基于单纯形搜索法和免疫进化微粒群算法,提出1个求解无约束最优化问题的新的混合算法—单纯形搜索法和免疫进化微粒群算法的混合算法.由于它不需要梯度信息,所以具有易实施、收敛速度快和计算准确的优点.为了证明混合算法能够改进免疫...基于单纯形搜索法和免疫进化微粒群算法,提出1个求解无约束最优化问题的新的混合算法—单纯形搜索法和免疫进化微粒群算法的混合算法.由于它不需要梯度信息,所以具有易实施、收敛速度快和计算准确的优点.为了证明混合算法能够改进免疫进化微粒群算法的性能,首先利用6个测试函数进行仿真计算比较,计算结果表明,新的混合算法在求解质量和收敛速率上都优于其它进化算法(IEPSO,PSOPC,GSPSO,LSPSO and CPSO);其次,将新混合算法和最新的3种混合算法进行鲁棒性分析比较,结果表明,新混合算法在解的搜索质量、效率和关于初始点的鲁棒性方面都优于其它算法.展开更多
Rendezvous in circular or near circular orbits has been investigated in great detail,while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored.Among the various optimization methods pro...Rendezvous in circular or near circular orbits has been investigated in great detail,while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored.Among the various optimization methods proposed for fuel optimal orbital rendezvous,Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution.Prussing has applied the primer vector optimization theory to minimum-fuel,multiple-impulse,time-fixed orbital rendezvous in a near circular orbit and achieved great success.Extending Prussing's work,this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous.Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations),the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar,coaxial elliptical orbits with arbitrary large eccentricity.A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution.Finally,the optimal multiple-impulse rendezvous solution including the time,direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem.The rendezvous error of the linearized equation is also analyzed.The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity.For better rendezvous accuracy of high eccentricity orbits,a combined method of multiplier penalty function with the simplex search method is used for local optimization.The simplex search method is sensitive to the initial values of optimization variables,but the simulation results show that initial values with the primer vector theory,and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence,because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.If the initial values are taken randomly,it is difficult to converge to the optimal solution.展开更多
文摘基于单纯形搜索法和免疫进化微粒群算法,提出1个求解无约束最优化问题的新的混合算法—单纯形搜索法和免疫进化微粒群算法的混合算法.由于它不需要梯度信息,所以具有易实施、收敛速度快和计算准确的优点.为了证明混合算法能够改进免疫进化微粒群算法的性能,首先利用6个测试函数进行仿真计算比较,计算结果表明,新的混合算法在求解质量和收敛速率上都优于其它进化算法(IEPSO,PSOPC,GSPSO,LSPSO and CPSO);其次,将新混合算法和最新的3种混合算法进行鲁棒性分析比较,结果表明,新混合算法在解的搜索质量、效率和关于初始点的鲁棒性方面都优于其它算法.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Rendezvous in circular or near circular orbits has been investigated in great detail,while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored.Among the various optimization methods proposed for fuel optimal orbital rendezvous,Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution.Prussing has applied the primer vector optimization theory to minimum-fuel,multiple-impulse,time-fixed orbital rendezvous in a near circular orbit and achieved great success.Extending Prussing's work,this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous.Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations),the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar,coaxial elliptical orbits with arbitrary large eccentricity.A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution.Finally,the optimal multiple-impulse rendezvous solution including the time,direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem.The rendezvous error of the linearized equation is also analyzed.The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity.For better rendezvous accuracy of high eccentricity orbits,a combined method of multiplier penalty function with the simplex search method is used for local optimization.The simplex search method is sensitive to the initial values of optimization variables,but the simulation results show that initial values with the primer vector theory,and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence,because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.If the initial values are taken randomly,it is difficult to converge to the optimal solution.
