Study On The Theory And Solution Methods Of Uncertain Optimization Problem Based On Interval Number

Uncertainty widely exists in practical problems, and studying the theories and solutionmethods of uncertain programming is significant for reflecting and solving the practicalproblems truthfully and effectively. There are three classes of uncertain programming basedon different description of the uncertain parameter that are stochastic programming, fuzzyprogramming and interval programming. However, in the practical application, it is difficultto get the probability distribution function of random parameter and the membership functionof fuzzy parameter. On the contrary, it is easier to get the range of the uncertain parameter. Sothe uncertain programming can be better solved using the interval programming method.However, there are some problems in the process of interval programming research, forexample, most of researches focus on the interval linear programming, but the intervalnonlinear programming is not be given enough attention and the interval programming theoryhas not formed a mature and complete system yet. Thus the further study for the intervalprogramming especially the interval nonlinear programming is significant for thedevelopment and progress of the interval programming theory.This paper conducts the research focusing on some problems of interval programmingtheory and aims at contributing some useful researches and trials on the interval programmingmathematic theory itself and the practical applications. As a result, the following studies arecarried out in this paper:(1) Firstly, the interval ranking method which is the basic problem of intervalprogramming is suggested, and the advantages and disadvantages of each method areintroduced, then a modified interval ranking method is proposed based on probability theory.(2) Secondly, for a general uncertain optimization problem, the interval objectivefunction and interval constraints can be transformed into deterministic forms, respectivelybased on the order relation of interval number and the modified interval ranking methodproposed formerly and the method of inverted constraint. As a result, a general uncertain optimization problem can be transformed into a deterministic one using the transformationprocess.(3) Thirdly, the corresponding solution methods are suggested for the transformationmodels, respectively based on optimistic and pessimistic decision makers. In the intervallinear programming, the PSO algorithm is proposed to solve the complicated constraints inthe transformation model. Similarly, in the interval nonlinear programming, the hybridintelligence algorithm is proposed based on the GA and ANN to solve the nested optimizationproblem in the transformation model.(4) In the end, two numerical examples are solved using the methods mentioned above.The results of the calculation show that the method proposed in this paper can solve theinterval optimization problems more effectively.