Uinform Design And Entropy Based Genetic Algorithm And Its Application In Linear System Control

In the world, many problems could be transformed into search or optimization problem.Genetic algorithm now becomes the powerful solution of such problems, especially for those unorthodox multivariate complex problems. Genetic algorithm is a oriented parallel heuristic random search algorithm by simulating the biology evolution and inherit process in natural. Its search mechanism which oriented by fitness and randly cross and mutate is very similar to "taiji" and make it have the capability of global optimization and local search simultaneity.But as an oriented random algorithm, it also has some shortcomings like premature convergence and instable results,etc.Against genetic algorithm strengths and weaknesses, this paper,uses its strong points and closes its gap, carrys forward the mind which blends uniform trial design and information entropy in genetic algorithm conceives a improved genetic algorithm to find and deal with the deceptive problem in search process. The test on three common benchmarks test functions indicates that this algorithm can converge stably, quickly and accuracly.The major work and innovation of this paper as follows:1) This paper first elaborates on genetic algorithm development and application from a unique perspective about genetic operator presence and development process and how combine concrete problem with them,and also gives the general development trend of genetic algorithm. 2) This paper first systematically elaborates on how use uniform design to generate an initial population and compares its result with the randomly generated though the disperse of the parametes of initial population in the graphs.3) This paper first roundly introduces the definition of population entropy in genetic algorithm,and defines the other three entropys:genes entropy G, individual characteristic entropy E and population characteristic entropy PE,and according to the simulation results,expounds the physical meanings about too large or small values of various entropys,and gives the relevant conclusions4) This paper uses foregoing entropys in genetic algorithm to find deceptive problem that exist in the search process and lead the process to leap out the problem, and also designes a fitness function which can adaptively adjust the individual fitness value according to the population entropy.5) This paper first applys genetic algorithm to solve the problems in linear systems control:The Riccati matix algebraic equation in LQ problem of unlimited time and Optimize the design of muti-input Kx-function observer.