The Algorithms Of Mixed Integer Nonlinear Programming And The Applications Of Multistage Stochastic Programs

Mixed Integer Nonlinear Programming (MINLP) and Multi-stage Stochastic Programming (M-SP) are optimized in the field of two kinds of more complex problems, but they have a wide range of applications in real life. MINLP is a kind of nonlinear programming problems, which incudes both continuous variables and discrete variables, is an important branch of integer programming. MINLP is NP-hard, the solution of it is extremely difficult. MSP includes uncertainties and belongs to multi-step decision optimization problem, due to the dynamic nature of the multi-step decision-making, the algorithm design of MSP is a big difficulty. But along with the social development, the problems in real life is becoming more and more complex, a lot of problems need to be modeled as with continuous variables and discrete variables, or contain planning problem of a random variable, so the research of how to create the algorithms of two types of optimization problems has important practical significance and value.In this paper, for two types of optimization problem carried out the following research:The first section summarizes the problem solving MINLP appropriate software algorithms and implementation of various types of basic arithmetic algorithms, which includes five deterministic al-gorithms and one heuristic algorithms, analysing the design structure of algorithms; software includes open source software and commercial software, the development status of the software introduced in detail. It provides favorable conditions for the research of mixed integer Nonlinear programming.The second part of multi-period multi-market participation optimization decisions made under con-ditions of a class of risk value (Conditional Value-at-Risk, CVaR) multistage stochastic programming model. Based on modern electricity network in the new energy, a lot of uncertainties constructed a kind of multi-stage economic dispatch problem that is modeled as a multi-stage stochastic programming. Using Stochastic Dual Dynamic Programming algorithm (SDDP) to solve the new model. Finally the model is confirmed in multi-market participation applicability by simple numerical experiments.