Related papers: Mapping NP-hard and NP-complete optimisation probl…
We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
With the advances in customized hardware for quantum annealing and digital/CMOS Annealing, Quadratic Unconstrained Binary Optimization (QUBO) models have received growing attention in the optimization literature. Motivated by an existing…
In this paper, we present a brief review and introduction to Quadratic Unconstrained D-ary Optimization (QUDO), Tensor Quadratic Unconstrained D-ary Optimization (T-QUDO) and Higher-Order Unconstrained Binary Optimization (HOBO)…
When solving large-scale multiobjective optimization problems, solvers can get stuck with the memory or time limit. In such cases, one is left with no information how far is the best feasible solution, found before the optimization process…
Combinatorial optimization (CO) problems are crucial in various scientific and industrial applications. Recently, researchers have proposed using unsupervised Graph Neural Networks (GNNs) to address NP-hard combinatorial optimization…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
In this paper, we present a polynomial-sized linear programming formulation of the Quadratic Assignment Problem (QAP). The proposed linear program is a network flow-based model. Hence, it provides for the solution of the QAP in polynomial…
Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
This article describes an improved brute-force solving strategy for Quadratic Unconstrained Binary Optimization (QUBO) problems that is faster than naive approaches and easily parallelizable. It exploits the Gray code ordering of natural…
We extend variational quantum optimization algorithms for Quadratic Unconstrained Binary Optimization problems to the class of Mixed Binary Optimization problems. This allows us to combine binary decision variables with continuous decision…
The Cable Routing Optimization Problem (CROP) is a Multi-Commodity Flow Problem (MCFP) central to industrial layouts and smart manufacturing. Historically, quantum optimization has modeled MCFPs as Quadratic Unconstrained Binary…
Combinatorial optimization problems play a central role in computer science with many real world applications. A number of relevant problems remain computationally difficult to solve as they lie in the NP-hard complexity class. We present a…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
We draw two incomplete, biased maps of challenges in computational complexity lower bounds.
We survey results on the hardness of approximating combinatorial optimization problems.