An Adaptive Normal Constraint Method for Bi-Objective Optimal Synthesis of Energy Systems

A novel approach is proposed for the efficient generation of the Pareto front for bi-objective optimal synthesis of energy systems. To avoid computationally expensive calculations of solutions not relevant to the decision maker, the proposed method adapts the computation of the Pareto front to the part relevant for practical energy systems. The algorithm produces an evenly distributed set of Pareto optimal solutions employing a modified normal constraint method. In contrast to the classical normal constraint method, the algorithm is no more initialized at the - usually computationally most expensive - single-objective optima but uses an aggregated objective function as starting point for an adaptive exploration of the Pareto front. The presented approach is applied to a real-world synthesis problem of a distributed energy supply system. It is shown that the adaptive normal constraint algorithm automatically generates the most relevant part of the Pareto front for the bi-objective optimal synthesis of an energy system computationally more efficient than the weighted sum method or the epsilon-constraint method.