Creating very large scale neighborhoods out of smaller ones by compounding moves

This paper discusses neighborhood search algorithms where the size of the neighborhood is “very large” with respect to the size of the input data. We concentrate on such a very large scale neighborhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts, swaps, and insertions. We present a systematic way of creating and searching CIM neighborhoods for routing problems with side constraints. For such problems, the exact search of the CIM neighborhood becomes NP-hard. We introduce a multi-label shortest path algorithm for searching these neighborhoods heuristically. Results of a computational study on the vehicle routing problem with capacity and distance restrictions shows that CIM algorithms are very competitive approaches for solving vehicle routing problems. Overall, the solutions generated by the CIM algorithm have the best performance among the current solution methodologies in terms of percentage deviation from the best-known solutions for large-scale capacitated VRP instances.

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

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

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

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

[5]  Richard K. Congram.  Polynomially searchable exponential neighbourhoods for sequencing problems in combinatorial optimisation , 2000 .

[6]  M. R. Rao,et al.  Combinatorial Optimization , 1992, NATO ASI Series.

[7]  M. Desrochers,et al.  A Generalized Permanent Labelling Algorithm For The Shortest Path Problem With Time Windows , 1988 .

[8]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[9]  James B. Orlin,et al.  Theory of cyclic transfers , 1989 .

[10]  Paolo Toth,et al.  The Granular Tabu Search and Its Application to the Vehicle-Routing Problem , 2003, INFORMS J. Comput..

[11]  Chris N. Potts,et al.  Dynasearch - interative local improvement by dynamic programming: Part I, The traveling salesman problem , 1995 .

[12]  Gilbert Laporte,et al.  Routing problems: A bibliography , 1995, Ann. Oper. Res..

[13]  Christian Prins,et al.  A simple and effective evolutionary algorithm for the vehicle routing problem , 2004, Comput. Oper. Res..

[14]  Fred W. Glover,et al.  Ejection Chains, Reference Structures and Alternating Path Methods for Traveling Salesman Problems , 1996, Discret. Appl. Math..

[15]  C. L. Liu.  Elements of Discrete Mathematics , 1985 .

[16]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..

[17]  James B. Orlin,et al.  New neighborhood search algorithms based on exponentially large neighborhoods , 2001 .

[18]  Leslie E. Trotter,et al.  On the capacitated vehicle routing problem , 2003, Math. Program..

[19]  Dushyant Sharma,et al.  Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem , 2001, Math. Program..

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

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

[22]  Catherine Roucairol,et al.  A Parallel Tabu Search Algorithm Using Ejection Chains for the Vehicle Routing Problem , 1996 .

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

[25]  Nicos Christofides,et al.  The vehicle routing problem , 1976, Revue française d'automatique, informatique, recherche opérationnelle. Recherche opérationnelle.

[26]  Paolo Toth,et al.  Models, relaxations and exact approaches for the capacitated vehicle routing problem , 2002, Discret. Appl. Math..

[27]  Ronald F. Kirby,et al.  The minimum route problem for networks with turn penalties and prohibitions , 1969 .

[28]  C. L Liu,et al.  Elements of discrete mathematics (McGraw-Hill computer science series) , 1977 .

[29]  Gilbert Laporte,et al.  9. Vehicle routing: modern heuristics , 2003 .

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

[31]  Teodor Gabriel Crainic,et al.  Fleet management and logistics , 1998 .

[32]  Paul M. Thompson,et al.  Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems , 1993, Oper. Res..

[33]  Jeffrey L. Rummel,et al.  A Subpath Ejection Method for the Vehicle Routing Problem , 1998 .

[34]  Chris N. Potts,et al.  An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem , 2002, INFORMS J. Comput..

[35]  Gerhard J. Woeginger,et al.  A study of exponential neighborhoods for the Travelling Salesman Problem and for the Quadratic Assignment Problem , 2000, Math. Program..

[36]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[37]  Jack J. Dongarra,et al.  Performance of various computers using standard linear equations software in a FORTRAN environment , 1988, CARN.