Related papers: Benders Adaptive-Cuts Method for Two-Stage Stochas…
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer…
The k-defensive domination problem is a powerful modeling tool for strategic decision-making in network security and disaster/emergency management, where multiple nodes may be simultaneously under attack. Despite its practical relevance,…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
In this paper, we investigate the probabilistic set covering problem (PSCP) in which the right-hand side is a binary random vector and the covering constraint is required to be satisfied with a prespecified probability. We consider the case…
This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage…
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
Two-stage Stochastic Programming (2SP) is a standard framework for modeling decision-making problems under uncertainty. While numerous methods exist, solving such problems with many scenarios remains challenging. Selecting representative…
The p-median problem is a classic discrete location problem with several applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most…
We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…
Intermodal logistics typically include the successive stages of intermodal shipment and last-mile delivery. We investigate this problem under a novel Logic-Based Benders Decomposition, which exploits the staged nature of the problem to…
In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP) called ISDDP was introduced which uses approximate (instead of exact with SDDP) primal dual solutions of the problems solved in the forward and backward passes of the…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…