This work uses a grid search to explore hyperparameter configurations for a multilayer perceptron on five classification data sets, considering trade-offs of classification accuracy against training or inference energy, and finds that structural parameters like hidden layer size is a major driver of the energy-accuracy trade-off. Machine learning accounts for considerable global electricity demand and resulting environmental impact, as training a large deep-learning model produces 284000kgs of the greenhouse gas carbon dioxide. In recent years, search-based approaches have begun to explore improving software to consume less energy. Machine learning is a particularly strong candidate for this because it is possible to trade off functionality (accuracy) against energy consumption, whereas with many programs functionality is simply a pass-or-fail constraint. We use a grid search to explore hyperparameter configurations for a multilayer perceptron on five classification data sets, considering trade-offs of classification accuracy against training or inference energy. On one data set, we show that 77% of energy consumption for inference can be saved by reducing accuracy from 94.3% to 93.2%. Energy for training can also be reduced by 30-50% with minimal loss of accuracy. We also find that structural parameters like hidden layer size is a major driver of the energy-accuracy trade-off, but there is some evidence that non-structural hyperparameters influence the trade-off too. We also show that a search-based approach has the potential to identify these tradeoffs more efficiently than the grid search.