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.