Distance-based path relinking for the vehicle routing problem

1 Path relinking for the vehicle routing problem Path relinking is a relatively new metaheuristic technique for combinatorial optimization, proposed by Glover (see e.g. [3]). Path relinking attempts to find new good solutions by examining the solutions that are on a path from an initial (incumbent) to a final (guiding) solution. By definition, each move on the path makes the solution more different from the initiating solution and more similar to the guiding solution. Moving on the path is done by a neighbourhood operator, just like in any local search algorithm. The technical difference with ordinary local search is that the neighbourhood search strategy that decides which move to execute is not based on the quality of the resulting solution, but on the distance in the solution space between the resulting solution and the guiding solution. A move that takes the solution closer to the guiding solution will be preferred over one that takes it further away, regardless of the quality of the resulting solution. Constructing a path relinking procedure therefore requires us to select a move operator to use and a distance measure in the solution space between two solutions. The distance measure than can be used to determine whether a move brings a solution closer to the guiding solution and whether the resulting solution can be considered to be " on a path from incumbent to guiding solution ". Usually, path relinking is not used as a standalone solution method, but combined with other metaheuristics, such as tabu search or GRASP, see e. Although the capacitated vehicle routing problem (CVRP) is one of the best-known combina-torial optimization problems, path relinking approaches for this problem are few and far between. This is partially due to the fact that a VRP solution is most naturally represented as a set of permutations of customers, each member of the set representing a tour. Contrary to problems that have a natural binary or vector representation, it is not immediately obvious what is meant by 744