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Real-world electricity consumption prediction may involve different tasks, e.g., prediction for different time steps ahead or different geo-locations. These tasks are often solved independently without utilizing some common problem-solving knowledge that could be extracted and shared among these tasks to augment the performance of solving each task. In this work, we propose a multi-task optimization (MTO) based co-training (MTO-CT) framework, where the models for solving different tasks are co-trained via an MTO paradigm in which solving each task may benefit from the knowledge gained from when solving some other tasks to help its solving process. MTO-CT leverages long short-term memory (LSTM) based model as the predictor where the knowledge is represented via connection weights and biases. In MTO-CT, an inter-task knowledge transfer module is designed to transfer knowledge between different tasks, where the most helpful source tasks are selected by using the probability matching and stochastic universal selection, and evolutionary operations like mutation and crossover are performed for reusing the knowledge from selected source tasks in a target task. We use electricity consumption data from five states in Australia to design two sets of tasks at different scales: a) one-step ahead prediction for each state (five tasks) and b) 6-step, 12-step, 18-step, and 24-step ahead prediction for each state (20 tasks). The performance of MTO-CT is evaluated on solving each of these two sets of tasks in comparison to solving each task in the set independently without knowledge sharing under the same settings, which demonstrates the superiority of MTO-CT in terms of prediction accuracy.