An approximate dynamic programming approach to discrete optimization
Massachusetts Institute of Technology. Operations Research Center.
Dimitris J. Bertsimas.
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We develop Approximate Dynamic Programming (ADP) methods to integer programming problems. We describe and investigate parametric, nonparametric and base-heuristic learning approaches to approximate the value function in order to break the curse of dimensionality. Through an extensive computational study we illustrate that our ADP approach to integer programming competes successfully with existing methodologies including state of art commercial packages like CPLEX. Our benchmarks for comparison are solution quality, running time and robustness (i.e., small deviations in the computational resources such as running time for varying instances of same size). In this thesis, we particularly focus on knapsack problems and the binary integer programming problem. We explore an integrated approach to solve discrete optimization problems by unifying optimization techniques with statistical learning. Overall, this research illustrates that the ADP is a promising technique by providing near-optimal solutions within reasonable amount of computation time especially for large scale problems with thousands of variables and constraints. Thus, Approximate Dynamic Programming can be considered as a new alternative to existing approximate methods for discrete optimization problems.
Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2000.Includes bibliographical references (leaves 181-189).
DepartmentMassachusetts Institute of Technology. Operations Research Center.
Massachusetts Institute of Technology
Operations Research Center.