Comparing a Weiszfeld's-Based Procedure and (1+1)-es for Solving the Planar Single-Facility Location-Routing Problem

We compare two iterative methods for solving the Planar Single-Facility Location-Routing Problem (PSFLRP), involving optimizing the continuous-valued location of a single depot by iteratively solving instances of the Vehicle Routing Problem (VRP). An Ant Colony Optimization (ACO) algorithm is used for solving the routing problem, a procedure using Weiszfeld's algorithm and a simple Evolution Strategy (ES) are applied to the overlying locational problem. Weiszfeld's algorithm is used to iteratively find the geometric median of the end-points, i.e., Each subtour's first and last stop from the depot. This approach is compared to a classical (1+1)-ES employing the 1/5-th success rule. The two methods are evaluated on common instances of the PSFLRP, showing that for obtaining comparable total lengths, the Weiszfeld's-based procedure requires less VRP evaluations (by the ACO algorithm) than the ES.

[1]  Kathrin Fischer,et al.  Combined location-routing problems—a neural network approach , 2009, Ann. Oper. Res..

[2]  Jan Dethloff,et al.  Solving a continuous location‐routing problem by use of a self‐organizing map , 2005 .

[3]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2006, Math. Program..

[4]  Dipl. Ing. Karl Heinz Kellermayer.  NUMERISCHE OPTIMIERUNG VON COMPUTER-MODELLEN MITTELS DER EVOLUTIONSSTRATEGIE Hans-Paul Schwefel Birkhäuser, Basel and Stuttgart, 1977 370 pages Hardback SF/48 ISBN 3-7643-0876-1 , 1977 .

[5]  T. Stützle,et al.  MAX-MIN Ant System and local search for the traveling salesman problem , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[6]  Dirk V. Arnold,et al.  Active covariance matrix adaptation for the (1+1)-CMA-ES , 2010, GECCO.

[7]  Saïd Salhi,et al.  A hierarchical algorithm for the planar single-facility location routing problem , 2012, Comput. Oper. Res..

[8]  Michel Gendreau,et al.  New Heuristics for the Vehicle Routing Problem , 2005 .

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

[10]  Richard F. Hartl,et al.  SavingsAnts for the Vehicle Routing Problem , 2002, EvoWorkshops.

[11]  G. Croes.  A Method for Solving Traveling-Salesman Problems , 1958 .

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

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

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

[15]  Christian Prins,et al.  A survey of recent research on location-routing problems , 2014, Eur. J. Oper. Res..

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

[17]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

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

[19]  Mark S. Daskin,et al.  What you should know about location modeling , 2008 .

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

[21]  Saïd Salhi,et al.  Local improvement in planar facility location using vehicle routing , 2009, Ann. Oper. Res..