A Two-phase Heuristic Algorithm for the Fixed-charge Capacitated Network Design Problem with Turn Penalties

In this paper, we consider the fixed-charge capacitated network design problem with turn penalties. The objective of the problem is to minimize the sum of flow costs for routing the commodities demand, fixed costs for using arcs and penalty costs for flows with 90-degree turns. A mixed integer programming model is presented for the problem and a two-phase heuristic algorithm is suggested to solve the problem. The arc-labeling algorithm is used to find a flow path with a minimum cost and it is embedded in the suggested heuristic algorithm as a sub-routine. In the suggested algorithm, an initial flow path network is obtained by a construction method and it is improved by an iterative improvement method. To evaluate the performance of the suggested algorithm, computational experiments are performed on randomly generated test problems. Results of computational experiments show that the suggested algorithm finds near-optimal solutions in a short computation time even for large-sized problems.