Grouping memetic search for the colored traveling salesmen problem

The colored traveling salesmen problem is a node routing with multiple salesmen, where the cities are divided into m exclusive city sets and one shared set. objective to minimize total distance of Hamiltonian circuits (routes) under following constraints: each be visited by corresponding salesman, while can any salesman. In this work, we present first grouping memetic algorithm for solving challenging problem. includes three main components: (i) greedy randomized heuristic population initialization; (ii) dedicated local search procedure optima exploration; (iii) backbone-based crossover operator solution recombination. We show computational results on 65 popular benchmark instances demonstrate competitiveness our algorithm. especially report improved upper bounds 38 (for more than 58% cases). also general CPLEX solver, including 10 proven optimal solutions. Finally, shed lights impacts key components make code publicly available.