A comparison of Mixed-Integer Linear Programming and Genetic Algorithm–Linear Programming to optimize a non-interconnected island energy system

This study compares a Mixed-Integer Linear Programming (MILP) formulation with a hybrid Genetic Algorithm–Linear Programming (GA–LP) framework for the joint optimization of technology sizing and hourly operation in the non-interconnected multi-energy system of Favignana, Italy. Both approaches use the same technology portfolio, twelve monthly representative days, techno-economic assumptions, and performance indicators. The MILP jointly optimizes technology capacities and operational variables within a single mixed-integer linear problem. The GA–LP framework instead decomposes planning and operation: the upper-level Genetic Algorithm explores the technology-design space, while a lower-level LP determines the optimal hourly dispatch for each fixed candidate design. This structure allows the exploration of a nonlinear design–performance relationship while excluding hourly dispatch variables from the evolutionary search, thereby reducing its dimensionality. Both formulations substantially improve the reference system in terms of annualized cost, primary energy consumption, and life-cycle CO2-equivalent emissions. MILP reduces annualized cost by approximately 55%–60% and CO2-equivalent emissions by approximately 65%–80%, depending on the objective. GA–LP achieves annualized-cost reductions of up to 70%, while emission reductions exceed 90% under environmental optimization. The two formulations produce different sizing and dispatch patterns because they adopt distinct planning–operation couplings and storage-operation constraints. MILP requires approximately 9 s per objective function, whereas GA–LP requires approximately 185–189 s. Overall, hybrid decomposition offers a flexible and computationally manageable option for complex island multi-energy planning.