混合整数非线性规划算法及多阶段随机优化应用

发布时间：2018-01-16 14:15

本文关键词：混合整数非线性规划算法及多阶段随机优化应用　出处：《湘潭大学》2016年硕士论文　论文类型：学位论文

【摘要】：混合整数非线性规划(Mixed Integer Nonlinear Programming, MINLP)以及多阶段随机规划(Multi-stage Stochastic Programming, MSP)是优化领域中较为复杂的两类问题,在实际生活中均有着广泛的应用MINLP是一类同时包含连续变量和离散变量的非线性规划问题,属于整数规划的重要分支.它具有NP-难的特性,其求解比较困难.MSP为包含不确定性因素的多步决策优化问题,由于多步决策的动态性,MSP算法设计存在较大困难.另一方面,随着社会经济发展,应用领域中的问题日益复杂,许多优化建模问题同时带有连续变量与离散变量或者含有随机变量.因此,如何建立两类优化问题的算法研究具有重要的现实意义及应用价值.本文针对两类优化问题开展了如下研究：第一部分总结了求解MINLP问题的各类基本算法及执行算法的相应软件.其中算法包括五种确定型算法与一种常用启发式算法,并对算法的设计结构进行了分析；然后总结开源软件与商业软件,对软件的开发状况做了详细介绍.这些总结为MINLP的相关研究提供便利条件.第二部分针对多市场参与下的多时间段优化决策问题提出一类条件风险值(Conditional Value-at-Risk, CVaR)下的多阶段随机规划模型.构建了模型求解的随机对偶动态规划算法(stochastic dual dynamic programming, SDDP)基于现代电力中新能源入网的很多不确定性因素,本文讨论了一类多阶段经济调度问题.最后通过简单数值实验证实模型在多市场参与下的可应用性.
[Abstract]:Mixed Integer Nonlinear Programming. MINLP) and multi-stage stochastic programming (MIP) and multi-stage Stochastic Programming. MSPs are two kinds of complex problems in optimization field. They are widely used in real life. MSPs are a class of nonlinear programming problems with both continuous and discrete variables. It is an important branch of integer programming. It has the characteristics of NP-hard, and its solution is difficult. MSP is a multi-step decision optimization problem with uncertain factors, because of the dynamic nature of multi-step decision. The design of MSP algorithm is difficult. On the other hand, with the development of social economy, the problems in application field are becoming more and more complex. Many optimization modeling problems have both continuous and discrete variables or random variables. How to establish algorithms for two kinds of optimization problems has important practical significance and application value. In this paper, two kinds of optimization problems are studied as follows:. The first part summarizes all kinds of basic algorithms for solving MINLP problem and the corresponding software of executing algorithm. The algorithm includes five deterministic algorithms and a common heuristic algorithm. The design structure of the algorithm is analyzed. Then summarize open source software and commercial software. The development of software is introduced in detail. These conclusions provide convenient conditions for the research of MINLP. In the second part, a class of conditional risk values are proposed for multi-time optimal decision making with multi-market participation. Conditional Value-at-Risk. A multi-stage stochastic programming model based on CVaR is presented. A stochastic dual dynamic programming algorithm for solving the model is constructed. Stochastic dual dynamic programming. SDDPs are based on a number of uncertainties associated with access to new energy sources in modern power. In this paper, a class of multi-stage economic scheduling problems is discussed. Finally, the applicability of the model under multi-market participation is verified by simple numerical experiments.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O221.2

【参考文献】