Solving Interval Quadratic Programming Problems by Using the Numerical Method and Swarm Algorithms

In this paper, we present a new approach which is based on using numerical solutions and swarm algorithms (SAs) to solve the interval quadratic programming problem (IQPP). We use numerical solutions for SA to improve its performance. Our approach replaced all intervals in IQPP by additional variable...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 11
Main Authors: Elsisy, M. A., El-Shorbagy, M. A., Hammad, D. A.
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Wiley
Subjects:
Algorithms
Heuristic methods
Kuhn-Tucker method
Linear programming
Mathematical optimization
Methods
Numerical analysis
Numerical methods
Optimization
Particle swarm optimization
Quadratic programming
ISSN:1076-2787, 1099-0526
Online Access:Get full text
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Summary:In this paper, we present a new approach which is based on using numerical solutions and swarm algorithms (SAs) to solve the interval quadratic programming problem (IQPP). We use numerical solutions for SA to improve its performance. Our approach replaced all intervals in IQPP by additional variables. This new form is called the modified quadratic programming problem (MQPP). The Karush–Kuhn–Tucker (KKT) conditions for MQPP are obtained and solved by the numerical method to get solutions. These solutions are functions in the additional variables. Also, they provide the boundaries of the basic variables which are used as a start point for SAs. Chaotic particle swarm optimization (CPSO) and chaotic firefly algorithm (CFA) are presented. In addition, we use the solution of dual MQPP to improve the behavior and as a stopping criterion for SAs. Finally, the comparison and relations between numerical solutions and SAs are shown in some well-known examples.
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ISSN:1076-2787
1099-0526
DOI:10.1155/2020/6105952