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Capturing the brachistochrone: Neural network supervised and reinforcement approaches
Published in ICIC International
2019
Volume: 15
   
Issue: 5
Pages: 1747 - 1761
Abstract
This paper attempts to answer the question regarding the capability of neural networks (NN) to capture an optimum control problem for finding a minimum time path constrained problem. It is called the Brachistochrone. This problem is a famous calculus of variations problem seeking the optimization of an integral that has a solution in the form of a curve or a two-dim function. The proposed neural network (NN) model did not only imitate the learning samples but could capture and understand the law of control (surface) for this benchmark problem as we will see in the paper. The genetic algorithm (GA) is used in extracting many solutions for the problem at different initial conditions. Samples of solution extracted by the genetic algorithm (GA) in addition to some solutions found by a classical numerical optimization algorithm (Nelder-Mead) are used in training a neural network in a supervised model. Another neural network with a different architecture, the grid architecture, and a new reinforcement-learning algorithm is used to train the neural network to capture the Brachistochrone. This time no supervisor is used in training. Results of simulations are presented, comparisons are made and promising findings are reached that indicate the capabilities of different neural networks paradigms to learn and capture optimum control strategies. © 2019, ICIC International.
About the journal
JournalInternational Journal of Innovative Computing, Information and Control
PublisherICIC International
ISSN13494198
Open AccessNo