This study addresses the higher demand of passengers during peak hours in urban rail transit by proposing an integrated optimization of train stopping plans and timetabling to reduce overcrowding and the total waiting...This study addresses the higher demand of passengers during peak hours in urban rail transit by proposing an integrated optimization of train stopping plans and timetabling to reduce overcrowding and the total waiting time.A nonlinear integer programming model is developed,incorporating passenger demand,operation costs,train capacity,and station congestion levels.The decision variables include the stopping plan and departure headways.The objective is to minimize total operation time,average operation time,and waiting time,while reducing congestion variance across stations.A case study using the NSGA-II algorithm shows that the optimized solution significantly alleviates station congestion compared to the all-stop plan.Additionally,it reduces average operation time,total operation time,and waiting time by 3.42%,9.40%,and 10.44%,respectively,demonstrating the model's feasibility and effectiveness.展开更多
The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one opt...The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos 72331001 and 72071015)the 111 Center(Grant No.B20071).
摘要This study addresses the higher demand of passengers during peak hours in urban rail transit by proposing an integrated optimization of train stopping plans and timetabling to reduce overcrowding and the total waiting time.A nonlinear integer programming model is developed,incorporating passenger demand,operation costs,train capacity,and station congestion levels.The decision variables include the stopping plan and departure headways.The objective is to minimize total operation time,average operation time,and waiting time,while reducing congestion variance across stations.A case study using the NSGA-II algorithm shows that the optimized solution significantly alleviates station congestion compared to the all-stop plan.Additionally,it reduces average operation time,total operation time,and waiting time by 3.42%,9.40%,and 10.44%,respectively,demonstrating the model's feasibility and effectiveness.
基金Supported by the Deutsche Forschungsgemeinschaft (DFG No. RO294/9).
摘要The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.