摘要
MINLP模型在优化综合与柔性分析中起着重要作用 ,具有两种表示方法 :代数法和逻辑法 ,后者在模型表达与求解方面有很多优点。MINLP模型中还可以集成启发性知识 ,也就是工程经验 ,以加快求解速度 ,并使结果更加合理。对于凸的MINLP问题 ,目前比较成熟的算法有分支界定法、外近似法和广义Bender函数法。对于非凸MINLP问题 ,其求解算法目前尚在研究中 ,已提出的有罚函数法、αBB算法和符号重建算法。此外 ,一些基于随机搜索的方法也得到了应用 ,并且在实践中取得了较好的结果。
The mixed integer nonlinear programming (MINLP) models are widely used in optimal synthesis and flexibility analysis. There are two types of MINLP model: the algebraic MINLP model and the logic MINLP model, and the latter has many advantages in expressing and solving.Logic and heuristic knowledge can also be integrated into MINLP model for process synthesis.Hard logic knowledge cannot be violated, and heuristic rule can be violated when needed. Every heuristic rule has a penalty factor, when it is broken, a penalty will be added into the object function. There are three solution algorithms for convex MINLP models: the branch and bound algorithm, the outer approximation algorithm and the generalized Benders decomposition algorithm. All these three methods generate a descending upper bond sequence and a increasing lower bond sequence, and the convergence of the two sequences is the optimal solution. The branch and bound algorithm make a computational tree, in which every node is a relaxed subproblem. The outer approximation algorithm solves a series of NLP subproblems and MILP main problems, and the main problems are the linearization of the original problem. The generalized Benders decomposition algorithm divides the variables into complex variables and simple variables, and projects the original problem into the complex variable space to get the MILP main problem. The solution algorithms for non convex MINLP models are underdeveloping, including the AP/OA/ER algorithm, the αBB algorithm and the symbolicreformulation algorithm. Stochastic optimization based algorithms are also presented and are used successfully.
出处
《计算机与应用化学》
CAS
CSCD
北大核心
2001年第1期23-30,共8页
Computers and Applied Chemistry
