This article compares three techniques for allocating tasks in a mesh-based multi-computer. Tasks are expressed as rectangles of a certain width and height corresponding to the topology of processors desired. The task allocation problem, is thus a variant of the bin-packing problem, with one major difference: in the bin-packing problem one seeks to minimize the height of the bin, while here we seek to maximize the utilization of processors in a multicomputer. The three techniques compared are a classical level-by-level algorithm, a connectionist simulated annealing variant of the Hopfield network, and a genetic algorithm. An extension to the dynamic processor allocation problem is modeled by fixing some rectangles in place and packing the request rectangles in the residual space on the mesh; this corresponds to a pre-existing condition, i.e., some tasks have already been allocated to the Processor Mesh. Implementation and experimental results are presented.
Mathematical Model and Algorithm for the Task Allocation Problem of Robots in the Smart Warehouse