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 mixed-integer 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.
Highlights
C HALLENGES, restrictions, and affects such as uncertainty [1]–[3], integrality [4]–[7], and conicity [8]–[11] arise naturally in real-world applications
We refer the reader to two papers that deal with important special cases of or related to the stochastic mixedinteger second-order cone programming (SMISOCP) problem (3, 4): The first paper is by Luo and Mehrotra [54] which extends the work of Sen and Sherali [51] for stochastic mixed-integer linear programming (SMILP) and proposes a decomposition method for (3, 4) in which x ∈ {0, 1}p × Rn−p in the first-stage problem in (3, 4) and y ∈ Zq × Rm−q in the second-stage problem in (3, 4)
Stochastic mixed-integer second-order cone programming is an important class of optimization problems that includes stochastic second-order cone programming and stochastic mixed-integer linear programming as special cases
Summary
C HALLENGES, restrictions, and affects such as uncertainty [1]–[3], integrality [4]–[7], and conicity [8]–[11] arise naturally in real-world applications. The (deterministic) mixed-integer secondorder cone programming (DMISOCP) models presented in [12] (see [13]–[15]) have proved to be useful in dealing with a variety of applications that involve integrality and conicity. For another example, stochastic mixed-integer linear programming (SMILP) [16] has been demonstrated to be effective in many applications involving integrality and uncertainty (see [17]–[19] and the references contained therein).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
