CLOSE: a heuristic to solve a precedence-constrained travelling salesman problem with delivery and pickup

Logistics Management sometimes involves pickup as well as delivery along the route. Courier service is a typical example. The imposition of precedence constraints among the places to be visited constitutes a variant of the classical Travelling Salesman Problem (TSP). This well-known np-hard problem is often solved by heuristics. The Precedence-Constrained TSP that incorporates Delivery and Pickup (PCTDP) is a much harder problem to solve. This paper addresses the PCTDP and presents a three-stage heuristic using clustering and shrink-wrap algorithms for finding an initial path as well as genetic algorithms for the final search to obtain the best solution. The proposed heuristic is tested over a range of trial datasets and is found to give encouraging results. With its ability to provide solutions of good quality at low computing times, the proposed heuristic has ample scope for application as an automated scheduler when implemented at the site of a logistics-planning cell.

[1]  Michael Jünger,et al.  A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints , 2000, Comput. Optim. Appl..

[2]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[3]  Pierre Hansen,et al.  Variable Neighbourhood Search , 2003 .

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  Shokri Z. Selim,et al.  Soft clustering of multidimensional data: a semi-fuzzy approach , 1984, Pattern Recognit..

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

[7]  K. Fagerholt,et al.  A travelling salesman problem with allocation, time window and precedence constraints — an application to ship scheduling , 2000 .

[8]  Francesca Guerriero,et al.  A cooperative parallel rollout algorithm for the sequential ordering problem , 2003, Parallel Comput..

[9]  Gilbert Laporte,et al.  Perturbation heuristics for the pickup and delivery traveling salesman problem , 2002, Comput. Oper. Res..

[10]  Juan José Salazar González,et al.  The One-Commodity Pickup-and-Delivery Travelling Salesman Problem , 2001, Combinatorial Optimization.

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

[12]  Gur Mosheiov,et al.  The Travelling Salesman Problem with pick-up and delivery , 1994 .

[13]  Arthur V. Hill,et al.  An algorithm for the traveling salesman problem with pickup and delivery customers , 1985 .

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

[15]  Jacques Desrosiers,et al.  A Dynamic Programming Solution of the Large-Scale Single-Vehicle Dial-A-Ride Problem with Time Windows , 1984 .

[16]  Francisco Herrera,et al.  Fuzzy connectives based crossover operators to model genetic algorithms population diversity , 1997, Fuzzy Sets Syst..

[17]  Michel Gendreau,et al.  The Traveling Salesman Problem with Backhauls , 1996, Comput. Oper. Res..

[18]  P. Healy,et al.  A new extension of local search applied to the Dial-A-Ride Problem , 1995 .

[19]  Hanif D. Sherali,et al.  New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints , 2005, Oper. Res. Lett..

[20]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[21]  Gilbert Laporte,et al.  Parallel Tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem , 2004, Parallel Comput..

[22]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[23]  Yoonho Seo,et al.  Discrete Optimization An efficient genetic algorithm for the traveling salesman problem with precedence constraints , 2002 .

[24]  Dusan Teodorovic,et al.  A fuzzy logic approach to dynamic Dial-A-Ride problem , 2000, Fuzzy Sets Syst..

[25]  Jacques Renaud,et al.  A heuristic for the pickup and delivery traveling salesman problem , 2000, Comput. Oper. Res..

[26]  Günther R. Raidl,et al.  Evolutionary local search for the edge-biconnectivity augmentation problem , 2002, Inf. Process. Lett..

[27]  Harilaos N. Psaraftis,et al.  A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem , 1980 .

[28]  Maged Dessouky,et al.  A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows , 2004 .

[29]  Haldun Süral,et al.  The single‐vehicle routing problem with unrestricted backhauls , 2003, Networks.

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

[31]  Ujjwal Maulik,et al.  Genetic algorithm-based clustering technique , 2000, Pattern Recognit..

[32]  K. Katayama,et al.  The efficiency of hybrid mutation genetic algorithm for the travelling salesman problem , 2000 .

[33]  Gur Mosheiov,et al.  The traveling salesman problem with delivery and backhauls , 1994, Oper. Res. Lett..

[34]  Sigrid Knust,et al.  A tabu search algorithm for scheduling a single robot in a job-shop environment , 2002, Discret. Appl. Math..

[35]  Lucio Bianco,et al.  Dynamic Programming Strategies for the Traveling Salesman Problem with Time Window and Precedence Constraints , 1997, Oper. Res..

[36]  I. Osman,et al.  A neural network algorithm for the traveling salesman problem with backhauls , 2003 .

[37]  David Alcaide,et al.  An approach to solve a hierarchical stochastic sequential ordering problem , 2003 .

[38]  Martin W. P. Savelsbergh,et al.  The General Pickup and Delivery Problem , 1995, Transp. Sci..

[39]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[40]  Harilaos N. Psaraftis.  Analysis of an O(N2) heuristic for the single vehicle many-to-many Euclidean dial-a-ride problem , 1983 .

[41]  Kenneth DeJong,et al.  Evolutionary Computational Approaches to Solving the Multiple Traveling Salesman Problem Using a Neighborhood Attractor Schema , 2002, EvoWorkshops.

[42]  Daniele Vigo,et al.  Heuristics for the traveling salesman problem with pickup and delivery , 1999, Comput. Oper. Res..

[43]  Lawrence Bodin,et al.  Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: I. Scheduling , 1985, Transp. Sci..

[44]  Francisco Herrera,et al.  Hybrid crossover operators for real-coded genetic algorithms: an experimental study , 2005, Soft Comput..

[45]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[46]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Static Multi-Vehicle Dial-a-Ride Problem , 2002 .

[47]  Roberto Baldacci,et al.  An exact algorithm for the Traveling Salesman Problem with Deliveries and Collections , 2003, Networks.