Robust Discrete Optimization
Name
HPCES021.pdf
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451.59 KB
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Adobe PDF
Checksum (MD5)
fa01a0c76dab239049fcc4c2a581a29d
Author(s)
Bertsimas, Dimitris J.
Sim, Melvyn
Date Issued
January 2003
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
Abstract
We propose an approach to address data uncertainty for discrete optimization problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. When both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows to control the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 - 1 discrete optimization problem on n variables, then we solve the robust counterpart by solving n + 1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0 -1 discrete optimization problem remains polynomially solvable. Moreover, we show that the robust counterpart of an NP-hard α-approximable 0 - 1 discrete optimization problem remains α-approximal.
Subjects
data uncertainty
discrete optimization problems
degree of conservatism
robust integer programming problem
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