Distributionally Robust Fractional 0-1 Programming

Abstract

This work concerns a stochastic fractional 0-1 program whose coefficients are assumed to be random and follow a given distribution. To solve such a problem, one would need to sample over the randomness of the coefficients. However, in many situations, the sample size would be limited, which makes it difficult for existing approaches (e.g, the sample average approximation approach) to give good solutions. To deal with this issue, we explore a distributionally robust optimization version (DRO) of the fractional problem. We show that the DRO can be reformulated as an equivalent variance regularization version and can be further transformed into a mixed-integer second order cone program (MISOCP), for which an off-the-shelf solver (i.e., CPLEX) can handle. We, then, perform computational results comparing our robust method against the conventional sample average approximation (SAA), using synthetic instances. Our results show that our approach is more effective than the SAA approach in protecting the decision-maker against bad scenarios.