理性运动极限及其在优化算法中的应用

Rational Move Limit and Its Application in Optimization Algorithms

优化求解有时需要提供近似模型代替实际复杂的问题,而近似模型只是在一定程度上逼近原始问题.优化模型如果在不可靠的近似函数上进行,就会导致迭代的目标函数值振荡、迭代收敛缓慢甚至不收敛,从而使最终结果有时可能不满足约束条件.通过给设计变量施加运动极限可以提高近似模型在一定范围内的可靠性.通常给定运动极限的方法是准则法,这种方法较为粗糙,不是根据近似函数本身的性质得出的理性结果.本文用累积信息的约束二阶估计近似显式代替准确的约束条件函数作为评价函数来构造运动极限的理性估计式,从而求得理性运动极限,并将这一方法应用于序列二次规划(SQP)算法中,数值算例表明了这一方法的可行性和有效性.

It is sometimes necessary that offering an approximate model to substitute the real complex problem in optimization solution,but which can only approximate the original problem at a certain extent.The optimization model on unreliable approximation function will lead to oscillations of the iterative objective functions,and make convergence of the iterations being slowly even impossibly.Finally,the results may not sometimes satisfy the constraint conditions.The approximate model will increase the reliability in certain domain when the move limits are imposed on design variables.The strategies of giving move limits belong to criterion method and they are usually rough,because they are not rational results according to properties of constraint functions.This paper constructs a second-order approximate explicit function by accumulated information which substitutes the accurate function of the constraint condition as evaluation function to construct rational estimation formula of the move limits.Eventually, Rational move limits are obtained and applied to SQP (Sequential Quadratic Programming). Examples show it is feasible and efficient.