Related papers: A Scalable Algorithm for Two-Stage Adaptive Linear…
Electric utility companies perform numerous technical interventions every day. Since it is generally not possible to complete all planned interventions within a single day, companies face two objectives: maximizing the total duration of…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order to accelerate the convergence of the CG…
The Set Partitioning Problem is a combinatorial optimization problem with wide-ranging applicability, used to model various real-world tasks such as facility location and crew scheduling. However, real-world applications often require…
In this article we introduce Graph Generation, an enhanced Column Generation (CG) algorithm for solving expanded linear programming relaxations of mixed integer linear programs. To apply Graph Generation, we must be able to map any given…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
Column Generation (CG) is a popular method dedicated to enhancing computational efficiency in large scale Combinatorial Optimization (CO) problems. It reduces the number of decision variables in a problem by solving a pricing problem. For…
Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the…
The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant…
Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…
In the day-ahead energy market, the offering strategy of distributed energy resource (DER) aggregators must be submitted before the uncertainty realization in the form of price-quantity pairs. This work addresses the day-ahead offering…
Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of…
We introduce a simple, accurate, and extremely efficient method for numerically solving the multi-marginal optimal transport (MMOT) problems arising in density functional theory. The method relies on (i) the sparsity of optimal plans [for…
We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the…