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

Scalable Finite Adaptability via Polyhedral Partition and Learning

Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more

Finite-Sample Optimality and Constraint Satisfaction: Learning-Based Optimal Control in Dynamic Dispatch Networks

Categories Data Science Theory, Production and Logistics, Transportation Tags , ,

Dynamic dispatch networks in logistics and transportation require real-time, constraint-aware decision-making under stochastic demand. This paper bridges mathematical optimization, optimal control theory, and reinforcement learning by establishing non-asymptotic theoretical guarantees for learning-based optimal control in constrained stochastic dispatch systems. We formulate the problem as a constrained Markov decision process, enforce feasibility via a projection-based policy … Read more

Pseudo-Compact Formulations and Branch-and-Cut Approaches for the Capacitated Vehicle Routing Problem with Stochastic Demands

Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Stochastic Programming Tags , , ,

In this paper, we address the Capacitated Vehicle Routing Problem with Stochastic Demands (CVRPSD), in which routes are planned a priori and recourse actions are performed to ensure demand fulfillment. These recourse actions are defined through policies and may include replenishment trips or demand backlogging subject to penalties. We develop the first family of pseudo-compact … Read more

On vehicle routing problems with stochastic demands — Scenario-optimal recourse policies

Categories Branch and Cut Algorithms, Stochastic Programming, Transportation Tags , ,

Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing … Read more

Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks

Categories Network Optimization, Robust Optimization, Transportation Tags , , , , ,

Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic … Read more

Normalization of ReLU Dual for Cut Generation in Stochastic Mixed-Integer Programs

Categories Stochastic Programming Tags , ,

We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we … Read more

Primal-dual resampling for solution validation in convex stochastic programming

Categories Convex Optimization, Optimization in Data Science, Stochastic Programming Tags , ,

Suppose we wish to determine the quality of a candidate solution to a convex stochastic program in which the objective function is a statistical functional parameterized by the decision variable and known deterministic constraints may be present. Inspired by stopping criteria in primal-dual and interior-point methods, we develop cancellation theorems that characterize the convergence of … Read more

Stochastic Mixed-Integer Programming: A Survey

Categories Stochastic Programming Tags ,

The goal of this survey is to provide a road-map for exploring the growing area of stochastic mixed-integer programming (SMIP) models and algorithms. We provide a comprehensive overview of existing decomposition algorithms for two-stage SMIPs, including Dantzig-Wolfe decomposition, dual decomposition, Lagrangian cuts, and decomposition approaches using parametric cutting planes and scaled cuts. Moreover, we explicitly … Read more