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The Quadratic Assignment Problem, QAP, is a classic combinatorial optimization problem, classified as NP-hard and widely studied. This problem consists in assigning N facilities to N locations obeying the relation of 1 to 1, aiming to…

The application of the Reformulation Linearization Technique (RLT) to the Quadratic Assignment Problem (QAP) leads to a tight linear relaxation with huge dimensions that is hard to solve. Previous works found in the literature show that…

The Quadratic Assignment Problem (QAP) is an important combinatorial optimization problem with applications in many areas including logistics and manufacturing. QAP is known to be NP-hard, a computationally challenging problem, which…

Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…

We report our progress on the project for solving larger scale quadratic assignment problems (QAPs). Our main approach to solve large scale NP-hard combinatorial optimization problems such as QAPs is a parallel branch-and-bound method…

We study the set of optimal solutions of the dual linear programming formulation of the linear assignment problem (LAP) to propose a method for computing a solution from the relative interior of this set. Assuming that an arbitrary…

In this paper we modify a fast heuristic solver for the Linear Sum Assignment Problem (LSAP) for use on Graphical Processing Units (GPUs). The motivating scenario is an industrial application for P2P live streaming that is moderated by a…

In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and…

The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. An effective heuristic for obtaining approximate solutions to the QAP is simulated annealing (SA). Here we describe an SA…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

Quadratic Assignment Problem (QAP) is a practical combinatorial optimization problems that has been studied for several years. Since it is NP-hard, solving large problem instances of QAP is challenging. Although heuristics can find…

The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…

We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing)…

The main goal of distribution network (DN) expansion planning is essentially to achieve minimal investment constrained with specified reliability requirements. The reliability-constrained distribution network planning (RcDNP) problem can be…

Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

The Linear Assignment Problem (LAP) is a fundamental combinatorial optimization task with applications ranging from computer vision to logistics. Classical exact solvers such as the Hungarian and Jonker-Volgenant (LAPJV) algorithms…

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…

While Graph Neural Networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve…

We present a parallel GPU-accelerated solver for branch Model Predictive Control problems. Based on iterative LQR methods, our solver exploits the tree-sparse structure and implements temporal parallelism using the parallel scan algorithm.…