Fractional-Neuro-Optimizer: A Neural-Network-Based Optimization Method

Abstract

Up to now, there have been many attempts in the use of artificial neural networks (ANNs) for solving optimization problems and some types of ANNs, such as Hopfield network and Boltzmann machine, have been applied for combinatorial optimization problems. However, there are some restrictions in the use of ANNs as optimizers. For example: (1) ANNs cannot optimize continuous variable problems; (2) discrete problems should be mapped into the neural networks' architecture; and (3) most of the existing neural networks are applicable only for a class of smooth optimization problems and global convexity conditions on the objective functions and constraints are required. In this paper, we introduce a new procedure for stochastic optimization by a recurrent ANN. The concept of fractional calculus is adopted to propose a novel weight updating rule. The introduced method is called fractional-neuro-optimizer (FNO). This method starts with an initial solution and adjusts the network's weights by a new heuristic and unsupervised rule to reach a good solution. The efficiency of FNO is compared to the genetic algorithm and particle swarm optimization techniques. Finally, the proposed FNO is used for determining the parameters of a proportional---integral---derivative controller for an automatic voltage regulator power system and is applied for designing the water distribution networks.