Optimization of Prime Modules Multiplicative Linear Congruential Generators for Genetic Algorithms

To improve the efficiency of Genetic Algorithms (GAs), huge modulus is usually applied to achieve good figure of merit of Prime Modules Multiplicative Linear Congruential Generator (PMMLCGs). As a result, the intermediate computing results likely integer overflows without special attention and the generating speed needs to be improved. It proposes the optimization methods for direct jump ahead in the random sequence, analyzes the impact of the two main influencing factors, that is, algorithms and the type of implementation, on the efficiency of typical PMMLCGs, both individual and combined. From numerical experiment results, it concludes that modulo decomposition method outperforms functionalities provided by CRT library, that contrary to usual expectations, bitwise shift method ranks last in terms of CPU times consumed, that whether floating-point arithmetic show the superiority over integer arithmetic depends on the complexity of PMMLCGs, and that the type of PMMLCGs coefficients has little negligible effects on PMMLCGs. Research results lay a solid foundation for the implementation of parallel GAs, and help to improve the efficiency of GAs.