为了有效推进无余量造船的精益造船方法，充分考虑船体三维曲板展开后的板材套料和板材成形等后续工艺环节，基于单元等长展开方法，提出船体三维曲板展开优化模型.以面积误差、边缘线性和平均应变能为目标函数，采用带有启发算子的多目标文化基因算法对船体三维曲板展开优化模型进行求解，基于层次分析法对多组求解所得的方案进行选择，获得最终的展开曲面.通过与测地线法的展开结果进行对比，验证该优化算法的有效性，同时进一步验证了算法中局部搜索算子和启发算子的有效性.
In order to effectively improve the management of ship building process, an optimization model for expansion of three-dimensional curved hull plate is proposed based on an expansion method with a constant unit length, taking the steel plate cutting and plate conforming technology into full consideration. The error of area, linear degree of borders, and mean strain energy are taken as objective functions. The multi-objective memetic algorithm (MOMA) with heuristic operator is adopted to solve the optimization model of three-dimensional curved plate expansion of ship hull. Based on the analytic hierarchy process(AHP) method, multiple solutions are selected to obtain the final expansion surface. By comparing with the geodesic expansion results, the effectiveness of the optimization algorithm is verified. Besides, the effectiveness of local search operator and heuristic operator in the algorithm is further verified.
［1］肖雄, 黄朝炎, 胡勇, 等. 三维曲面船体外板数学展开方法研究［J］. 船海工程, 2013, 42(1): 74-77.
XIAO Xiong, HUANG Chaoyan, HU Yong, et al. Study on the method of mathematical expansion of 3-D curvature hull plate［J］. Ship & Ocean Engineering, 2013, 42(1): 74-77.
［2］HINDS B K, MCCARTNEY J, WOODS G. Pattern development for 3D surfaces［J］. Computer-Aided Design, 1991, 23(8): 583-592.
［3］AZARIADIS P, ASPRAGATHOS N. Design of plane developments of doubly curved surfaces［J］. Computer-Aided Design, 1997, 29(10): 675-685.
［4］WANG C C L, TANG K, YEUNG B M L. Freeform surface flattening based on fitting a woven mesh model［J］. Computer-Aided Design, 2005, 37(8): 799-814.
［5］SHIN K H. A method for planar development of free-form surfaces made of anisotropic materials［J］. Journal of Mechanical Science and Technology, 2011, 25(11): 2817-2825.
［6］SEONG W J, JEON Y C, NA S J. Ship-hull plate forming of saddle shape by geometrical approach［J］. Journal of Materials Processing Technology, 2013, 213(11): 1885-1893.
［7］张雪彪, 纪卓尚, 刘玉君, 等. 基于参数曲面表达的帆形船体外板展开方法［J］. 中国造船, 2005, 46(3): 92-97.
ZHANG Xuebiao, JI Zhuoshang, LIU Yujun, et al. Plane development method of convex hull plate based on parametric surface representation［J］. Shipbuilding of China, 2005, 46(3): 92-97.
［8］李纯金, 杨秋林. 基于自适应三角化的船舶曲面分段网格细分［J］. 舰船科学技术, 2018, 40(11): 25-28.
LI Chunjin, YANG Qiulin. Ship plate section surface mesh segmentation based on adaptive triangulation［J］. Ship Science and Technology, 2018, 40(11): 25-28.
［9］刘寅东, 战翌婷. 船体外板展开算法及程序实现［J］. 船舶工程, 2007, 29(3): 34-36.
LIU Yindong, ZHAN Yiting. Arithmetic and program realization for shell expansion［J］. Ship Engineering, 2007, 29(3): 34-36.
［10］HAN Y Y, GONG D W, LI J Q, et al. Solving the blocking flow shop scheduling problem with makespan using a modified fruit fly optimisation algorithm［J］. International Journal of Production Research, 2016, 54(22): 6782-6797.
［11］WANG C, TIAN N, JI Z C, et al. Multi-objective fuzzy flexible job shop scheduling using memetic algorithm［J］. Journal of Statistical Computation and Si-mulation, 2017, 87(14): 2828-2846.
［12］蔡斌. 基于文化基因算法的车间作业调度理论研究及实践［D］. 重庆: 重庆大学, 2012.
CAI Bin. Research on the job shop scheduling problem with memetic algorithms［D］. Chongqing: Chongqing University, 2012.
［13］SAATY T L, VARGAS L G. Hierarchical analysis of behavior in competition: Prediction in chess［M］∥The Logic of Priorities. Dordrecht, The Netherlands: Springer, 1982: 207-226.
