Stochastic Programming

SDDmiP.jl: A Software Package with a Provably Convergent Benders Algorithm for Multi-Stage Stochastic Mixed-Integer Programming

Categories Optimization Software and Modeling Systems, Stochastic Programming Tags , , , , , ,

We present an open-source software package that implements a provably convergent Benders-type decomposition algorithm for multistage stochastic integer programs. In addition to standard cut families, such as Benders, strengthened Benders, and Lagrangian cuts, the algorithm incorporates rectified linear unit (ReLU) cuts, which provide convergence guarantees for general mixed-integer state variables. However, the dual problems used … Read more

A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition

Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more

Beyond Isolated Operating Rooms: Risk-Aware Surgical Episode Scheduling in Single-Entry Networks

Categories Applications - OR and Management Sciences, Scheduling, Stochastic Programming Tags , , , ,

Long wait times for elective surgery are a persistent challenge in publicly funded health systems, where hospitals must coordinate limited capacity before, during, and after the operation under considerable uncertainty. We study how a network of collaborating hospitals, such as the University Health Network in the City of Toronto, can centralize intake and jointly schedule … Read more

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , ,

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

Model-Uncertainty-Aware Residuals-Based Sample Average Approximation

Categories Robust Optimization, Stochastic Programming Tags , , ,

We consider a contextual stochastic optimization (CSO) problem, where one has observations of the uncertain parameters together with concurrent observations of covariates, and the goal is to choose decisions that minimize expected cost conditioned on new covariate observations. The empirical residuals-based sample average approximation (ER-SAA) of the CSO problem constructs scenarios of uncertainty by combining … Read more

Route `Em and Count `Em: A Two-Stage Stochastic Programming Model for Anti-Submarine Operations

Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , ,

Tracking targets in undersea warfare requires successful detection by an active search asset. Maximizing detection likelihood requires strategic placement and routing of the search assets in the search region over the planning horizon. We develop a two-stage stochastic integer programming model that maximizes the expected total reward for target detections under uncertainty in target motion … Read more

Adaptive Scenario Partitioning for Stochastic Bilevel Linear Programs

Categories Bilevel Optimization, Constrained Nonlinear Optimization, Stochastic Programming Tags , , , ,

This paper develops an adaptive scenario partitioning approach for stochastic bilevel linear programs. The method extends the Adaptive Partitioning Method, originally designed for two-stage stochastic programs, to settings in which a leader makes a first-stage decision while anticipating scenario dependent optimal responses from a follower. The proposed approach solves a sequence of aggregated master problems … Read more

Distributionally Robust Optimization with General Uncertainty Structure

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

We develop an exact solution framework for a broad class of Distributionally Robust Optimization (DRO) problems with general uncertainty structure. Within the class of moment- and confidence-set-based ambiguity sets, existing exact methods are largely limited to max-of-affine functions under ambiguity sets with strictly nested confidence sets. To enlarge this scope while preserving tractability, we introduce … Read more

Stage-wise hybrid nested Benders’ decomposition-stochastic dual dynamic programming for virtual power plants

Categories Dynamic Programming, Energy, Stochastic Programming Tags , , ,

Participants in energy markets make sequential decisions across multiple time horizons under uncertainty, leading to large-scale multistage stochastic optimization problems. Stochastic dual dynamic programming is widely used for its tractability, but its application to modern energy markets is challenged by nested dependencies induced by participation across multiple interrelated markets under increasing uncertainty from distributed energy … Read more