An Annealing Approach to the Mating-Flight Trajectories in the Marriage in Honey Bees Optimization Algorithm

Marriage in Honey Bees Optimization (MBO) is a new swarm intelligence technique inspired by the marriage process of honey bees. It has been shown to be very effective in solving a special group of propositional satisfiability problems called 3-SAT. In the current MBO implementation, the acceptance of a drone for mating is determined probabilistically using a variation of the annealing function. However, the algorithm does not exactly implement an annealing approach as it follows a pure exploration strategy. Currently, all state transitions made during the queens’ mating-flight are generated independent of the queens’ fitness, are always accepted as long as they are created, and used to spawn the drones. The objective of this paper is to investigate a more conventional annealing approach for the mating-flight process to balance search exploration with search intensification. It is proposed that the trajectories of the queens’ mating-flight in the search space are accepted according to a probabilistic function of the queens’ fitness. This modified MBO algorithm is tested using a group of randomly generated hard 3-SAT problems to compare its behavior and efficiency against the original implementation. We found that the proposed annealing function improved one of the MBO implementations and MBO outperformed all the standalone SAT heuristics including WalkSAT.