Abstract
The transit network design and frequency setting problem is related to the generation of transit routes with corresponding frequency schedule. Considering not only the influence of transfers but also the delay caused by congestion on passengers’ travel time, a multi-objective transit network design model is developed. The model aims to minimize the travel time of passengers and minimize the number of vehicles used in the network. To solve the model belongs to a NP-Hard problem and is intractable due to the high complexity and strict constraints. In order to obtain the better network schemes, a multi-population genetic algorithm is proposed based on NSGA-II framework. With the algorithm, network generation, mode choice, demand assignment, and frequency setting are all integrated to be solved. The effectiveness of the algorithm which includes the high global convergence and the applicability for the problem is verified by comparison with previous works and calculation of a real-size case. The model and algorithm can be used to provide candidates for the sustainable policy formulation of urban transit network scheme.
Highlights
If the lines are selected from a given line pool to form the network, the rationality of these lines will largely depend on the quality of the line pool [20]. The metaheuristic methods, such as genetic algorithm [8, 21, 22], simulated annealing algorithm [13], tabu search algorithm [23], swarm intelligence algorithm [24] and other metaheuristics [25, 26] are usually applied in the transit network design problem
An e ective algorithm based on improved NSGA-II is put forward, in which the network generation, the mode choice, the passenger demand assignment considering passenger trip rule, and the frequency setting are all integrated. e algorithm has high global convergence and good applicability to the problem, which are veri ed by numerical experiments and case application
Taking the four solutions including the solution 1 with = 1, the solution 2 with = 2, the solution 3 with = 3and the solution 4 with = 3(as shown in Figure 10) as examples, the network scheme corresponding to the solution 1 requires the least number of buses and the lowest user cost, but the direct rate which is 90.95% has the least advantage. ere is little di erence for the direct rate among the solutions 2, 3, and buses than the solution
Summary
Trip covering e sum of operator cost, user cost, and unsatis ed demand costs Travel cost, attractivenessTrip coverage Travel cost, tra c captureTravel cost, operation cost e number of satis ed passengers, transfers, and travel timeNet pro t of the railway networkConstruction cost, time savings, patronageTravel cost, costs related to construction and exploitation Discounted pro tPassenger cost, unmet demand Travel timeTravel time, operation costDemand Mode choice depended Mode choice depended. Trip covering e sum of operator cost, user cost, and unsatis ed demand costs Travel cost, attractiveness. Trip coverage Travel cost, tra c capture. Operation cost e number of satis ed passengers, transfers, and travel time. Net pro t of the railway network. Costs related to construction and exploitation Discounted pro t. Demand Mode choice depended Mode choice depended
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