The Logarithmic Random Bidding for the Parallel Roulette Wheel Selection with Precise Probabilities

Abstract: The roulette wheel selection is a critical process in heuristic algorithms, enabling the probabilistic choice of items based on assigned fitness values. It selects an item with a probability proportional to its fitness value. This technique is commonly employed in ant-colony algorithms to randomly determine the next city to visit when solving the traveling salesman problem. Our study focuses on parallel algorithms designed to select one of multiple processors, each associated with fitness values, using random wheel selection. We propose a novel approach called logarithmic random bidding, which achieves an expected runtime logarithmic to the number of processors with non-zero fitness values, using the CRCW-PRAM model with a shared memory of constant size. Notably, the logarithmic random bidding technique demonstrates efficient performance, particularly in scenarios where only a few processors are assigned non-zero fitness values.