Abstract: For solving dynamic optimization problems with fixed boundary, a novel strategy named as graded optimization was developed. It had two alternative schemes, of which the one was to deal with the constraint of fixed boundary prior to objective optimization, while the other one was to treat them in the reversed procedure. By using this strategy a fixed boundary problem was reduced to a series of free boundary problems that could be solved by using existing,sophisticated optimization methods. For boxing constraint of control, trigonometric function transformation was developed to achieve an unconstrained problem. Graded optimization had the abilities to avoid the demerits of penalty function strategy. Case studies showed that graded optimization could meet fixed boundary requirements with reasonable accuracy and trigonometric function transformation was feasible.

Key words: 动态优化, 边值固定, 罚函数, 分级优化

摘要： 针对边值固定的化工动态优化问题, 提出了分级优化策略, 包括约束优先与目标优先两种方案, 它们的基本思想是将原问题转化为一系列的边值无约束问题, 采用目前成熟的优化算法加以集成即可实现. 对于控制变量受箱型约束的问题, 采用三角函数转换将其转化为控制无约束问题. 分级优化策略避免了罚函数策略的缺陷. 实例研究显示了分级优化策略能以足够的精度满足边值约束, 三角函数转换法是可行的.

关键词: 动态优化, 边值固定, 罚函数, 分级优化