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Over the past decade, decision diagrams (DDs) have been used to model andsolve integer programming and combinatorial optimization problems. Despitesuccessful performance of DDs in solving various discrete optimizationproblems, their extension to model mixed integer programs (MIPs) such as thoseappearing in energy applications has been lacking. More broadly, the questionwhich problem structures admit a DD representation is still open in the DDscommunity. In this paper, we address this question by introducing a geometricdecomposition framework based on rectangular formations that provides bothnecessary and sufficient conditions for a general MIP to be representable byDDs. As a special case, we show that any bounded mixed integer linear programadmits a DD representation through a specialized Benders decompositiontechnique. The resulting DD encodes both integer and continuous variables, andtherefore is amenable to the addition of feasibility and optimality cutsthrough refinement procedures. As an application for this framework, we developa novel solution methodology for the unit commitment problem (UCP) in thewholesale electricity market. Computational experiments conducted on astochastic variant of the UCP show a significant improvement of the solutiontime for the proposed method when compared to the outcome of modern solvers.

On the Structure of Decision Diagram-Representable Mixed Integer Programs with Application to Unit Commitment