This data is collected from the simulation results of three experiments to fairly compare BSA with particle swarm optimization (PSO), artificial bee colony (ABC), firefly algorithm (FF), and differential evolution (DE) on minimising 16 benchmark problem by taking these conditions into account. The conditions are initialising control parameters, the dimension of the problems, their search space, and number of iterations needed to minimize a problem, the performance of the computer used to code the algorithms and their programming style, getting a balance on the effect of randomization, and the use of different type of optimization problem in terms of hardness and their cohort. Hence, this dataset is about the unbiased comparison of BSA with PSO, ABC, FF, and DE on solving 16 benchmark problems with different levels of hardness scores in three tests. The experimental results demonstrate that in solving various cohorts of numerical optimisation problems such as problems with different hardness score levels, problem dimensions, and search spaces, BSA is statistically superior to the aforementioned algorithms.