The value of the fitness function J(e(k)).While for some applications this value may not be important, for others it is critical(e.g, in many function optimization problems) Information about the way that the population has evolved, which areas of the search space were visited, and how the fitness function has evolved over time. You may want to design the code that implements the genetic algorithm to provide plots or printouts of all the relevant genetic algorithm data There is then the question of how to terminate the genetic algorithm. There are many ways to terminate a genetic algorithm, many of them similar to termination conditions used for conventional optimization algorithms. To introduce a few of these, let be a small number and M, >0 and M2>0 be integers. Consider the following options for terminating the genetic algorithm Stop the algorithm after generating generation P(M2)that is, after M2 generations Stop the algorithm after at least M2 generations have occurred and at least MI steps have occurred where the maximum(or average)value of for all population members has increased by no more than e Stop the algorithm once takes on a value above some fixed value Of course, there are other possibilities for termination conditions. The above ones are easy to implement on a computer but sometimes you may want to watch the parameters evolve and decide your self when to stop the algorith Initialization of the genetic algorithm is done by first choosing the representation to be used (including the structure of the chromosomes, the number base, and the number of digits to be used). Next, you need to specify the size of the population, decide which genetic operations will be used, specify the crossover and mutation probabilities pc and and pick a termination method (if it is ne Sometimes for problems that are solved by the genetic algorithm it is known that the parameters that are manipulated by the genetic algorithm will lie in a certain fixed range (e.g, you may know that you would never want to make the proportional gain of a PID controller negative). Suppose, for the sake of discussion, that is a scalar and we know a priori that it will stay in a certain interval--say [0min 0max ]. It is important to note that crossover and mutation can generate strings that are out d range even if parameters all start within the proper ranges(provide an example of this ). due to this there is a problem when it comes to implementing the genetic algorithm of what to do when the algorithm generates a chromosome that is out of range. There are several approaches to solving this problem For instance, if a scalar parameter 0 is to lie in and at time k crossover or mutation makes e(k)>0m then simply choose 0(k)=Omx. If at time k crossover or mutation makes o(k)>0m,then simply choose 0(k)=0min. An alternative approach would be to simply repeat the crossover or mutation operation again and hope that the newly generated parameters will be in range. Of course, this may not solve the problem since the next time they are generated they may also be out of range(and the number of tries that it takes to get in range is random) 4.4.2 Genetic Algorithms for Fuzzy System Design and Tuning There are basically two ways that the genetic algorithm can be used in the area of fuzzy systems: They can be used for the off-line design of fuzzy systems and in their on-line tuning. Both of these options are considered next Computer-Aided design of Fuzzy Systems The genetic algorithm can be used in the(off-line) computer-aided design of control systems since it can artificially evolve an appropriate controller that meets the performance specifications to the greatest extent possible. To do this, the PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cn• The value of the fitness function ( ) * J k q ( ) . While for some applications this value may not be important, for others it is critical (e.g., in many function optimization problems). • Information about the way that the population has evolved, which areas of the search space were visited, and how the fitness function has evolved over time. You may want to design the code that implements the genetic algorithm to provide plots or printouts of all the relevant genetic algorithm data. There is then the question of how to terminate the genetic algorithm. There are many ways to terminate a genetic algorithm, many of them similar to termination conditions used for conventional optimization algorithms. To introduce a few of these, let be a small number and M1 > 0 and M2 > 0 be integers. Consider the following options for terminating the genetic algorithm: • Stop the algorithm after generating generation P(M2)—that is, after M2 generations. • Stop the algorithm after at least M2 generations have occurred and at least M1 steps have occurred where the maximum (or average) value of J for all population members has increased by no more than ε. • Stop the algorithm once J takes on a value above some fixed value. Of course, there are other possibilities for termination conditions. The above ones are easy to implement on a computer but sometimes you may want to watch the parameters evolve and decide yourself when to stop the algorithm. Initialization of the genetic algorithm is done by first choosing the representation to be used (including the structure of the chromosomes, the number base, and the number of digits to be used). Next, you need to specify the size of the population, decide which genetic operations will be used, specify the crossover and mutation probabilities pc and pm, and pick a termination method (if it is needed). Sometimes for problems that are solved by the genetic algorithm it is known that the parameters that are manipulated by the genetic algorithm will lie in a certain fixed range (e.g., you may know that you would never want to make the proportional gain of a PID controller negative). Suppose, for the sake of discussion, that is a scalar and we know a priori that it will stay in a certain interval—say [q q min , max ]. It is important to note that crossover and mutation can generate strings that are out of a fixed range even if parameters all start within the proper ranges (provide an example of this). Due to this there is a problem when it comes to implementing the genetic algorithm of what to do when the algorithm generates a chromosome that is out of range. There are several approaches to solving this problem. For instance, if a scalar parameter θ is to lie in [q q min , max ] , and at time k crossover or mutation makes max q q ( ) k > then simply choose max q q ( ) k = . If at time k crossover or mutation makes max q q ( ) k > , then simply choose min q q ( ) k = . An alternative approach would be to simply repeat the crossover or mutation operation again and hope that the newly generated parameters will be in range. Of course, this may not solve the problem since the next time they are generated they may also be out of range (and the number of tries that it takes to get in range is random). 4.4.2 Genetic Algorithms for Fuzzy System Design and Tuning There are basically two ways that the genetic algorithm can be used in the area of fuzzy systems: They can be used for the off-line design of fuzzy systems and in their on-line tuning. Both of these options are considered next Computer-Aided Design of Fuzzy Systems The genetic algorithm can be used in the (off-line) computer-aided design of control systems since it can artificially evolve an appropriate controller that meets the performance specifications to the greatest extent possible. To do this, the PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn