In this paper, one MOEA/D variant using two crossover strategies (MOEA/D-TCS) and two constraint handling methods are proposed to deal with four combined cooling, heating, and power (CCHP) scenarios in summer and winter. MOEA/D-TCS maintains a balance between global search and local search by combining a modified spiral updating position of whale optimization algorithm and the simulated binary crossover of genetic algorithm, and it is able to obtain a wide and even Pareto set for each CCHP scenario. The two constraint handling methods enable infeasible solutions to get rid of infeasible regions over a short period of time, guaranteeing that the reserved solutions of MOEA/D-TCS satisfy all constraints. Experimental results show that each CCHP scenario with the battery has lower energy consumption, operation cost and carbon dioxide emission than the corresponding CCHP scenario without the battery, and hence the battery is helpful to the improvements of the flexibilities and efficiencies of energy cascade utilization for the CCHP systems in summer and winter. Also, MOEA/D-TCS performs better than the other seven multi-objective evolutionary algorithms and achieves larger hypervolumes and coverage rates for four CCHP scenarios.