调速泵结构配置协调分解优化算法及实现

Harmonious decomposition algorithm and its application in global optimization of pump configurations

建立多级调速泵结构配置连续非线性规划和整数非线性规划二阶段模型.非线性整数规划子问题采用外逼近算法求解.针对连续非线性规划主问题,提出基于割角法的可行域协调分解优化算法,证明割角法陷阱问题并建立判断准则排除已知的陷阱区域,在此基础上构建系列松弛问题得到原优化问题渐进收紧的下界估计,并最终收敛到原优化问题全局最优解.三级调速泵结构配置实例验证了算法的有效性,并给出与其他算法的比较结果.

A two-stage model,which consists of nonlinear continuous programming and nonlinear integer programming sub-problems,is proposed for solving the multi-level pumps configuration problem.The integer nonlinear programming subproblem is solved by using a traditional outer approximation algorithm;the continuous nonlinear programming main-problem is optimized using a novel harmonious decomposition algorithm based on the cutting angle method（CAM）.Some properties of cutting angle method（CAM） are studied and the ill-posed trap limitation is found and proved theoretically.In view of the deficiencies of CAM,we propose a harmonious decomposition algorithm using judgement criterions to exclude the known trap regions in feasible domain;and then,compute the gradually tightening lower bounds on the main optimization problem by building a sequence of piecewise linear relaxation problems.The sequence of solutions to these relaxation problems converges to the global minimum of the optimization problem.Experiment results from a 3-level pump configuration instance show that the proposed method provides better performances than the other optimization methods listed in paper.