| Summary: | 碩士 === 淡江大學 === 電機工程學系 === 87 === Genetic Algorithm is a very important and effective optimizer because of its global searching capability. In this decade, Genetic Algorithms are applied in various problems in many disciplines. In general, the searching result does not depend on the initial guess since GA searches multiple points simultaneously, for which three operators (named as selection, crossover and mutation) are applied on some randomly generated initial population consisting of many individuals to achieve the goal of survival of the fittest. However, the price paid for the multiple-point searching scheme is the increase of computation time. Hence, various techniques are continuously proposed to improve the computational efficiency, which is quite important for GA. In this thesis, the non-uniform probability density functions are first employed in the crossover and mutation operators of GA during the course of searching to improve the computational efficiencies. The capability of escaping from local optima is improved such that the global optimum can be easily achieved. In addition, the convergence speed is also raised. Consider the fact that the parameters are encoded during the course of optimization using GA. After encoding, the most left hand side bit is the most significant bit MSB, while, the most right hand side bit is the least significant bit LSB. It is recognized that the correctness of those bits about the MSB determines the correctness of the parameters. The correctness of those bits about the LSB only determines the precision of the parameters. On the other hand, the changes of those bits near MSB imply a large range searching in parameter space, while, the changes of those bits near LSB imply a small range searching in parameter space. For the crossover and mutation operators of a classical GA, the weighting difference of different bits are not recognized and implemented. That is, the probability of crossover and mutation for each bit is the same in a classical GA. In this thesis, some non-uniform probability density functions are first introduced for the crossover and mutation operators. One objective is to enhance the crossover and mutation probability for the bits near MSB region when the best individual of current generation is still far from the global optimum region. This certainly would increase the escaping capability of GA from the local optimum. The other objective is to enhance the crossover and mutation probability for the bits near LSB region when the best individual of current generation is near the global optimum region. This would increase the convergence speed. In order to achieve the above objectives some mechanisms are required to suitably move the probability density functions. Therefore, two mechanisms are proposed, called Cyclical GA and Adaptive GA, in this thesis, and their efficiency improvements are checked. We found both GAs work for different testing functions, including those that are hard to converge for classical GA.
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