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Keywords:

  • family traveling salesperson problem;
  • distance minimization;
  • randomized heuristics;
  • biased random-key genetic algorithm;
  • GRASP

Abstract

This paper introduces the family traveling salesperson problem (FTSP), a variant of the generalized traveling salesman problem. In the FTSP, a subset of nodes must be visited for each node cluster in the graph. The objective is to minimize the distance traveled. We describe an integer programming formulation for the FTSP and show that the commercial grade integer programming solver CPLEX 11 can only solve small instances of the problem in reasonable running time. We propose two randomized heuristics for finding optimal and near-optimal solutions of this problem. These heuristics are a biased random-key genetic algorithm and a GRASP with evolutionary path-relinking. Computational results comparing both heuristics are presented in this study.