A highly accurate differential evolution–particle swarm optimization algorithm for the construction of initial value problem solvers. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Th. Famelis, I.; Alexandridis, A.; Tsitouras, Ch.
• Is Part Of: Engineering optimization. Volume 50:Issue 8(2018)
• Page Start: 1364
• Page End: 1379
• Publication Date: 2018-08-03
• Subjects: Differential evolution -- particle swarm optimization -- initial value problems -- Runge–Kutta pairs; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2017.1400545
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: In this work a new evolutionary computation technique is introduced for the construction of initial value solvers based on Runge–Kutta (RK) pairs. The derivation of RK pairs corresponds to solving a nonlinear optimization problem with a multimodal objective function in a high dimensional search space; additional difficulty stems from the fact that only solutions with accuracy at least equal to machine epsilon are acceptable. The proposed approach involves hybridizing a Differential Evolution (DE) strategy with elements from Particle Swarm Optimization (PSO) in order to produce a method for solving optimization problems with high accuracy. The resulting methodology is applied to two different problems of RK pair derivation of orders 5 and 4 and compared with standard DE techniques. Numerical experiments show that the proposed hybrid DE-PSO satisfies the strict accuracy requirements imposed by the particular problem, while outperforming its rivals.