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Multi objective profitable tour problem

The multi objective formulation of the profitable tour problem uses two objective functions from Gurobi set up as setObjectiveN instead of the usual setObjective function. However the formulation treats the objectives as a single objective function. In terms of multi-objective optimization (MOO) problems, they use the "Weighted Sum" method for multiple objectives. For each objective you have to put in a priority and a weight. By default the priority for each objective function is 1.

Gurobi does not allow you to use ModelSense to determine if the objective is a maximization problem or minimization problem. Instead, Gurobi considers the default of minimization. To consider a maximization objective, please consider a weight of -1 for that objective function.