Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of method...Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of methods have been proposed for solving it. However, most researchers only discuss the properties of different models and algorithms without taking into account the impacts of actual implementation. In fact, the true performance of a method may differ greatly across various implementations. In this paper, several popular optimization solvers for implementations of column generation and Lagrangian relaxation are discussed. In order to test scalability and optimality, three groups of networks with different structures are used as case studies. Results show that column generation outperforms Lagrangian relaxation in most instances, but the latter is better suited to networks with a large number of commodities.展开更多
基金supported by research funds from the National Natural Science Foundation of China (Nos. 61521091, 61650110516, 61601013)
文摘Multi-commodity flow problems（MCFs） can be found in many areas, such as transportation, communication, and logistics. Therefore, such problems have been studied by a multitude of researchers, and a variety of methods have been proposed for solving it. However, most researchers only discuss the properties of different models and algorithms without taking into account the impacts of actual implementation. In fact, the true performance of a method may differ greatly across various implementations. In this paper, several popular optimization solvers for implementations of column generation and Lagrangian relaxation are discussed. In order to test scalability and optimality, three groups of networks with different structures are used as case studies. Results show that column generation outperforms Lagrangian relaxation in most instances, but the latter is better suited to networks with a large number of commodities.
