Parallel Machine Code Genetic Programming

AIMGP is a very fast linear genetic programming approach that evolves machine code programs. We report on a parallelization of AIMGP for a parallel transputer system resulting in an almost linear speedup. In linear genetic programming (GP) computer programs of imperative programmming languages like C or machine code are evolved (Banzhaf et al. 1998). AIMGP (Automatic Induction of Machine code by GP) is a variant of linear GP where the evolving programs are represented as variable length sequences of binary machine code instructions that are directly executed during tness calculation without interpretation. The method results in a signi cant speedup compared to interpreting GP systems. For the parallelization of AIMGP described here we employ a steady state evolutionary algorithm using tournament selection. Parallelization of evolutionary algorithms is usually based on the observation that a population of solutions may be broken up into sub-populations (demes) while each of these subpopulations is run on a separate processor. Migration of individuals among the various demes causes evolution to occur in the population as a whole. This approach is inspired by the island model in biology and has been applied by Andre and Koza for the rst multiprocessor implementation of a (traditional) GP system on a network of transputers (Andre et al. 1996). The processing units of the Parsytec Power Explorer (sixteen here) are arranged in a matrix topology in that every node is connected to exactly four adjacent neighbors. These links determine the possible migration paths of the individuals. The migration technique used here is motivated by nature where migration is more-or-less continuous. During each migration, only one individual is selected from each deme node following a non-elitist migration strategy. An identical copy of that individual is moved to all four adjacent nodes in the transputer network. In this way, the deme from which the emigration originated is unchanged. The rate of migration is controlled by the frequency with which migrations occur (every 1000 tournaments here). In this contribution results in relation to scalability are documented for a regression problem using the two dimensional objective function: f(x; y) = 5(x + y) 3x. In general a combination of parallel hardware and parallel algorithm is scalable if on average the product of the overall runtime and the number of processors remains constant with varying numbers of processors. In a perfectly scalable system the overall speed grows linearly with the number of processing units. In real systems scalability is restricted by the communication overhead between the nodes. Table 1 shows the overall runtime of the parallel system until the optimal solution ( tness 0) has been found for di erent numbers of processors and demes respectively. Increasing the number of processing units results in a scaling factor of about 3=4 here which comes close to a linear improvement of speed performance (scaling factor 1). Table 1: Average runtime ( ) and standard deviation ( ) in 10 evaluations for di erent processor numbers and a constant overall population size (16000). #Processors 1 4 16 #Individuals/Processor 16000 400