A graph theoretic-based approach to distribution network planning with routes interaction regarding the fix-charge transportation problem

This paper aims to take distribution network planning problem into consideration, since a well-configured network can provide an appropriate platform for effective and efficient management of the set. The fix-charge transportation approach is addressed here to account for the problem. Hence, a nonlinear mixed-integer programming model is proposed to minimise the configuration costs, in addition to the routes interaction consideration. Likewise, a graph theoretic-based methodology, i.e., the minimum spanning tree concept, is pursued by the Prüfer number representation to deal with trees coding and decoding procedure. Due to the problem solution complexity, genetic and simulated annealing algorithms are applied to deal with large-sized problems. Moreover, a robust tuning is utilised to the key parameters of the solution methodologies using the Taguchi method. Finally, some numerical examples are developed in order to compare the performance of the solution approaches with that of CPLEX.