Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

The Shunt-In Shunt-Out Problem in Rail Freight Transport: an Event-Based Simulation Framework for Sustainable Rolling Stock Management

peer reviewedR-AGR-3881 - BRIDGES 2020/14767177-ANTOINE/CFL Cont (01/01/2021 - 31/12/2023) - CONNORS Richard11. Sustainable cities and communitie

A Network-Based Method for the EMU Train High-Level Maintenance Planning Problem

Electric Multiple Unit (EMU) high-level maintenance planning is a typical discrete system. EMU high-level maintenance (HM) planning determines when to undergo HM or execute transportation task for train-sets, based on practical requirements such as passenger transport demand, workshop maintenance capacity, and maintenance regulations. This research constructs a time-state network that can display the transformation processes between different states. On this basis, a path based model and its improvement are developed to minimize the HM costs with consideration of all necessary regulations and practical constraints. To handle the solution space, a path set generation method is presented. A real-world instance from Shanghai Railway, which is the largest affiliate in China Railway Corporation, was conducted to demonstrate the efficiency and effectiveness of the proposed approach, which indicates that the model can be solved to optimum within short computational times by the state-of-the-art solver Gurobi. Moreover, a sensitivity analysis was also performed to evaluate the effects of the variation in average daily operating mileage, HM capacity at the depot and the assumed minimum value of cumulative mileage

Optimizing the High-Level Maintenance Planning Problem of the Electric Multiple Unit Train Using a Modified Particle Swarm Optimization Algorithm

Electric multiple unit (EMU) trains’ high-level maintenance planning is a discrete problem in mathematics. The high-level maintenance process of the EMU trains consumes plenty of time. When the process is undertaken during peak periods of the passenger flow, the transportation demand may not be fully satisfied due to the insufficient supply of trains. In contrast, if the process is undergone in advance, extra costs will be incurred. Based on the practical requirements of high-level maintenance, a 0–1 programming model is proposed. To simplify the description of the model, candidate sets of delivery dates, i.e., time windows, are generated according to the historical data and maintenance regulations. The constraints of the model include maintenance regulations, the passenger transportation demand, and capacities of workshop. The objective function is to minimize the mileage losses of all EMU trains. Moreover, a modified particle swarm algorithm is developed for solving the problem. Finally, a real-world case study of Shanghai Railway is conducted to demonstrate the proposed method. Computational results indicate that the (approximate) optimal solution can be obtained successfully by our method and the proposed method significantly reduces the solution time to 500 s