Bi-objective version of team orienteering problem (BTOP)

In the Team Orienteering Problem (TOP) a set of locations is given, each with a score. The objective is to determine a fixed number of routes (teams), limited in length, that visit some locations and maximize the sum of the collected scores. For the first time we introduce bi-objective TOP which has a second objective, to balance all team's scores for the purpose of obtaining fair teams. So the second objective is minimizing the off-balance in a solution, in other words, Minimizing the difference between highest and lowest score. To solve this problem, we use NSGA-II algorithm with traditional operators and we propose new operators for NSGA-II algorithm to consider the second objective in population production. Finally, we evaluate both algorithms on standard benchmarks of TOP. Because the optimal Pareto set (PFtrue) is unknown for this problem we use two quality indicators, Spacing and Overall Nondominated Vector Generation, which do not need optimal Paerto set for evaluation.