A mixed-integer linear programming method utilizing the hierarchical relationship between design and operation variables proposed to solve the optimal design problem of energy supply systems efficiently is extended to search K-best solutions: At the upper level, the optimal values of design variables are searched by the branch and bound method with operation variables relaxed to continuous ones; At the lower level, the values of operation variables are optimized independently at the respective periods set for variations in energy demands by the branch and bound method with the values of design variables given tentatively during the search at the upper level; The obtained solution is used to renew K-best incumbent solutions, and the upper bound for the value of the objective function for K-best solutions is replaced with the largest value of the objective function among K-best incumbent solutions. This method is implemented into a commercial solver. A practical case study on the optimal design of a cogeneration system is conducted, and the validity and effectiveness of the proposed method are clarified.
