The Design and Study of Algorithms for Stochastic and Fuzzy Programming

Abstract: There are often uncertainties in the phenomena of nature. Of these uncertainties, the most often seen is stochastic uncertainty. With the development of the study, scholars found that there is also fuzzy uncertainty. Mainly, uncertain programming includes stochastic programming and fuzzy programming. For these programming, there are many applications in the production process, management science. To solve these programming, traditionally the main method is converting them into certain programming. This is indirect method, there are many shortcomings of this method, because most uncertain programming can't be converted into certain ones, what's more, if converted, the converted certain programming is often nonlinear, so it's also hard to cope with. With the development of computers, many hard questions can be solved by computers, the common method is putting stochastic simulation (also fuzzy simulation) into modern intelligent algorithms, and this method can be called direct method. From the perspective of algorithm, every algorithm has its merits and shortcomings, so itis of great importance to design new algorithm and modify the existing-algorithms according to the characteristics of the object functions, so as to make results more accurate and to make algorithm easier, this is our intent.Firstly in this paper steepest-descent algorithm is put into modern intelligent algorithm (particle swarm optimization) to solve certain model, by example the results show that it is applicable. Secondly this paper successfully solved the stochastic programming by putting stochastic simulation into gradient-descent algorithm. Thirdly fuzzy simulation is put into down-hill algorithm and simulated annealing to solve the fuzzy simulation;the results show that it is also applicable. Finally stochastic simulation and fuzzy simulation are put into particle swarm optimization algorithm to solve stochastic model and fuzzy model.To the algorithm study of stochastic programming and fuzzy programming, thinking of this paper is a reference…
Key words: uncertain programming; particle swarm optimization; descent algorithm; simulated annealing; stochastic simulation; fuzzy simulation

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