Fast Distributed Near-Optimum Assignment of Assets to Tasks

We investigate the assignment of assets to tasks where each asset can potentially execute any of the tasks, but assets execute tasks with a probabilistic outcome of success. There is a cost associated with each possible assignment of an asset to a task, and if a task is not executed there is also a cost associated with the non-execution of the task. Thus any assignment of assets to tasks will result in an expected overall cost which we wish to minimise. We formulate the allocation of assets to tasks in order to minimise this expected cost, as a nonlinear combinatorial optimisation problem. A neural network approach for its approximate solution is proposed based on selecting parameters of a Random Neural Network (RNN), solving the network in equilibrium, and then identifying the assignment by selecting the neurons whose probability of being active is highest. Evaluations of the proposed approach are conducted by comparison with the optimum (enumerative) solution as well as with a greedy approach over a large number of randomly generated test cases. The evaluation indicates that the proposed RNN based algorithm is better in terms of performance than the greedy heuristic, consistently achieving on average results within 5% of the cost obtained by the optimal solution for all problem cases considered. The RNN based approach is fast and is of low polynomial complexity in the size of the problem, while it can be used for decentralised decision making.