Model enhancement: Improving theoretical optimization with simulation

Many optimization techniques are based on mathematical representations. In this case, important modeling simplifications need to be made. The solution thus provided, even if proven to be theoretically one of the best, might not be so good in practice. Simulation can be used to evaluate the actual performance of the solution. We propose here a coupling between optimization and simulation that tries to improve the solution provided by a mathematical model. This approach, named “model enhancement” here, still focuses on optimizing the theoretical objective function, contrary to the common optimization–simulation coupling that focuses on improving the objective function evaluated from simulation. We propose to illustrate this approach on a routing problem, and present numerical results on the quality of the solution and the efficiency of both coupling approaches.