积式决策多目标规划及其新型粒子群寻优算法

Multi-objective Programming with Product Arbitration and a New Particle Swarm Optimization Algorithm

针对冗余自由度机器人连续轨迹多目标逆解规划问题,分析了多目标决策方法的基本原理,提出并证明了积式决策方法的可行性,并提出商式外点罚函数法,以在积式决策模型框架下处理约束.积式决策优化模型具有复杂的局部极值点结构,需要求解器具有极强的全局极值点搜索能力.为此,设计了高斯巡游粒子群优化算法.以5组通用的无约束和约束最优化测试函数为对象,比较了本文提出的高斯巡游粒子群优化算法和标准粒子群优化算法的全局极值点搜索能力,分别求解100次,结果表明,本文所提算法的求解成功率高于标准粒子群算法.针对具备复杂局部极值点结构的7维优化测试函数,所提算法寻优成功率仍达80%,而标准粒子群算法的寻优成功率下降为0,证明了所提算法具备较强的寻优能力,尤其是在高维空间上,可应用于多自由度机器人路径规划问题求解.

To resolve multi-objective programming problem of the continuous trajectory for redundant robots, the principle of the multi-objective arbitration is analyzed. A product arbitration method is designed and its feasibility is shown. The quotient exterior point penalty function method is proposed to deal with the constraints in the product arbitration model. The product arbitration based optimization model has complex local extremum point structure, and requires the solver to possess very strong ability to search the global extremum. Therefore, a Gaussian rovering particle swarm optimization （GR-PSO） method is proposed. The GR-PSO and the standard PSO algorithm are used to search the global extremum of five constrained and unconstrained optimization testing functions for a hundred times respectively. The results show that the success ratio of the GR-PSO is superior to the standard PSO obviously. In resolving a 7-dimensional optimization testing function with complex local extremum point structure, the success ratio of GR-PSO is 80%, and that of the standard PSO is zero, which shows the GR-PSO has stronger ability to search the global extremum point in resolving high-dimensional optimization problem. The GR-PSO can resolve the path planning problem for robots with multiple degrees of freedom.