An approximation algorithm for solving standard quadratic optimization problems

Article type: Research Article

Authors: Gao, Lunshan^{a; b; *}

Affiliations: [a] School of Applied Computer Science & IT, Conestoga College, 108 University Ave, Waterloo, ON. Canada | [b] Physics and Computer Science, Wilfrid Laurier University, 75 University Ave W., Waterloo, ON. Canada

Correspondence: [*] Corresponding author. Lunshan Gao. E-mail: [email protected].

Abstract: Standard quadratic optimization problems (StQPs) are NP-hard in computational complexity theory when the matrix is indefinite. This paper describes an approximate algorithm of finding inner optimal values of StQPs. The approximate algorithm fuzzifies variable x ∈ Rn with normalized possibility distributions and simplifies the solving of StQPs. The approximation ratio is discussed and determined. Numerical results show that (1) the new algorithm achieves higher accuracy than the semidefinite programming method and linear programming approximation method; (2) the novel algorithm consumes less than one out of fourth computational time that is consumed by linear programming approximation method; (3) the computational time of the new algorithm does not correlate with the matrix densities whereas the computational times of the branch-and-bound and heuristic algorithms do.

Keywords: Standard quadratic optimization problem, approximation ratio, fuzzification, triangular fuzzy number, normalized possibility distribution

DOI: 10.3233/JIFS-200374

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 4383-4392, 2020