Storage equipment, such as batteries and thermal energy storage (TES), has become increasingly important recently for peak-load shifting in energy systems. Mathematical programming methods, used frequently in previous studies to optimize operating schedules, can always be used to derive a theoretically optimal solution, but are computationally time consuming. Consequently, we use meta-heuristics, such as genetic algorithms (GAs), particle swarm optimization (PSO), and cuckoo search (CS), to optimize operating schedules of energy systems that include a battery, TES, and an air-source heat pump. In this paper, we used a GA, differential evolution (DE), our own proposed mutation-PSO (m-PSO), CS, and the self-adaptive learning bat algorithm (SLBA), of which m-PSO was the fastest, and CS was the most accurate. CS obtained the semi-optimal solution 135 times as fast as dynamic programming (DP), a mathematical programming method with 0.22% tolerance. Thus, we showed that metaheuristics, especially m-PSO and CS, have advantages over DP for optimization of the operating schedules of energy systems that include a battery and TES. (C) 2015 Elsevier Ltd. All rights reserved.