【摘要】：參數(shù)規(guī)劃是含有連續(xù)變量、離散變量與參數(shù)的一類數(shù)學(xué)規(guī)劃問題,該問題廣泛應(yīng)用于工程、經(jīng)濟、模型預(yù)測控制等領(lǐng)域,對此類問題的研究具有重要的理論意義及實際應(yīng)用價值.多參數(shù)線性規(guī)劃與多參數(shù)混合整數(shù)線性規(guī)劃是參數(shù)規(guī)劃的重要分支,本文針對這兩類多參數(shù)線性規(guī)劃的計算問題展開研究:第一部分在Rivotti[1]的多參數(shù)線性規(guī)劃理論基礎(chǔ)上,針對約束函數(shù)含有參數(shù)的多參數(shù)線性規(guī)劃問題,構(gòu)建了一種新的多參數(shù)線性規(guī)劃算法(multi-parametric linear programming, MPLP).算法的基本思想是基于靈敏度理論,利用最優(yōu)解的仿射表達式得到初始解,通過一組最優(yōu)域系統(tǒng)地刻畫參數(shù)空間,并且在參數(shù)空間內(nèi)遞歸探索問題的解.通過三個數(shù)值算例證明MPLP算法的有效性.第二部分考慮約束函數(shù)含有參數(shù)的多參數(shù)混合整數(shù)線性規(guī)劃問題的計算.把問題分解成混合整數(shù)線性規(guī)劃主問題與多參數(shù)線性規(guī)劃子問題,算法在主問題與子問題之間迭代,直至主問題不可行終止.數(shù)值結(jié)果表明算法是有效的.
[Abstract]:Parametric programming is a kind of mathematical programming problem with continuous variables, discrete variables and parameters. This problem is widely used in engineering, economy, model predictive control and other fields. The study of this kind of problems has important theoretical significance and practical application value. Multi-parameter linear programming and multi-parameter mixed integer linear programming are important branches of parameter programming. In this paper, the computational problems of these two kinds of multiparameter linear programming are studied. The first part is based on Rivotti's theory of multi-parameter linear programming. A new multi-parameter linear programming algorithm (multi-parametric linear programming, MPLP).) is proposed to solve the problem of multi-parameter linear programming with constraint functions. The basic idea of the algorithm is based on the sensitivity theory, using the affine expression of the optimal solution to obtain the initial solution, and systematically characterizing the parameter space through a set of optimal domains, and recursively exploring the solution of the problem in the parameter space. The effectiveness of MPLP algorithm is proved by three numerical examples. In the second part, we consider the computation of mixed integer linear programming problem with multiple parameters. The problem is decomposed into mixed integer linear programming main problem and multi-parameter linear programming subproblem. The algorithm iterates between the main problem and the subproblem until the main problem is infeasible. Numerical results show that the algorithm is effective.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O221.4

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