Improvement of Quantum-Behaved Particle Swarm Optimization Algorithm and Its Application to Ship Hull Waterlines Approximation Based on Non-Uniform Rational B-Spline

Abstract

Nowadays, the optimization algorithm used in the ship design is a hot research area. The computation efficiency and stability of the algorithm depended on the number of design variables, the algorithm parameters, and operation process. In order to improve design efficiency and stability, this paper focuses on the waterlines approximation with as less control parameters as possible applying the improved quantum-behaved particle swarm optimization (QPSO) algorithm based on NURBS (Non-Uniform Rational B-Spline). The optimization model is constructed with the homogeneous coordinate component of the fitted waterline's control points as the design variables. The objective function is set to minimize the maximum relative difference between the widths of the approximated waterlines and the original ones corresponding to the same stations. The appropriate constraints are set according to the characteristics of the free segments of the waterline. The QPSO algorithm is used to solve this optimization problem. With view to the correlation among the design variables, the algorithm is improved by introducing the memory factor to ensure the design variables within the feasible region during the evolution process. Based on this improved QPSO algorithm, the waterlines of the full-scale hull form are approximated and the hull surface is constructed using the skinning algorithm with them. Compared with the related reference results, this approximation method has higher precision and can satisfy the engineering design requirements. It is indicated that it is feasible to represent the hull form using the reduced data. Furthermore, the success rate and the average relative difference comparison between the basic QPSO and the improved QPSO show the reliability and stability of the algorithm. This method proposed in this paper provides a foundation for the hull surface design based on the reduced data. Meanwhile, the improved QPSO algorithm can be used in the similar optimization problem with the design variables correlated with each other.