一种求解变量有界非线性规划的全局最优解新方法  

A Novel Global Optimization Method to Solve Nonlinear Programming Problem with Bounded Variables

作　　者：金霞[1,2] 段富海[1] 江秀红[1] 

机构地区：[1]大连理工大学机械工程学院,辽宁大连116023 [2]朝阳师范高等专科学校,辽宁朝阳122000

出　　处：《上海交通大学学报》2016年第6期861-867,共7页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金项目(51275068);航空科学基金项目(20150863003)资助

摘　　要：提出了一种求解变量有界非线性规划的全局最优解新方法——不可行域移除(IRIR)法.在优化过程中,先计算原最优化问题的不可行域,然后在原最优化问题的求解空间中移除确定的不可行域,使得新的求解空间不断缩小,并通过研究不可行域的线性表达,在不影响最优解的前提下将非线性约束转化为线性约束,以求解非线性规划问题,其特点是所得最优解对原最优化问题约束函数的凸性和优化迭代起始点的位置不敏感.同时,阐述了IRIR法的原理和实现过程,在序列二次规划(SQP)算法的基础上,应用数值算例和弹簧设计2个典型实例,以验证IRIR法的可行性和正确性.结果表明:IRIR法可以有效降低原最优化问题的求解难度,且无需引入新参数,是一种具有较高求解能力和实用价值的全局最优化方法,但其不适用于求解设计变量无界的最优化问题.A novel global optimization method,increasingly removing infeasible region（IRIR）,to solve the nonlinear programming problem with bounded variables,was presented.In the IRIR,the original infeasible regions were computed and removed from the original solution space,and the updated solution space was gradually reduced.The infeasible regions were expressed by linear inequalities so that the original nonlinear constraints were transformed into linear inequality constraints,and the nonlinear programming problem could be solved in the premise that the optimum design point was not excluded from the updated solution space.The characteristic of the IRIR is that the optimum obtained is insensitive to the starting point and the convexities of constraint functions.The principle and computational process of the IRIR were elaborated.Based on the sequential quadratic programming（SQP）algorithm,the application of the IRIR to two optimization problems,a numerical test problem and a spring design problem,illustrates the feasibility and correctness of the IRIR.The optimization results show that the IRIR can effectively lower the difficulty of solving the nonlinear programming problem.Besides,it is not necessary to introduce the addi-tional parameter.The IRIR is a novel global optimization method with a high applicability and practicality.But,it is not applicable to problems with unbounded variables.

关 键 词：全局优化 非线性规划 可行域 序列二次规划算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]