Eleventh Industrial Mathematical and Statistical Modeling Workshop for Graduate Students

Analytic and discrete optimization approaches for routing an aircraft in hostile air spaces have been developed. Using these approaches, an aircraft’s optimal risk path (where the risk is being detected by enemy radars) with constraints on aircraft speed, altitude and turn capability, mission range, mission time, fuel, etc. is computed. In the discrete optimization approach, we use different methods to find the optimal path. We reformulate the problem as a constrained shortest path problem (CSPP) on a grid graph and use linear and dynamic programming to solve the CSPP. A stochastic model uses a random walk on a similar grid to find the aircraft’s optimum path. The analytical approach based on the calculus of variations reduces the original optimization problem to a system of nonlinear differential equations.