Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Abstract

Second-order cone programming problems are a tractable subclass of convex optimization problems that can be solved using polynomial algorithms. In the last decade, stochastic second-order cone programming problems have been studied, and efficient algorithms for solving them have been developed. The mixed-integer version of these problems is a new class of interest to the optimization community and practitioners, in which certain variables are required to be integers. In this paper, we describe five applications that lead to stochastic mixedinteger second-order cone programming problems. Additionally, we present solution algorithms for solving stochastic mixed-integer second-order cone programming using cuts and relaxations by combining existing algorithms for stochastic second-order cone programming with extensions of mixed-integer second-order cone programming. The applications, which are the focus of this paper, include facility location, portfolio optimization, uncapacitated inventory, battery swapping stations, and berth allocation planning. Considering the fact that mixed-integer programs are usually known to be NP-hard, bringing applications to the surface can detect tractable special cases and inspire for further algorithmic improvements in the future. INDEX TERMSSecond-order cone programming, Mixed-integer programming, Stochastic programming, Applications, Algorithms ACRONYMS CVaR Conditional value-at-risk. DMISOCP Deterministic mixed-integer second-order cone programming. FEU 40-foot equivalent unit. FLP Facility location problem. SMBSOCP Stochastic mixed-binary second-order cone programming. SMILP Stochastic mixed-integer linear programming. SMISOCP Stochastic mixed-integer second-order cone programming. SSOCP Stochastic second-order cone programming. TEU 20-foot equivalent unit.

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