Determination of Optimal Linear Congruence Generators Parameters with Heuristic Optimization Algorithms

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Abstract
Random number generators play a critical role in many scientific and engineering applications, particularly in simulation, cryptography, and optimization. Among these generators, Linear Congruential Generators (LCGs) are widely used due to their simplicity and computational efficiency. However, the statistical quality of the generated sequences strongly depends on the proper selection of generator parameters. In this study, the determination of optimal LCG parameters is formulated as a heuristic optimization problem. The Improved Grey Wolf Optimizer (IGWO) is employed to search for suitable multiplier, increment, and seed values. The proposed approach aims to achieve a uniform distribution of generated numbers while maintaining low correlation between consecutive values. The performance of the optimized LCG is evaluated using the objective fitness function as well as additional statistical performance metrics derived from the generated sequences. The effectiveness of the proposed IGWO-based optimization approach is demonstrated through repeated independent runs using the same fitness evaluation framework. Experimental results demonstrate that the proposed approach provides improved parameter selection for LCGs and enhances the statistical properties of the generated random sequences.

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