Metaheuristic optimisation methods for approximate solving of singular boundary value problems. Issue 4 (4th July 2017)

• Record Type: Journal Article
• Authors: Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong
• Is Part Of: Journal of experimental & theoretical artificial intelligence. Volume 29:Issue 4(2017)
• Page Start: 823
• Page End: 842
• Publication Date: 2017-07-04
• Subjects: Singular boundary value problems -- weighted residual function -- metaheuristics -- approximate solution -- particle swarm optimisation -- water cycle algorithm; Artificial intelligence -- Periodicals; 006.3
• DOI: 10.1080/0952813X.2016.1259271
• Languages: English
• ISSNs: 0952-813X

Abstract

Abstract: This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.