Strategic design and multi-objective optimisation of distribution networks based on genetic algorithms

The paper addresses the optimal design of distribution networks (DNs). Considering a distributed system composed of stages connected by material links labelled with suitable performance indices, a procedure employing multi-objective genetic algorithms (MOGAs) is presented to select the optimal DN configuration. The paper enhances a deterministic procedure for DN strategic configuration by employing MOGACOP, a real-valued chromosome MOGA that can be applied to the case of constrained nonlinear function. The main MOGA characteristics are the presence of three populations: two reference sets of individuals satisfying all constraints, namely, a set of Pareto optimal individuals (frontier population) and a set of individuals covering the previous population (archive population), together with a search set which, on the contrary, includes individuals that are allowed to not satisfy all constraints (laboratory population). MOGACOP allows solving the DN design nonlinear problem, which exhibits a multi-objective function that varies linearly only with some variables and nonlinearly with the remaining variables. The proposed MOGA application allows finding a Pareto frontier of optimal solutions, which is compared with the frontier obtained by solving the same problem with Integer Linear Programming (ILP), where piecewise constant contributions are linearly approximated. The two found curves represent, respectively, the upper and the lower limit of the region including the real Pareto curve. Both the genetic optimisation and the ILP models are applied under structural constraints to a case study describing the distribution chain of a large enterprise of southern Italy producing consumer goods.