Optimum B-spline curve fitting using a modified simulated annealing method

Abstract

This article considers a curve-fitting problem, with the objective of generating optimum B-spline curves in terms of minimum deviation and smooth curvature variations. For this purpose, an objective function is developed that can manage the error optimisation problem with various fairness requirements. The optimisation problem was solved using a modified simulated annealing method. The new implementation comprises an adaptive cooling procedure in which the temperature change is adaptively dependent on the objective function evolution. The proposed method gives the algorithm more freedom during the cooling process that results in an improved convergence speed. To achieve a further improvement in the performance of the method, parallel simulated annealing was implemented using the proposed cooling process. The main features of this algorithm are described and its encouraging results are presented. The obtained results confirm that the proposed method can effectively be used in various curve approximation problems.