Related papers: Improving Lower Bounds for the Quadratic Assignmen…
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…
This paper discusses efficient parallel algorithms for obtaining strong lower bounds and exact solutions for large instances of the Quadratic Assignment Problem (QAP). Our parallel architecture is comprised of both multi-core processors and…
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…
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…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…
The Quadratic Assignment Problem (QAP) is an NP-hard problem which has proven particularly challenging to solve: unlike other combinatorial problems like the traveling salesman problem (TSP), which can be solved to optimality for instances…
The Quadratic Assignment Problem (QAP) is one of the models used for the multi-row layout problem with facilities of equal area. There are a set of n facilities and a set of n locations. For each pair of locations, a distance is specified…
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 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…
This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…
As a variant of the routing and wavelength assignment problem (RWAP), the RWAP with partial path protection (RWAP-PPP) designs a reliable optical-fiber network for telecommunications. It assigns paths and wavelengths to meet communication…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…
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 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…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
This paper focuses on the error bounds for several equivalent rank-one doubly nonnegative (DNN) conic reformulations of the quadratic assignment problem (QAP), a class of challenging combinatorial optimization problems. We provide three…
Optimal assignment of classes to classrooms \cite{dickey}, design of DNA microarrays \cite{carvalho}, cross species gene analysis \cite{kolar}, creation of hospital layouts cite{elshafei}, and assignment of components to locations on…
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…
Quadratic assignment problem (QAP) is a fundamental problem in combinatorial optimization and finds numerous applications in operation research, computer vision, and pattern recognition. However, it is a very well-known NP-hard problem to…
The scaling of quantum processors is currently limited by technical challenges such as decoherence and cross-talk. As the number of qubits grows, interference increases the computational noise. Distributed quantum computing addresses these…