Related papers: Solving Challenging Large Scale QAPs
Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Branch and bound algorithms have to cope with several additional difficulties in the multi-objective case. Not only the bounding procedure is considerably weaker, but also the handling of upper and lower bound sets requires much more…
We present a data-parallel software package for fitting Gaussian Approximation Potentials (GAPs) on multiple nodes using the ScaLAPACK library with MPI and OpenMP. Until now the maximum training set size for GAP models has been limited by…
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…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific…
Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems…
Mixed-Integer Quadratically Constrained Quadratic Programs arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions interact with nonconvex quadratic constraints. These problems are…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it…
We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…
Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware…
High dimensional unconstrained quadratic programs (UQPs) involving massive datasets are now common in application areas such as web, social networks, etc. Unless computational resources that match up to these datasets are available, solving…
We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations, which shows up in many practical applications such as the…
The intractability of deterministic solutions in solving $\mathcal{NP}$-Hard Combinatorial Optimisation Problems (COP) is well reported in the literature. One mechanism for overcoming this difficulty has been the use of efficient COP…
Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. To resolve this, we propose a learning-to-optimize approach using…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…