232 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 90 NR 4/2014 Jarosław JAJCZYK Poznan University of Technology, Institute of Electrical Engineering and Electronics Optimization calculations with the genetic algorithm method on a computer cluster Abstract. The work presents a way to execute optimization calculations with the genetic algorithm method on a parallel computer of the cluster type. The scope of electromagnetic calculations which should be performed while determining the objective function was outlined. Sample indicators describing the quality of paralleling the calculation process were provided. Streszczenie. W pracy przedstawiono sposób realizacji obliczeń optymalizacyjnych metodą algorytmu genetycznego na komputerze równoległym typu klaster. Zakreślono zakres obliczeń elektromagnetycznych, które należy wykonać podczas wyznaczania funkcji celu. Podano przykładowe wskaźniki opisujące jakość zrównoleglenia procesu obliczeniowego (Obliczenia optymalizacyjne metodą algorytmu genetycznego na klastrze komputerowym). Keywords: optimization, genetic algorithm, computer cluster, parallel computing. Słowa kluczowe: optymalizacja, algorytm genetyczny, klaster komputerowy, obliczenia równoległe. doi:10.12915/pe.2014.04.56 Introduction Using computers in technical applications have become common. Contemporary computing machines are used in solving various problems regarding the design of equipment, selection of components, or determining optimal operation parameters. Thanks to computer technology, calculation results are obtained faster and with a higher level of precision [1,2,3,4,5]. What is more, considerable computation power of mobile devices makes it possible to apply them more and more commonly. Thanks to that, more mobility of the calculation stands may be obtained and wireless communication allows for cooperation with other devices. The possibility to use computers for numeric calculations becomes particularly helpful in the context of complex problems. In such cases, an analytical solution often cannot be achieved and numeric calculations, although they do lead to the result, mean a long waiting time before the solution is obtained due to the complexity of the calculations themselves. Using parallel computers becomes an advantageous solution in such situations. This approach is particularly helpful while executing optimization during which calculations are repeated multiple times in order to identify the optimal solution. This, of course, has a negative influence on the calculation time. Paralleling the calculations, including optimization calculations, is often difficult to implement due to the complexities resulting from the need to exchange data between the calculation units. Often the time costs connected with the communication between computers (processors) lead to a reverse effect instead of shortening the waiting time before the solution is obtained. An efficient solution of this problem in optimization calculations is a combination of parallel calculations and optimization with the use of a genetic algorithm (GA). In many cases, proper configuration of such an algorithm limits the data exchange between particular calculation units to a level that has practically no influence on the waiting time before the solution is obtained [2,5,6,7]. The work presents the results which reflect the quality of paralleling optimization calculations of a three-phase busduct. The subject of optimization was its geometrical dimensions. The genetic algorithm method was used as the optimization method. A computer cluster formed by PC computers connected with a broadband computer network was used to run the calculations. The efficiency of the implementation of the optimization problem analyzed with the use of a genetic algorithm on a computer cluster was examined. Organization of optimization calculations Optimization with the use of the GA method involves defining the quality factors for the solutions (individuals) that form a specific group (population) of solutions on the basis of which the next population is built [6,7]. What is characteristic of the GA method is the fact that the calculations of the fitness of particular individuals are performed independently of one another. This fact can successfully be used to parallel the algorithm. The following could be distinguished among different methods of paralleling a genetic algorithm: a centralized synchronous organization, a centralized semi-synchronous organization, a distributed asynchronous organization, a network organization, a community organization, and a pollen organization [7]. The use of some of those methods results in the need to assure uninterrupted communication and sending large amounts of data between the calculation nodes. The first two of the methods listed above are characterized by the lowest time costs connected with the communication among particular computers. Fig.1. The organization of the parallel genetic algorithm A synchronous centralized organization of a parallel GA algorithm was used in the present work (Fig. 1). In this case, one computer on which the main process is run is responsible for all genetic operations and for distributing the tasks to other calculation units which are responsible for the identification of the fitness characteristics of particular individuals [2,5,6,7]. Thanks to the fact that computation power consumption of the main process is low in comparison to the subordinate Genetic operations Calculation of objective function Calculation of objective function Calculation of objective function Calculation of objective function Calculation of objective function Calculation of objective function Calculation of objective function Calculation of objective function