Probabilistic Bicriteria Optimization

We consider a multiperiod system operation problem with two conflicting objectives, mini-mizing cost and risk. Risk stems from uncertain disruptions to the system during operation.While a general model would hedge against disruptions in each time period, we study spe-cial cases in which only a modest number of disruptions occur. To optimize for risk, weemploy a convex approximation based on constraint sampling. We develop a stratified sam-pling scheme based on distributional information on the time of disruption. We establishthat our scheme yields significant savings in sampling costs—up to an order of magnitudein the number of time periods—over naive sampling. Moreover, in the absence of distri-butional information, we exhibit a sampling strategy that has comparable performance tooptimal stratification. We numerically demonstrate that stratification improves cost overnaive sampling, improving the solution’s proximity to the efficient frontier of the bicriteria problem.

Papers

Tara Rengarajan, Nedialko B. Dimitrov, and David P. Morton. Convex Approximations of a Probabilistic Bicriteria Model with Disruptions. INFORMS Journal on Computing, July 2011, doi: 10.1287/ijoc.1110.0483

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