Research And Application Of Interval Optimization Algorithm With Width-limited Variables

Interval optimization algorithm is a kind of optimization method which takes interval numbers as the variables based on interval theory.Compared with the point optimization algorithm,interval optimization algorithm can provide a better feasible region for the complex industrial process,reduce the influence of noise and disturbance effectively,and solve the optimization problem with uncertainty in the industrial process.In order to reduce the impact of excessive expansion of interval arithmetic problems,and try to make the solution interval close to the correct value,the traditional interval optimization methods make the interval width very small.This processing is acceptable in the algorithm research.Due to the control requirements or tracking accuracy of control loop limits,interval widths generally have certain requirements which make the solutions not close to point.And now the traditional interval algorithm may not obtain the correct interval solutions with unrestrained excessive expansion in industrial process control.Based on the analysis of the existing theories and algorithms,this thesis proposes an interval optimization algorithm whose variables' widths are restricted to meet the demands.Research contents of this thesis mainly include the following aspects:(1)Summarize the interval algorithm and classify the domestic and international's study on interval algorithm.Introduce the basic knowledge like interval numbers,interval arithmetic,interval extension form,interval arithmetic properties;Introduce and analyze the existing optimization methods:Interval dichotomy and Interval particle swarm optimization algorithm.(2)Analysis the reasons why the above two kinds of interval optimization methods cannot effectively solve the optimization problems when the interval variables' widths are limited.This thesis puts forward a way to solve correlation problem of interval computation:Interval integral approximation.Modify the above two algorithms on the basis of the method.(3)Introduce the basic concept of multi-objective optimization algorithm,analysis the multi-objective optimization algorithm.And then propose a kind of multi-objective interval particle swarm optimization algorithm with the concepts like interval dominance,crowding distance.(4)Analysis the fermentation process of glutamic acid and establish a BP neural network model for this process.Then,the BP neural network was extended to the interval BP neural network.On the basis of the establishment of the fermentation model,the whole fermentation process is divided into two stages which can be respectively optimized by the above single-objective optimization and multi-objective optimization to get the highest acid production rate and the optimal interval value of the decision variables.