Related papers: An Expansion-Based Approach for Quantified Integer…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
Quantified Answer Set Programming (QASP) extends Answer Set Programming (ASP) by allowing quantification over propositional variables, similar to Quantified Boolean Formulas (QBF). In this paper, we interpret models of QASP formulas in…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major challenge is that QLSAs are inexact and sensitive to the condition number of the coefficient matrices of linear systems.…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
For mixed-integer programs (MIPs), strong branching is a highly effective variable selection method to reduce the number of nodes in the branch-and-bound algorithm. Extending it to nonlinear problems is conceptually simple but practically…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
Many verification and synthesis approaches rely on solving techniques for quantified Boolean formulas (QBF). Consequently, solution witnesses, in the form of Boolean functions, become more and more important as they represent…
Combinatorial optimization problems are pivotal across many fields. Among these, Quadratic Unconstrained Binary Optimization (QUBO) problems, central to fields like portfolio optimization, network design, and computational biology, are…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Current algorithms for bounded model checking use SAT methods for checking satisfiability of Boolean formulae. These methods suffer from the potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulae…
Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…