Related papers: Scenario Reduction for the Two-Stage Stochastic Un…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
We study a class of two-stage stochastic programs, namely, those with fixed recourse matrix and fixed costs, and linear second stage. We show that, under mild assumptions, the problem can be solved with just one scenario, which we call an…
Multi-stage stochastic optimization lies at the core of decision-making under uncertainty. As the analytical solution is available only in exceptional cases, dynamic optimization aims to efficiently find approximations but often neglects…
Mobility systems featuring shared vehicles are often unable to serve all potential customers, as the distribution of demand does not coincide with the positions of vehicles at any given time. System operators often choose to reposition…
We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity…
This paper proposes a Separable Projective Approximation Routine-Optimal Power Flow (SPAR-OPF) framework for solving two-stage stochastic optimization problems in power systems. The framework utilizes a separable piecewise linear…
In two-stage robust optimization the solution to a problem is built in two stages: In the first stage a partial, not necessarily feasible, solution is exhibited. Then the adversary chooses the "worst" scenario from a predefined set of…
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based…
In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…
We study the arbitrary cost case of the unweighted Stochastic Score Classification (SSClass) problem. We show two constant approximation algorithms and both algorithms are 6-approximation non-adaptive algorithms with respect to the optimal…
Two-stage stochastic programs (2SPs) are important tools for making decisions under uncertainty. Decision-makers use contextual information to generate a set of scenarios to represent the true conditional distribution. However, the number…
Two-stage stochastic unit commitment (2S-SUC) problems have been widely adopted to manage the uncertainties introduced by high penetrations of intermittent renewable energy resources. While decomposition-based algorithms such as…
This paper addresses a central challenge of jointly considering shorter-term (e.g. hourly) and longer-term (e.g. yearly) uncertainties in power system planning with increasing penetration of renewable and storage resources. In conventional…
In this work, we study a single-machine scheduling problem that aims at minimizing the total cost of a schedule subject to start-time dependent costs. This framework naturally captures scenarios where costs fluctuate throughout the day,…
We propose a hybrid algorithmic strategy for complex stochastic optimization problems, which combines the use of scenario trees from multistage stochastic programming with machine learning techniques for learning a policy in the form of a…
The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many…
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…