Solution of boolean quadratic programming problems by two augmented Lagrangian algorithms based on a continuous relaxation

Many combinatorial optimization problems and engineering problems can be modeled as boolean quadratic programming (BQP) problems. In this paper, two augmented Lagrangian methods (ALM) are discussed for the solution of BQP problems based on a class of continuous functions. After convexification, the...

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Vydáno v:Journal of combinatorial optimization Ročník 39; číslo 3; s. 792 - 825
Hlavní autoři: Nayak, Rupaj Kumar, Mohanty, Nirmalya Kumar
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2020
Springer Nature B.V
Témata:
Algorithms
Boolean
Boolean algebra
Combinatorial analysis
Combinatorics
Computing time
Continuity (mathematics)
Convex and Discrete Geometry
Knapsack problem
Lagrangian function
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Quadratic programming
Theory of Computation
Continuous relaxation
Augmented Lagrangian method
Max-cut problems
Binary quadratic programming problem
Image deconvolution
QKP
ISSN:1382-6905, 1573-2886
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Shrnutí:Many combinatorial optimization problems and engineering problems can be modeled as boolean quadratic programming (BQP) problems. In this paper, two augmented Lagrangian methods (ALM) are discussed for the solution of BQP problems based on a class of continuous functions. After convexification, the BQP is reformulated as an equivalent augmented Lagrangian function, and then solved by two ALM algorithms. Within this ALM algorithm, L-BFGS is called for the solution of unconstrained nonlinear programming problem. Experiments are performed on max-cut problem, 0–1 quadratic knapsack problem and image deconvolution, which indicate that ALM method is promising for solving large scale BQP by the quality of near optimal solution with low computational time.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-019-00517-8