Robust optimization: Difference between revisions

Revision as of 12:59, 2 December 2006

Revision as of 13:07, 2 December 2006

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'''Robust optimization'''. A term given to an approach to deal with uncertainty, similar to the recourse model of [[stochastic programming]], except that feasibility for all possible realizations (called scenarios) is replaced by a [[penalty function]] in the objective. As such, the approach integrates [[goal programming]] with a scenario-based description of problem data. To illustrate, consider the LP:

:Min <math>\min_{t} cx + dy: Ax=b, Bx + Cy = e, x, y \le 0,</math>

where d, B, C and e are random variables with possible realizations {(d(s), B(s), C(s), e(s): s in {1,...,N}} (N = number of scenarios). The robust optimization model for this LP is:

Min<math>\min f(x, y(1), ..., y(N)) + wP(z(1), ..., z(N)): Ax=b, x >=\le 0,</math>

B(s)x + C(s)y(s) + z(s) = e(s), and y(s) >= 0, for all s = 1,...,N,

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The above makes robust optimization similar (at least in the model) to a [[goal program]]. Recently, the robust optimization community defines it differently – it optimizes for the worst-case scenario. Let the uncertain MP be given by

<math>\min f(x; s): x in X(s),</math>

where S is some set of scenarios (like parameter values). The robust optimization model (according to this more recent definition) is: