The combination of renewable energy technologies and distributed energy systems is an effective way to reduce carbon emissions and improve energy utilization. In this study, a multi-energy complementary distributed energy system (MC-DES) integrating photovoltaic, solar thermal collector, ground source heat pump, energy storage, and energy metering devices is proposed. The system employs sensor devices to measure the cooling, heating, and electric loads of the users and satisfies diversified energy demands through the synergistic operation of the energy supply and energy storage devices. To obtain the optimal capacity configuration scheme of MC-DES, a multi-objective configuration optimization model considering annual economic cost (AEC), primary energy consumption (PEC), and carbon dioxide emission (CDE) is established. A multi-objective exponential distribution optimizer (MOEDO) algorithm based on the fitness allocation mechanism and external archive maintenance mechanism is proposed to solve the configuration optimization problem. A hotel building is used as a case study to verify the effectiveness of the MOEDO algorithm, and the impact of different renewable energy technologies on the system performance is analyzed. The results show that compared with the conventional NSGA-III, MOPSO, and MOEA/D algorithms, the MOEDO algorithm reduces AEC of the MC-DES system by 3.42, 3.76, and 11.58%, while PEC is reduced by 3.44, 10.11, and 3.44% and CDE is reduced by 4.93, 11.20, and 1.58%, respectively. In addition, compared with the traditional separation production system, the economic, energy-saving, and environmental performances of the MC-DES are improved by 20.25, 58.62, and 68.44%, respectively.