Optimal Risk Path Algorithms

  • Michael Zabarankin
  • Stanislav Uryasev
  • Panos Pardalos
Part of the Applied Optimization book series (APOP, volume 66)


Analytical and discrete optimization approaches for routing an aircraft in a threat environment have been developed. Using these approaches, an aircraft’s optimal risk trajectory with a constraint on the path length can be efficiently calculated. The analytical approach based on calculus of variations reduces the original risk optimization problem to the system of nonlinear differential equations. In the case of a single radarinstallation, the solution of such a system is expressed by the elliptic sine. The discrete optimization approach reformulates the problem as the Weight Constrained Shortest Path Problem (WCSPP) for a grid undirected graph. The WCSPP is efficiently solved by the Modified Label Setting Algorithm (MLSA). Both approaches have been tested with several numerical examples. Discrete nonsmooth solutions with high precision coincide with exact continuous solutions. For the same graph, time in which the discrete optimization algorithm computes the optimal trajectory is independent of the number of radars. The discrete approach is also efficient for solving the problem using different risk functions.


optimal risk path length constraint system of nonlinear differential equations analytical solution discrete optimization approach network flow algorithms 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Michael Zabarankin
    • 1
  • Stanislav Uryasev
    • 1
  • Panos Pardalos
    • 1
  1. 1.Center for Applied Optimization, Dept. of Industrial and Systems EngineeringUniversity of FloridaUSA

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