,et al.  Ant System: An Autocatalytic Optimizing Process , 1991 .

[4]  Charles Fleurent,et al.  Genetic Hybrids for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

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

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

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

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

[9]  Yves Crama,et al.  Local Search in Combinatorial Optimization , 2018, Artificial Neural Networks.

[10]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[11]  W. R. Pulleyblank,et al.  Precedence Constrained Routing and Helicopter Scheduling: Heuristic Design , 1992 .

[12]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

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

[14]  Harilaos N. Psaraftis,et al.  k-Interchange procedures for local search in a precedence-constrained routing problem , 1983 .

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

[16]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[17]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[18]  Stephen Chen,et al.  Commonality and Genetic Algorithms , 1996 .

[19]  Jan Karel Lenstra,et al.  Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows , 1993, Transp. Sci..

[20]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[21]  Kavindra Malik,et al.  A Lagrangian relax-and-cut approach for the sequential ordering problem with precedence relationships , 1994, Ann. Oper. Res..

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

[23]  Éric D. Taillard,et al.  Robust taboo search for the quadratic assignment problem , 1991, Parallel Comput..

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

[25]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..

[26]  G. Reinelt The traveling salesman: computational solutions for TSP applications , 1994 .

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

[28]  Luca Maria Gambardella,et al.  Solving symmetric and asymmetric TSPs by ant colonies , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[29]  Martin Grötschel,et al.  A Cutting Plane Approach to the Sequential Ordering Problem (with Applications to Job Scheduling in Manufacturing) , 1993, SIAM J. Optim..

[30]  David Connolly An improved annealing scheme for the QAP , 1990 .

[31]  M. Savelsbergh An efficient implementation of local search algorithms for constrained routing problems , 1990 .

[32]  L. Escudero An inexact algorithm for the sequential ordering problem , 1988 .

[33]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[34]  Norbert Ascheuer,et al.  Hamiltonian path problems in the on-line optimization of flexible manufacturing systems , 1996 .

[35]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

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