Related papers: Combinatorial n-fold Integer Programming and Appli…
Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can…
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…
Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control…
In this work, an integer linear programming (ILP) based model is proposed for the computation of a minimal cost addition sequence for a given set of integers. Since exponents are additive under multiplication, the minimal length addition…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…
Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We consider the 0-1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…