OPTIMIZATION USING NEURAL NETWORKS

Artificial neural networks can achieve high computation rates by employing a massive number of simple processing elements with a high degree of connectivity between the elements. Neural networks with feedback connections provide a computing model capable of exploiting fine-grained parallelism to solve a rich class of optimization problems. Network parameters are explicitly computed, based upon problem specifications, to cause the network to converge to an equilibrium that represents a solution. This paper presents a systematic approach to designing neural networks for optimization applications. It reviews the theoretical basis for applying neural networks to optimization and presents a design rule that facilitates the construction of time evolution equations describing a network's behavior. The design role is employed to specify the connection strengths and external inputs that enforce constraints expressed as equalities as well as constraints expressed as inequalities. The approach is demonstrated by designing a network that finds good solutions to a complex, nonlinear resource allocation problem-the problem of allocating weapons to counter offensive threats. The neural solution, which employs more than 46000 neural elements and more than 49 million connections, has been simulated on a high-speed parallel processor. This network has produced excellent solutions to a realistic threat scenario. The results demonstrate that it is possible to employ a systematic approach in designing neural networks for optimization problems and that large-scale neural networks are capable of yielding high-quality solutions to complex problems.