Opposition-based learning boosted orca predation algorithm with dimension learning: a case study of multi-degree reduction for NURBS curves

Abstract

The approximate degree reduction of ball non-uniform rational B-splines (NURBS) curves is a pivotal and knotty technique in computer-aided design/computer-aided manufacture. As we all know, the multi-degree reduction of NURBS ones is a mathematical optimization problem that a swarm intelligence algorithm can deal with. This paper uses an improved orca predation algorithm (IOPA) to accomplish the optimal multi-degree reduction of NURBS curves. Firstly, by incorporating a dimension learning strategy and opposition-based learning strategy into the orca predation algorithm (OPA), an IOPA is developed to increase the population diversity and enhance its capability of jumping out of the local minima. Secondly, the superiority of the proposed IOPA is comprehensively verified by comparing it with the original OPA and numerous celebrated and newly developed algorithms on the IEEE Congress on Evolutionary Computation (CEC) 2014 test suite and IEEE CEC2017 benchmark functions, respectively. Meanwhile, the practicability of IOPA is also highlighted by solving three real-world engineering design problems. Furthermore, statistical testing of IOPA has been conducted to validate its significance. Finally, the optimization model of multi-degree reduction for NURBS curves is established by minimizing the distance between the original curve and the approximate curve. The IOPA is utilized to solve the optimization model, and the optimal approximate NURBS curves are obtained. Some representative numerical examples illustrate the ability of the proposed IOPA to effectively solve the multi-degree reduction problem of NURBS curves in terms of precision, robustness, and convergence characteristics.