An A-Posteriori Multi-Objective Optimization Method for MILP-Based Distribution Expansion Planning

Distribution expansion planning (DEP) is a mixed integer nonlinear programming (MINLP) problem and contains various options to be considered where the nonlinearity makes it difficult to solve. Over the years, different heuristic and classical optimization methods have been introduced to solve this problem. In a few classical optimization methods, this problem has been linearized. In this contribution, an $\epsilon $ -constraint based multi-objective method was proposed for mixed integer linear programming (MILP) based DEP model considering network loss. Operational network loss was linearized and incorporated in the model, then the operational loss cost was obtained by modeling the production cost. In order to model the production cost, the well-known supply price curve was considered, where the price of energy for each loading condition was obtained based on a linear model. Using the $\epsilon $ -constraint method, the Pareto optimal front was formed, which provides the decision maker with a range of solutions showing relationship among conflicting objectives. Then, a Fuzzy satisfying method was utilized to obtain the best compromised solution. Simulations were performed on an 18-node primary distribution network. Results showed the effectiveness of the proposed method for the MILP-based multi-objective DEP models.