ELSEVIER Fuzzy Sets and Systems 87 (1997) 265-276 FUZZY sets and systems Real-valued genetic algorithms for fuzzy grey prediction system Yo-Ping Huang*, Chih-Hsin Huang Department of Computer Science and Engineerin 9, Tatung Institute of Technology, Taipei, Taiwan 104, ROC Received June 1995; revised December 1995 Abstract A genetic-based fuzzy grey prediction model is proposed in this paper. Instead of working on the conventional bit by bit operation, both the crossover and mutation operators are real-valued handled by the presented algorithms. To prevent the system from turning into a premature problem, we select the elitists from two groups of possible solutions to reproduce the new populations. To verify the effectiveness of the proposed genetic algorithms, two simple functions are first tested. The results show that our method outperforms the conventional one no matter whether from the viewpoint of the number of iterations required to find the optimum solutions or from the final solutions obtained. The real-valued genetic algorithms are then exploited to optimize the fuzzy controller which is designed to perform the compensation job. Two different types of fuzzy inference rules are considered to compensate for the predicted errors from the grey model. The difficulty encountered in applying the genetic algorithms to adjusting the fuzzy parameters is also discussed. Based on the simulation results from the problems of the weather forecast, we found that the proposed methodology is very effective in determining the quantity of compensation for the predicted outputs from the traditional grey approach. © 1997 Elsevier Science B.V. Keywords: Genetic algorithms; Fuzzy grey system; Fuzzy inference models 1. Introduction Recently, genetic algorithms have been widely ap- plied to different optimization problems [3-5]. Unlike the conventional algorithms which optimize the prob- lems from a single direction, the genetic algorithms search for the optimal solutions from multiple direc- tions. This allows the genetic-based method to have a better chance of finding the optimal or near-optimal solutions. Besides, due to the simplicity in program- ming, the genetic algorithms can be considered to replace the gradient descent method [6, 9] to automat- ically optimize both the parameters and the structure in the fuzzy system. * Corresponding author. In order to search for the optimal solution for a given problem, a fitness function is defined to evaluate the performance for each chromosome. The well-known roulette wheel selection criterion [4] is adopted here to decide whether a chromosome can survive or not in the next generation. The survival chromosomes are then put into a mating pool for the crossover and mutation operations. Once a pair of strings have been selected for crossover, a randomly selected site is assigned into the to-be-crossed strings. One substring then ex- changes part of its string (from the crossover site to the end of the string) with the other's. The newly-crossed strings join the rest of the chromosomes to form a new population. The mutation operation follows the crossover to offer a chance for each bit to flip. The evolution continues until some preset criteria are met. 0165-0114/97/$17.00 ~) 1997 Elsevier Science B.V. All rights reserved PII S0165-0114(96)00011-5