摘要
针对一类非线性极小极大问题目标函数非光滑的特点给求解带来的困难,利用改进的粒子群算法并结合极大熵函数法给出了此类问题的一种新的有效算法。首先利用极大熵函数将无约束和有约束极小极大问题转化为一个光滑函数的无约束最优化问题,将此光滑函数作为粒子群算法的适应值函数;然后用数学中的外推方法给出一个新的粒子位置更新公式,并应用这个改进的粒子群算法来优化此问题。数值结果表明,该算法收敛快?数值稳定性好,是求解非线性极小极大问题的一种有效算法。
Concerning the fact that the unsmoothness objective function of a class of nonlinear minimax problem caused difficult solution, a new algorithm was proposed. This algorithm used improved Particle Swarm Optimization combined with maximum entropy function method. Firstly, the maximum entropy function was used to transform the unconstrained and constrained minimax problems into a smooth function of unconstrained optimization problems; this smooth function was used as Particle Swarm Optimization＇s fitness function. Then a new position update equation was proposed by using the strategy of extrapolation in Mathematics, Thus, a new class of Particle Swarm Optimization was given, The new algorithm was applied to solving the minimax problems. The numerical results show that the algorithm converges faster and has numerical stability, and it is an effective algorithm for nonlinear minimax problems.
出处
《计算机应用》
CSCD
北大核心
2008年第5期1194-1196,1199,共4页
journal of Computer Applications
基金
陕西省教育厅自然科学研究项目(07JK376)
陕西省自然科学研究项目(2007A21)
关键词
粒子群算法
进化算法
极小极大问题
极大熵函数
particle swarm optimization
evolutionary computation
minimax problems
maximum entropy method
