Two-stage design optimization based on artificial immune system and mixed-integer linear programming for energy supply networks

A two-stage optimization approach based on an artificial immune system (AIS) and mixed-integer linear programming (MILP) was developed to efficiently solve large-scale structural design problems of energy supply networks and obtain multiple and diverse design candidates. By focusing on a hierarchical relationship between design and operation variables, a structural design problem, formulated using MILP, is decomposed into an upper-level design problem and a lower-level operation problem. The upper-level design problem is solved using an AIS, in which multiple and diverse sets of suboptimal solutions are searched in a short computation time. In the lower-level optimization, design variables are fixed at the values searched in the upper-level optimization and operation variables are optimized using MILP. Moreover, the lower-level optimization for multiple sets of design variables is separately conducted using parallel computing. The developed approach was applied to the structural design of an energy supply network, consisting of candidates of cogeneration units and heat pump water heating units under power and heat interchange, for a housing complex with four dwellings. The diversity and energy-saving performance of multiple design candidates were analyzed. The computational efficiency was also demonstrated in comparison to the results obtained using only a commercial MILP solver.