An improved cooperation search algorithm for the multi-degree reduction in Ball Bézier surfaces

Abstract

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However for some complex problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, an improved cooperation search algorithm (CCSA) is proposed by incorporating the mutation and crossover operators in DE algorithms to alleviate the shortcoming. The two operators can be used to increase population's diversity significantly, and thus improve population's exploration capability and accuracy significantly. CCSA has been tested on 23 benchmark functions and CEC 2017 benchmark suite. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction of Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains are treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which achieves the automatic and intelligent degree reduction of Ball Bézier surfaces.

Geometric analysis of non-degenerate shifted-knots Bézier surfaces in Minkowski space

“…Pradhan and Mohan [ 30 ] presented a novel method for maintaining the continuity of contour lines on topographic sheets, integrating the principles of Sign of Gradient (SG), Euclidean Distance (ED), and a customized Bézier Curve (BC) drawing method. Cao et al [ 31 ] proposed an efficient multi-degree reduction method for Ball Bézier surfaces under varying interpolation constraints, employing metaheuristic methods.…”