Buf-pga : a Butter Blockiny-topology Parallel Ga as a Function Optimizer Extended Abstract

Genetic algorithms (GAs) are receiving increased attention in di cult search and optimization applications, however in solving larger and more di cult search problems, adequate solutions may not be found in an expected range of time. Consequently multiple e orts have been conducted to make GAs faster and implementing them in parallel is one of the most promising choices [4]. Parallel GAs may be categorized as follows : micro-grain parallel GAs, ne-grain parallel GAs, and coarse-grain parallel GAs. Fine-grain parallel GAs which are subject of this work, partition the population into a large number of very small subpopulations. The ideal case is to have just one individual for every processing element available as its subpopulation. This model is suited for massively parallel computers, however, it can be implemented on any other multiprocessor as well. There is a considerable number of related research reported using di erent topologies such as ladder-like, two dimensional grid, hypercube, and so on. Although some topologies like butter y attracted little attention [5], despite of their suitable features for this model. The butter y is one of the most versatile and e cient networks yet discovered for parallel computation. It is well suited for both special-purpose and general-purpose tasks, and it can e ciently simulate any other network of the same size [2]. Massive communications capability of the butter y provides a way to disseminate good solutions across the entire population. Therefore, this topology appears to be a corrective choice for the architecture of a ne-grain parallel GA. In this paper, a proposed ne-grain parallel GA based on the butter y topology, henceforth referred to as Buf -PGA, has been discussed and its performance is compared with a 2-dimensional grid ne-grain parallel GA. Our implementation deals with several subpopulations distributed in the network, which leads to overcoming the problem of premature convergence. Di erent regions of the search space are being evaluated at the same time and variability has been maintained for a longer period. Taking a hint from nature, we have no global selection and no global tness-distribution. Natural selection is a local phenomenon taking place in an individual's local environment. We patterned after nature by de ning a neighborhood around each node which provides an environment for that node's individuals to nd a mate and to breed. In the nature, individuals are not restricted to their local environment all the time. Following this fact, our proposed neighborhood is not xed and can be expanded with a not-so-high probability. We have successfully applied Buf -PGA to a number of problems, including function optimization. De Jong standard functions are used as a benchmark problem and computer