  This paper presents an evolutionary metaheuristic called Multiple Search
Neuroevolution (MSN) to optimize deep neural networks. The algorithm attempts
to search multiple promising regions in the search space simultaneously,
maintaining sufficient distance between them. It is tested by training neural
networks for two tasks, and compared with other optimization algorithms. The
first task is to solve Global Optimization functions with challenging
topographies. We found to MSN to outperform classic optimization algorithms
such as Evolution Strategies, reducing the number of optimization steps
performed by at least 2X.
  The second task is to train a convolutional neural network (CNN) on the
popular MNIST dataset. Using 3.33% of the training set, MSN reaches a
validation accuracy of 90%. Stochastic Gradient Descent (SGD) was able to match
the same accuracy figure, while taking 7X less optimization steps. Despite
lagging, the fact that the MSN metaheurisitc trains a 4.7M-parameter CNN
suggests promise for future development. This is by far the largest network
ever evolved using a pool of only 50 samples.
