A Generalized ‘surrogate Problem’ Methodology for On-line Stochastic Discrete Optimization¤

We consider stochastic discrete optimization problems where the decision variables are non-negative integers and propose a generalized “surrogate problem” methodology that modi...es and extends previous work in [1]. Our approach is based on an on-line control scheme which transforms the problem into a “surrogate” continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both actual and surrogate system states. In contrast to [1], the proposed methodology applies to arbitrary constraint sets. It is shown that, under certain conditions, the solution of the original problem is recovered from the optimal surrogate state. Applications of this approach include solutions to multicommodity resource allocation problems, where, exploiting the convergence speed of the method, one can overcome the obstacle posed by the presence of local optima. ¤This work was supported in part by the National Science Foundation under Grants EEC-95-27422 and ACI98-73339, by AFOSR under contract F49620-98-1-0387, by the Air Force Research Laboratory under contract F30602-99-C-0057 and by EPRI/ARO under contract WO8333-03.