Abstract
This paper presents a novel variant of the Family Traveling Salesman Problem (FTSP), a well-known NP-hard problem introduced by Morán-Mirabal et al. (2014). In the FTSP, the set of nodes is partitioned into several subsets called families, and the aim is to determine the minimum-cost cycle that begins and ends at the depot and visits a predefined number of nodes in each family. We extend the FTSP by requiring that m tours be generated, each having a number of nodes between a minimum and a maximum quantity, thus yielding the family multiple traveling salesman problem (FmTSP). We present a two-index MIP formulation and develop an ALNS metaheuristic as a solution method for large-sized instances. Our proposed ALNS was initially employed to solve the FTSP benchmark instances and allowed us to improve some of the best-known solutions. The results for new derived instances requiring multiple tours show that our ALNS also achieves optimality for all instances with proven-optimal solutions.
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