Abstract
In this paper a three-step parameters tuning model for time-constrained Genetic Algorithms (GAs) was presented. The first step involved modeling the objective function using multiple regression model where the fitness value was the response variable and the GA parameters were the regressors. The second step involved constraint modeling using the objective function found in the first step and using the upper and lower limits of the GA parameters along with an upper limit on the execution time as constraints. The third step involved optimizing the constraint model found in the second step using a suitable deterministic optimization method to determine the optimal GA parameters taking into consideration four aspects that affect the GA performance. These aspects were: the problem under consideration, the GA parameters used, the execution time, and the power of the computer used.The validation of this model was demonstrated using two capacitated lot sizing problems. The model was able to predict the fitness values and the optimal parameters of the GA for these problems to a high degree of precision. Moreover, the results showed that tuning the GA parameters using multiple regression along with a suitable deterministic optimization method was an effective and robust method that enhanced the performance of the GA. The statistical analysis showed that in order to do a proper tuning for a certain GA, the designer of the GA must take into consideration not only the type of problem but also the size of the problem, the allowable execution time, and the hardware used in executing the GA. Furthermore, the results agreed with the "No Free Lunch" theorem.
Highlights
Genetic algorithms are search algorithms based on the mechanism of the natural selection
If a Travel Salesman Problem (TSP) is considered, the complexity of the problem increases as the number of nodes increases, the matter that calls for using a different set of parameters in the Genetic Algorithms (GAs) for each different TSP problem according to its complexity
The third step involved optimizing the constraint model found in the second step using a suitable deterministic optimization method to determine the optimal GA parameters taking into consideration four aspects that affect the GA performance
Summary
Genetic algorithms are search algorithms based on the mechanism of the natural selection. GA can have many parameters that need to be tuned to optimize its performance These parameters include, and not limited to, population size, generation number, crossover rate, execution time, and mutation rate. For example Ramadan used a linearly adaptive crossover rate and mutation rate parameters in multiple objective GA to optimize the reliability testing These adaptive rates are considered as parameters control not parameters tuning as the values of the parameters are changed according to the generation number. Unlike Meta-EA, the Racing searching method does not need a distance metric; it can be used to compare different GAs. In this paper, the GA parameters tuning problem is solved in three steps: the first step involved modeling the objective function using multiple regression model where the fitness value was the response variable and the GA parameters were the regressors. Tests of hypotheses were conducted to test whether there is a significance difference between the average performances of the GA under the associated aspect
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