Ant colony system for a VRP with multiple time windows and multiple visits

Abstract The Vehicle routing problem with time windows is frequently found in literature, while multiple time windows are not often considered. In this paper a mathematical formulation of the vehicle routing problem with multiple time windows is presented, taking into account periodic constraints. An algorithm based on Ant Colony System is proposed and implemented. Computational results related to a purpose-built benchmark are finally reported.

[1]  Martin W. P. Savelsbergh,et al.  Local search in routing problems with time windows , 1984 .

[2]  Daniela Favaretto,et al.  Ant colony system for variants of traveling salesman problem with time windows , 2004 .

[3]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

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

[5]  R. Sinnott Virtues of the Haversine , 1984 .

[6]  Richard F. Hartl,et al.  Applying the ANT System to the Vehicle Routing Problem , 1999 .

[7]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[8]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

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

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

[11]  Marco Dorigo,et al.  An Investigation of some Properties of an "Ant Algorithm" , 1992, PPSN.

[12]  Mwp Martin Savelsbergh,et al.  VEHICLE ROUTING WITH TIME WINDOWS: OPTIMIZATION AND APPROXIMATION. VEHICLE ROUTING: METHOD AND STUDIES. STUDIES IN MANAGEMENT SCIENCE AND SYSTEMS - VOLUME 16 , 1987 .

[13]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

[14]  Jean-François Cordeau,et al.  VRP with Time Windows , 1999, The Vehicle Routing Problem.

[15]  Corso Elvezia,et al.  Ant colonies for the traveling salesman problem , 1997 .