همگرایی الگوریتم ژنتیک عشایری در محک زدن توابع ریاضی

Nomadic genetic algorithm is a type of multi-population migration based genetic algorithm that gives equal importance to low fit individuals and adaptively chooses its migration parameters. It has been applied to several real life applications and found to perform well compared to other genetic algorithms. This paper exploits the working of nomadic genetic algorithm (NGA) for benchmark mathematical functions and compares it with the standard genetic algorithm. To compare its performance with standard GA (SGA), the prominent mathematical functions used in optimization are used and the results proved that NGA outperforms SGA in terms of convergence speed and better optimized values

Genetic algorithms [1] and [2] are a part of evolutionary computing which is a rapidly growing area of artificial intelligence. They are adaptive methods used to solve search and optimization problems. They are based on the genetic processes of biological organisms. By mimicking the principles of natural evolution, i.e. “Survival of the Fittest”, GAs are able to evolve solutions to real world problems. This paper describes both standard genetic algorithm and a variant of the standard genetic algorithm called nomadic genetic algorithm. It is a specialized form of genetic algorithm that works on the principle of “Birds of the same feather flock together”. Generally in standard GA different kinds of selection mechanisms like Roulette wheel selection, rank based selection, tournament selection, etc. are employed based on the type of application. All these selection mechanisms aim to select high fit individuals in different proportion for the purpose of mating. The low fit individuals are given very less chance for mating or they are totally discarded in some selection schemes thus reducing the diversity in the population. But the worst individuals, if given a chance may also result in better offspring in the next generation. This phenomenon is given importance in this variant of standard GA. Here, the individuals in the population are grouped into different communities or groups, based on their fitness value. Individuals, in a community mate with each other. Here again, different kinds of selection mechanisms could be used within the community. If any offspring comes up with a better fitness, it leaves its community and joins a different community, i.e. the group of similar fitness value. It employs most of the principles of standard GA except that, it allows for migration of individuals within the different communities in the population that the individuals are grouped into. The selection procedure followed in nomadic genetic algorithm insists on mating within the same community thus providing equal chances of mating even to the weakest section of the population. This allows the nomadic genetic algorithm to maintain the diversity of individuals in the population, also ensuring faster convergence. To prove the performance of NGA, the benchmark mathematical functions have been taken up for implementation and testing. The same set of functions are implemented for the SGA and the results are compared in terms of the number of generations required to converge and also the optimized values.

The results clearly prove that the migration based nomadic genetic algorithm performs very well when compared to standard GA in terms of minimizing the objective function value and number of generations to converge. The minimization of other mathematical functions which come under benchmark problems is currently under study. The NGA offers a well synchronized method for solution to any theoretical and practical problems with the virtue of giving importance to low fit individuals.