The capacitated family traveling salesperson problem

Abstract

The capacitated family traveling salesperson problem (CFTSP) is about a graph in which nodes are partitioned into disjoint and differently weighted families. The objective is to find the shortest route that visits a given number of nodes in each family with a set of capacitated agents. The CFTSP is a new variant of the family traveling salesman problem (FTSP). Nevertheless, existing exact and metaheuristic methods for the FSTP cannot be straightforwardly applied due to the feasibility condition that requires agents to stay within their capacity. Thus, we propose integer linear programming formulations with five different subtour inequalities sets that are tested and compared with the classical approaches. In addition, we propose a biased random‐key genetic algorithm with four decoder algorithms that find high‐quality solutions in short computational times. Based on our experiments, we have found that our methods are effective in addressing subtour avoidance and ensuring feasible assignments.