Related papers: A generic Branch-and-Cut algorithm for bi-objectiv…
We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box…
The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on…
In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
Multi-start algorithms are a common and effective tool for metaheuristic searches. In this paper we amplify multi-start capabilities by employing the parallel processing power of the graphics processer unit (GPU) to quickly generate a…
An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
Inventory management, vehicle routing, and delivery scheduling decisions are simultaneously considered in the context of the inventory routing problem. This paper focuses on the continuous-time version of this problem where, unlike its more…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…