The Basic Algorithm for the Constrained Zero-One Quadratic Programming Problem with k-diagonal Matrix and Its Application in the Power System

Zero-one quadratic programming is a classical combinatorial optimization problem that has many real-world applications. However, it is well known that zero-one quadratic programming is non-deterministic polynomial-hard (NP-hard) in general. On one hand, the exact solution algorithms that can guarant...

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 1; p. 138
Main Authors Gu, Shenshen, Chen, Xinyi
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2020
Subjects
Algorithms
Capital budgeting
Combinatorial analysis
combinatorial optimization
Dynamic programming
Exact solutions
Heuristic methods
k-diagonal matrix
Linear programming
Measuring instruments
Optimization
Phasors
Polynomials
power system
Quadratic programming
Traveling salesman problem
Variables
zero-one quadratic problem
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Summary:Zero-one quadratic programming is a classical combinatorial optimization problem that has many real-world applications. However, it is well known that zero-one quadratic programming is non-deterministic polynomial-hard (NP-hard) in general. On one hand, the exact solution algorithms that can guarantee the global optimum are very time consuming. And on the other hand, the heuristic algorithms that generate the solution quickly can only provide local optimum. Due to this reason, identifying polynomially solvable subclasses of zero-one quadratic programming problems and their corresponding algorithms is a promising way to not only compromise these two sides but also offer theoretical insight into the complicated nature of the problem. By combining the basic algorithm and dynamic programming method, we propose an effective algorithm in this paper to solve the general linearly constrained zero-one quadratic programming problem with a k-diagonal matrix. In our algorithm, the value of k is changeable that covers different subclasses of the problem. The theoretical analysis and experimental results reveal that our proposed algorithm is reasonably effective and efficient. In addition, the placement of the phasor measurement units problem in the power system is adopted as an example to illustrate the potential real-world applications of this algorithm.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8010138