Related papers: Faster exact solution of sparse MaxCut and QUBO pr…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
This paper presents key enhancements to our previous work~\cite{naghmouchi2024mixed} on a hybrid Benders decomposition (HBD) framework for solving mixed integer linear programs (MILPs). In our approach, the master problem is reformulated as…
We present herein a new approach based on the simultaneous application of the deep learning and statistical physics methods to solve the combinatorial optimization problems. The recent modern advanced techniques, such as an artificial…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
Quadratic Unconstrained Binary Optimization (QUBO) provides a versatile framework for representing NP-hard combinatorial problems, yet existing solvers often face trade-offs among speed, accuracy, and scalability. In this work, we introduce…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…
Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum…
Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…
Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…