Using low-dimensional patterns in optimizing simulators: An illustration for the military airlift problem

Optimization models are sometimes promoted because they provide "optimal" solutions as defined by a cost model. Simulation models, by contrast, are guided by rules that are specified by experts in operations. While these may seem heuristic in nature, they often reflect issues that are difficult to capture in a cost-based objective function. "Optimizing simulators" combine the intelligence of optimization with the flexibility of simulation in the handling of system dynamics, but still suffer from the limitation that the behavior is entirely determined by a cost model. In this paper, we show how a cost-based model can be guided through a set of low-dimensional patterns which are essentially simple rules determined by a domain expert. Patterns are incorporated through a penalty term, scaled by a coefficient that controls that tradeoff between minimizing costs and minimizing the difference between model behavior and the exogenous patterns.