Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand

We examine neighborhood structures for heuristic search applicable to a general class of vehicle routing problems (VRPs). Our methodology utilizes a cyclic-order solution encoding, which maps a permutation of the customer set to a collection of many possible VRP solutions. We identify the best VRP solution in this collection via a polynomial-time algorithm from the literature. We design neighborhoods to search the space of cyclic orders. Utilizing a simulated annealing framework, we demonstrate the potential of cyclic-order neighborhoods to facilitate the discovery of high quality a priori solutions for the vehicle routing problem with stochastic demand (VRPSD). Without tailoring our solution procedure to this specific routing problem, we are able to match 16 of 19 known optimal VRPSD solutions. We also propose an updating procedure to evaluate the neighbors of a current solution and demonstrate its ability to reduce the computational expense of our approach.

[1]  Barrett W. Thomas,et al.  Challenges and Advances in A Priori Routing , 2008 .

[2]  Vinícius Amaral Armentano,et al.  Minimizing total tardiness in parallel machine scheduling with setup times: An adaptive memory-based GRASP approach , 2007, Eur. J. Oper. Res..

[3]  Nicola Secomandi,et al.  A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands , 2001, Oper. Res..

[4]  Alan L. Erera,et al.  A Paired-Vehicle Recourse Strategy for the Vehicle-Routing Problem with Stochastic Demands , 2007, Transp. Sci..

[5]  Billy E. Gillett,et al.  A Heuristic Algorithm for the Vehicle-Dispatch Problem , 1974, Oper. Res..

[6]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..

[7]  C. Novoa,et al.  A Set-Partitioning-Based Model for the Stochastic Vehicle Routing Problem , 2006 .

[8]  Nicola Secomandi,et al.  Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands , 2009, Oper. Res..

[9]  F. Tillman.  The Multiple Terminal Delivery Problem with Probabilistic Demands , 1969 .

[10]  Graham Kendall,et al.  A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem , 2009, INFORMS J. Comput..

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

[12]  Gilbert Laporte,et al.  An Integer L-Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands , 2002, Oper. Res..

[13]  Michel Gendreau,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem with Stochastic Demands and Customers , 1996, Oper. Res..

[14]  John Holt,et al.  New optimality cuts for a single‐vehicle stochastic routing problem , 1999, Ann. Oper. Res..

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

[16]  Gilbert Laporte,et al.  An Improved Petal Heuristic for the Vehicle Routeing Problem , 1996 .

[17]  Dimitris Bertsimas,et al.  A Vehicle Routing Problem with Stochastic Demand , 1992, Oper. Res..

[18]  Jens Lysgaard,et al.  A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands , 2007, Oper. Res. Lett..

[19]  Fred Glover,et al.  Extensions of the Petal Method for Vehicle Routeing , 1993 .

[20]  Dušan Teodorović,et al.  A simulated annealing technique approach to the vehicle routing problem in the case of stochastic demand , 1992 .

[21]  Moshe Dror,et al.  Vehicle Routing with Stochastic Demands: Properties and Solution Frameworks , 1989, Transp. Sci..

[22]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning , 1991, Oper. Res..

[23]  Bruce L. Golden,et al.  The vehicle routing problem : latest advances and new challenges , 2008 .

[24]  Daniele Vigo,et al.  Recent advances on two-dimensional bin packing problems , 2002, Discret. Appl. Math..

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

[26]  Dimitris Bertsimas,et al.  Computational Approaches to Stochastic Vehicle Routing Problems , 1995, Transp. Sci..

[27]  Jacques Renaud,et al.  The column-circular, subsets-selection problem: complexity and solutions , 2000, Comput. Oper. Res..

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

[29]  Tito Homem-de-Mello,et al.  Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method , 2005, Ann. Oper. Res..

[30]  Nicola Secomandi,et al.  Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands , 2000, Comput. Oper. Res..

[31]  Jacques Renaud,et al.  A sweep-based algorithm for the fleet size and mix vehicle routing problem , 2002, Eur. J. Oper. Res..

[32]  Michel Gendreau,et al.  A Hybrid Monte Carlo Local Branching Algorithm for the Single Vehicle Routing Problem with Stochastic Demands , 2010, Transp. Sci..

[33]  Gilbert Laporte,et al.  An Exact Algorithm for the Vehicle Routing Problem with Stochastic Demands and Customers , 1995, Transp. Sci..

[34]  Kamlesh Mathur,et al.  Stochastic Vehicle Routing Problem with Restocking , 2000, Transp. Sci..

[35]  Russell Bent,et al.  A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows , 2004, Transp. Sci..

[36]  Michael J. Brusco,et al.  A morphing procedure to supplement a simulated annealing heuristic for cost‐ andcoverage‐correlated set‐covering problems , 1999, Ann. Oper. Res..

[37]  Nicola Secomandi,et al.  Analysis of a Rollout Approach to Sequencing Problems with Stochastic Routing Applications , 2003, J. Heuristics.