A New Single-Parameter Bees Algorithm

Based on bee foraging behaviour, the Bees Algorithm (BA) is an optimisation metaheuristic algorithm which has found many applications in both the continuous and combinatorial domains. The original version of the Bees Algorithm has six user-selected parameters: the number of scout bees, the number of high-performing bees, the number of top-performing or "elite" bees, the number of forager bees following the elite bees, the number of forager bees recruited by the other high-performing bees, and the neighbourhood size. These parameters must be chosen with due care, as their values can impact the algorithm's performance, particularly when the problem is complex. However, determining the optimum values for those parameters can be time-consuming for users who are not familiar with the algorithm. This paper presents BA₁, a Bees Algorithm with just one parameter. BA₁ eliminates the need to specify the numbers of high-performing and elite bees and other associated parameters. Instead, it uses incremental k-means clustering to divide the scout bees into groups. By reducing the required number of parameters, BA₁ simplifies the tuning process and increases efficiency. BA₁ has been evaluated on 23 benchmark functions in the continuous domain, followed by 12 problems from the TSPLIB in the combinatorial domain. The results show good performance against popular nature-inspired optimisation algorithms on the problems tested.