摘要
过程系统优化问题的最优解通常是在某些确定值下求得的。但许多参数和条件是随机变化的,可能是微小的波动,也可能是设备的损坏等,使得原始的系统最优解偏离初始值成为次优解甚至不可行解。这种随机变化的性质称为不确定性。为了解决不确定参数存在条件下原有系统最优解改变的问题,需要建立不同的模型来获得更为可靠和合理的解决方案。根据不确定参数的性质可以将其描述为区间、概率分布函数或模糊集的形式,对应的优化方法有随机规划(期望值模型、机会约束规划、相关机会规划)、模糊规划和鲁棒优化(线性规划、二次规划、半定规划)方法。根据不确定参数的性质及决策者的考量,针对不同的目标函数,可选择相应的优化方法进行建模求解。简单地介绍了这些方法的一般模型方程(主要区别在于目标函数的内容及约束的不同形式),并对它们的求解方法进行讨论(一般是建立复杂模型,通过简化手段转化为对应的确定等价式,再用相应算法求解),通过回顾这些方法在系统工程领域中的广泛应用,可以看出它们的适用范围、发展历程及发展规律(综合化、复杂化、智能化)。最后对这三种方法进行了比较,提出发展中面临的难题,并做出总结和展望。
Process system is usually optimized under the condition with nominal value. However, parameters and conditions are changing with time, making the solution deviate from the original optimal value or even infeasible. The random variation is called uncertainty. In order to solve the optimization problems caused by the existence of uncertain parameters, different models need to be established to obtain more reliable and reasonable solutions. According to the nature of the uncertain parameters, it can be described as an interval form, a probability distribution function or a fuzzy set. The corresponding optimization methods are stochastic programming, fuzzy programming and robust optimization methods. Stochastic methods include expected value model, chance constrained programming model and dependent-chance programming model, while robust optimization methods consist of linear programming model, secondary programming model and semidefinite programming model. Once the form of the uncertain parameter is selected and the objective function is determined by decision makers, the corresponding optimization model is also determined. The general model equations of these methods are briefly introduced and the main difference are the contents of objective functions and the different forms of constraints. The solution methods are discussed next, and the general procedure is that complex models are first established, and then they are transformed into corresponding equivalents. By reviewing the development of these methods in system engineering, we can see their application scope and development direction, and they are developing towards integration, complexity, and intelligence. The three methods are compared, the problems faced in the development are put forward, and the conclusions and prospects are made finally.
作者
刘波
王彧斐
冯霄
LIU BoWANG Yufei;FENG Xiao(School of Chemical Engineering and Environment,China University of Petroleum,Beijing 102249,China;School of Chemical Engineering&Technology,Xi'an Jiaotong University,Xi'an 710049,Shaan Xi,China)
出处
《计算机与应用化学》
CAS
北大核心
2019年第6期672-679,共8页
Computers and Applied Chemistry
基金
国家自然科学基金资助项目(21576286)
关键词
不确定性
最优化
随机规划
模糊规划
鲁棒优化
uncertainty
optimization
stochastic programming
fuzzy programming
robust optimization
