In recent times, deep learning-based black box forecasting models have gained notable recognition for their ability to predict energy demand with considerably higher accuracy. This study presents a novel hybrid adaptive deep learning model (HyADLeM) to forecast residential heating loads, comprising long short-term memory (LSTM) or gated recurrent unit (GRU) or both, based on the selection of these neural networks by multi-objective optimisation algorithms (MOOAs) such as non- dominated sorting genetic algorithm-II (NSGA-II), NSGA-III, multi-objective particle swarm optimisation (MOPSO), and multi-objective ant colony optimisation (MOACO). Additionally, it aims to compare the hyperparameter optimisation performance of the MOOAs, along with the forecasting performances of the proposed model employed with the MOOAs. Hyperparameters, including the number of hidden layers, type of hidden layers, number of neurons in each hidden layer, batch size, window size, and learning rate, were optimised by the MOOAs. The optimisation objectives were to minimise the normalised mean biased error (nMBE) and the coefficient of variation of root mean square error (CV(RMSE)) and computation time. The MOOAs were compared based on their Pareto-solution diversity, computation time and error metrics such as CV(RMSE), nMBE, coefficient of variation of mean absolute error (CV(MAE)) and mean absolute percentage error (MAPE). The results demonstrate that the NSGA-III-HyADLeM was 32% faster than the worst-performing model during training, despite having a more complex model architecture. Also, it outperformed all the other MOOA-based HyADLeM in terms of CV(RMSE), NMBE, CV(MAE) and MAPE.