Comparison of Parameter Tuning Strategies for Team Orienteering Problem (TOP) Solved with Gurobi

The team orienteering problem (TOP) describes the time-restricted optimization process where agents attempt to maximize rewards gained from visiting nodes distributed on a given map. When solving large TOP using traditional mixed-integer linear programming approaches (MILP), even with solvers such as Gurobi, finding an optimal solution can often be computationally intractable. Machine learning (ML) approaches have recently been developed to provide high-quality approximate solutions to combinatorial optimization problems quickly. ML solution quality can be compared to traditional optimization techniques such as those employed by Gurobi. Just as ML models require significant parameter tuning to maximize performance, traditional solvers can benefit from parameter tuning. To make fair comparisons between ML solutions and traditional solver solutions, both must undergo a parameter tuning process. Two parameter tuning methods are compared and explored; a designed experiment approach and the Gurobi tuning tool, with heuristics restricted, will be used to identify optimal parameters that work across a set of TOP instances. Default settings for Gurobi will be used as a baseline. Optimal parameter settings will be developed with multiple time limits and problem size combinations. The goal of this research is to identify robust Gurobi parameter settings for families of TOPs to ensure that comparisons of ML solutions with traditional MILP solution approaches are fair and that the MILP solver is not disadvantaged by poor parameter settings. Experimental results suggest a full-factorial approach to parameter tuning is effective for the TOP.