A Cascade Approach for Staircase Linear Programs with an Application to Air Force Mobility Optimization.

Abstract

We develop a method to approximately solve a large staircase linear program that optimizes decisions over time. Also developed is a method to bound that approximation's error. A feasible solution is derived by a proximal cascade, which sequentially considers overlapping subsets of the model's time periods, or other ordinally defined set. In turn, we bound the cascade's deviation from the optimal objective value by a Lagrangian cascade which penalizes infeasibility by incorporating dual information provided by the proximal cascade solution. When tested on a large temporal LP developed for US Air Force mobility planners, we often observe gaps between the approximation and bound of less than 10 percent, and save as much as 80 percent of the time required to solve the original problem. We also address methods to reduce the gap, including constraint extension of the Lagrangian cascade, as well as exploitation of dual multipliers within the proximal cascade.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1997
Accession Number
ADA324288

Entities

People

  • Steven F. Baker

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Case Studies
  • Computations
  • Deployment
  • Linear Programming
  • Logistics
  • Mathematical Programming
  • Mathematics
  • New York
  • Operations Research
  • Optimization
  • Refueling In Flight
  • Simplex Method
  • Tanker Aircraft
  • United States

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Aerodynamics.
  • Robotics and Automation.