Research On Multi-objective Discrete Differential Evolution Algorithm In The Problem Of EMU Operation

The problem of using EMU is to arrange the connection of EMU reasonably,so that the number of EMUs can be reduced as much as possible on the premise of completing the tasks specified in the train operation diagram.At the same time,the network of EMU must meet the time and space constraints such as the time of departure and arrival,the station of departure and arrival,the layout of maintenance resources,the accumulated travel time and mileage,etc.Obviously,the application of EMU is a combinatorial optimization problem with constraints.Differential Evolution Algorithm(DE)is a kind of intelligent optimization algorithm based on population,which has the advantages of simple evolutionary principle,few control parameters and strong robustness.The mutation operator and crossover operator are designed by referring to the evolution of natural populations.The DE algorithm does not need to rely on external information,and is especially suitable for solving optimization problems under complex conditions.According to the different characteristics of the EMU network,the research focuses on the mathematical model and optimization algorithm of the EMU application plan.The main work is as follows:(1)In order to improve the utilization efficiency of EMU,the optimization model of the sequential train based on directed graph is established.Given the EMUs scheduling problem of passenger dedicated line,the "adjacent node" is taken as the selection range of the sequential train number,thus the invalid search is reduced and the search space is always in the feasible domain,so that the EMU connection time model is obtained.(2)For the EMU scheduling model with multiple hub stations,a Randomized Swap Differential Evolution Algorithm(RSDE)is proposed.Taking the modified priority coding scheme suitable for any paired EMU network,a random permutation algorithm is proposed based on the group theory for the mutation operation and the priority index crossing(PIX)operator is adopted.Considering the difference of evolutionary information carried by individuals,an adaptively adjusted contraction factor is proposed.Taking the Wuhan-Guangzhou passenger line as the research object,the performance of the proposed algorithm is tested in the MATLAB programming environment.The simulation results show that the algorithm can achieve better optimization performance than the comparison algorithm.(3)Considering the higher requirements for the operation of EMU,under the constraints of EMU running standards and maintenance operations at all levels,a multi-objective optimization model for the operation of EMU under complex conditions is established by minimizing the connection time of EMU and reducing the number of maintenance times of EMUs.(4)For multi-objective optimization model of EMU,a non-dominated sort RSDE(NS-RSDE)based on the stagnation criterion is proposed.Individuals based on priority encoding are decoded into EMU intersections,and large penalty value is assigned to individuals who violate maintenance standards.For the NS-RSDE algorithm,in order to optimize the connection time and maintenance times simultaneously,the population is sorted by the fast non-dominated sorting algorithm,and the population is attracted to the Pareto non-dominated frontier.Single point interpolation variation is called to induce the population to jump out of the local extreme value and enhance the exploration ability of the population.Finally,the simulation study of 176 train running tasks on Wuhan-Guangzhou passenger dedicated line is conducted,and the comparison with other algorithms verifies the high efficiency of NS-RSDE algorithm.