A hybrid scatter search for the probabilistic traveling salesman problem

The probabilistic traveling salesman problem (PTSP) is an important theoretical and practical topic in the study of stochastic network problems. It provides researchers with a modeling framework for exploring the stochastic effects in routing problems. This paper focuses on developing the hybrid scatter search (HSS) by incorporating the nearest neighbor rule (NNR), threshold accepting (TA) and edge recombination (ER) crossover into a scatter search conceptual framework to solve the PTSP. A set of numerical experiments were conducted to test the validity of the HSS based on the test problems from Tang and Miller-Hooks' study. The numerical results showed that the HSS can effectively solve the PTSP in most of the tested cases in terms of objective function value. Moreover, the results also indicated that incorporating threshold accepting into the scatter search framework can further increase the computation efficiency while maintaining solution quality. These findings show the potential of the proposed HSS in solving the large-scale PTSP.

[1]  Scaling features in complex optimization problems , 1995 .

[2]  Patrick Jaillet,et al.  Probabilistic Traveling Salesman Problems , 1985 .

[3]  D. Bertsimas.  Probabilistic combinatorial optimization problems , 1988 .

[4]  Xiaoyu Song,et al.  BDD minimization by scatter search , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  L. Darrell Whitley,et al.  Scheduling Problems and Traveling Salesmen: The Genetic Edge Recombination Operator , 1989, International Conference on Genetic Algorithms.

[6]  Jean-Yves Potvin,et al.  Genetic Algorithms for the Traveling Salesman Problem , 2005 .

[7]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[8]  Rafael Martí,et al.  Scatter Search: Diseño Básico y Estrategias avanzadas , 2002, Inteligencia Artif..

[9]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[10]  Luca Maria Gambardella,et al.  An Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem , 2002, PPSN.

[11]  F. Glover.  Scatter search and path relinking , 1999 .

[12]  J. M. Singer,et al.  Searching for backbones — an efficient parallel algorithm for the traveling salesman problem , 1996 .

[13]  R. L. Collins,et al.  A Minimal Technology Routing System for Meals on Wheels , 1983 .

[14]  Joshua D. Knowles,et al.  Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms , 2005, Eur. J. Oper. Res..

[15]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[16]  Patrick Jaillet,et al.  A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers Are Visited , 1988, Oper. Res..

[17]  D. Bertsimas,et al.  Further results on the probabilistic traveling salesman problem , 1993 .

[18]  Gerhard J. Woeginger,et al.  On the nearest neighbor rule for the traveling salesman problem , 2004, Oper. Res. Lett..

[19]  Elise Miller-Hooks,et al.  Approximate Procedures for Probabilistic Traveling Salesperson Problem , 2004 .

[20]  Peter Greistorfer,et al.  A Tabu Scatter Search Metaheuristic for the Arc Routing Problem , 2002 .

[21]  G. Dueck,et al.  Record Breaking Optimization Results Using the Ruin and Recreate Principle , 2000 .

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

[23]  Fred Glover,et al.  Scatter Search and Path Relinking: Advances and Applications , 2003, Handbook of Metaheuristics.

[24]  Jürgen Branke,et al.  Solving the Probabilistic TSP with Ant Colony Optimization , 2004 .

[25]  Christos D. Tarantilis,et al.  A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem , 2004, Eur. J. Oper. Res..

[26]  Belén Melián-Batista,et al.  Parallelization of the scatter search for the p-median problem , 2003, Parallel Comput..

[27]  T. Fink,et al.  Characterization of the probabilistic traveling salesman problem. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Gilbert Laporte,et al.  A Priori Optimization of the Probabilistic Traveling Salesman Problem , 1994, Oper. Res..

[29]  Luca Maria Gambardella,et al.  Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic , 2002, Ant Algorithms.

[30]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

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

[32]  Wout Dullaert,et al.  A multi-start local search algorithm for the vehicle routing problem with time windows , 2004, Eur. J. Oper. Res..

[33]  Patrick Jaillet,et al.  A Priori Optimization , 1990, Oper. Res..

[34]  Dimitris Bertsimas,et al.  The probabilistic vehicle routing problem , 1988 .

[35]  L. Platzman,et al.  Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space , 1988 .