With the climate change and depletion of fossil energy, distributed energy systems (DESs) have attracted widespread attention. In this study, a DES driven by solar, geothermal, aerothermal, natural gas and power grid is constructed with energy conversion devices modeled based on part load performance. A novel operation strategy for the DES is presented considering the complementary characteristics of different energy sources. Besides, a multi-objective nonlinear optimization model for the device capacity is proposed with economic, environmental and energy objectives considered simultaneously. To solve the optimization model, an integrated solution method combining Non-dominated Sorting Genetic Algorithm-II, Technique for Order Preference by Similarity to an Ideal Solution and Shannon entropy approach is developed. A case study of an indoor swimming pool in Changsha city of China is undertaken. Optimal equipment capacity and corresponding energy management strategies of the case are obtained. The final number and capacity of air source heat pump (ASHP) are determined via improving its part load ratio. Additionally, three schemes are set to investigate the effects of constant efficiency/COP of energy conversion devices and operation strategies on the capacity optimization of DESs. Results indicate that constant efficiency/COP of equipment yields an 11.7% drop in annual total cost (ATC), a 10.4% increment in annual total CO2 emission (ATE) and a 12.5% reduction in coefficient of energy performance (CEP). ATC and ATE of the optimal solution acquired under a conventional operation strategy increase by 6.8% and 3.7%, while CEP decreases by 66.9%. This work provides a guidance for the future application of DESs.