Diversity enhanced and local search accelerated gravitational search algorithm for data fitting with B-splines

Abstract

Gravitational search algorithm (GSA) has shown an effective performance for solving real-world optimization problems. However, it suffers from premature convergence because of quick losing of diversity. To enhance its performance, this paper proposes a novel GSA algorithm, called GSA---PWL (piecewise linear)---SQP (sequential quadratic programming), which employs a diversity enhancing mechanism and an accelerated local search strategy to achieve a trade-off between exploration and exploitation abilities. A comprehensive experimental study is conducted on a set of benchmark functions. Comparison results show that GSA---PWL---SQP obtains a promising performance on the majority of the test problems. Furthermore, the GSA---PWL---SQP is applied to data fitting with B-splines to solve very difficult continuous multimodal and multivariate nonlinear optimization problem. The method of data fitting based on GSA---PWL---SQP yields very accurate results even for curves with singularities and/or cusps and is very efficient in terms of data points error, AIC and BIC criteria.