一种基于内点算法的三重目标过滤器优化算法的研究与仿真

 大规模非线性最优化一直是规划中的研究热点.内点算法是一种有效的求解大规模不等式约束问题的算法,然而大多数过滤内点算法仅考虑了可行性和稳定性,忽略了辅助性对算法性能的影响,为此本文在综合过滤器法和内点算法特点的基础之上,提出了一种新的适用于大规模非线性优化的基于内点算法的三重目标过滤器法.新算法依据内点算法的卡罗需-库恩-塔克(KKT)条件,以可行性、辅助性和稳定性作为搜索步长的目标,将等式约束违反量,障碍目标函数和辅助条件作为过滤器选项计算搜索步长.通过搭建计算机仿真环境进行数值测试,从迭代次数、函数估计次数和运行时间3方面与基本过滤器法相比.测试结果表明,相同条件下三重目标过滤器法可以获得更大的搜索步长,实现快速收敛的目的.该算法具有良好的全局收敛性、鲁棒性和有效性.

Research and Simulation on the Triple-objective Filter Optimization Algorithm Based on Interior Point Algorithm

The large scale nonlinear optimization has become a research focus in the planning, the interior-point algorithm is an effective method for solving large-scale inequality constraints, however most of the filter interior-point algorithm only consider the feasibility and stability, ignoring the adjuvant on the performance of algorithm, so that in this paper, in the light of the Karush-Kuhn-Tucker (KKT) conditions of the interior-point algorithm, a new algorithm, with feasibility, auxiliary and stability as the objective of the search step, use the amount of the violation of equality constraints, the obstacle objective function and auxiliary conditions as a filter option to calculate the search step and build a computer simulation environment for the numerical test, compared with the basic filter method from the number of iterations, function estimated times and run time. The test results show that under the same conditions the new algorithm, compared with the basic filter method, can get more search steps, and achieve fast convergence, having good global convergence, robustness and effectiveness.