Optimal Placement Algorithm for Beehives with Pollination Probability Model

Abstract

The beehive placement problem is an important optimization problem widely applied in industrial and logistics domains. This paper proposes pollination probability model and beehive covering model, converting beehive placement problem into spatial partition problem. We perform Voronoi diagram on the farmland based on triangulated beehive points set and define an energy function on each block, decreasing the value of the energy function by continuously moving the hive to the geometric center of each block, iterating until the maximum number of iterations is reached or the maximum moving distance is less than ε. After the iteration, the minimum pollination probability in each block will be calculated. If the probability of a block is less than ξ, the number of beehives will be increased and the algorithm will be re-run until all blocks satisfy the condition. Simply enter the shape of the farmland into the model to get the optimal hive placement, the model works with all common polygonal shapes and can be applied to other similar problems with little modification.