For the layout problem of rural highway network, which is often characterized by a cluster of geographically dispersed nodes, neither the Prim algorithm nor the Kruskal algorithm can be readily applied, because the calculating speed and accuracy are by no means satisfactory. Rather than these two polynomial algorithms and the traditional genetic algorithm, this paper proposes an improved genetic algorithm. It encodes the minimum spanning trees of large-scale rural highway network layout with Prufer array, a method which can reduce the length of chromosome; it decodes Prufer array by using an efficient algorithm with time complexity o(n) and adopting the single transposition method and orthoposition exchange method, substitutes for traditional crossover and mutation operations, which can effectively overcome the prematurity of genetic algorithm. Computer simulation tests and case study confirm that the improved genetic algorithm is better than the traditional one.
Focusing on the multi-depot vehicle routing problem (MDVRP) for hazardous materials transportation, this paper presents a multi-objective optimization model to minimize total transportation energy consumption and transportation risk. A two-stage method (TSM) and hybrid multi-objective genetic algorithm (HMOGA) are then developed to solve the model. The TSM is used to find the set of customer points served by each depot through the global search clustering method considering transportation energy consumption, transportation risk, and depot capacity in the first stage, and to determine the service order of customer points to each depot by using a multi-objective genetic algorithm with the banker method to seek dominant individuals and gather distance to keep evolving the population distribution in the second stage, while with the HMOGA, customer points serviced by the depot and the serviced orders are optimized simultaneously. Finally, by experimenting on two cases with three depots and 20 customer points, the results show that both methods can obtain a Pareto solution set, and the hybrid multi-objective genetic algorithm is able to find better vehicle routes in the whole transportation network. Compared with distance as the optimization objective, when energy consumption is the optimization objective, although distance is slightly increased, the number of vehicles and energy consumption are effectively reduced.
It is of great importance to optimize the schemes of long through-type bus lines to adapt to the urban rail transit network. Focusing on the long through-type bus lines close to metro stations, a bilevel programming model on the adjustment schemes of bus lines is proposed, taking the impacts of urban rail transit network into account. The upper level model aims at adjusting the setting decisions of stop stations and vehicle headways of bus lines to minimize the passenger travel cost and maximize the benefits of bus operators. The lower level model is a passenger flow assignment model based on Logit-SUE considering the crowding perception of passengers in bus vehicles. Moreover, the constraint of average load factor of the bus line sections is considered. Then the genetic algorithm is applied to solve the proposed model, and a numerical example is conducted to verify the effectiveness. Results show that the value of the objective function of the model is improved by 27.2%, in comparison with the original scheme. Even though the average travel cost of passengers increases slightly, the bus line operation cost and the imbalance degree of load factors are reduced by 46.1% and 18.6%, respectively. The sensitivity analyses show that it is better to divide the long through-type bus line into several separate bus lines with independent operation, respectively, under the condition of unbalanced passenger flow distribution. Meanwhile, the multiple bus lines are more adapted to the unbalanced passenger flow distribution when the weight of the benefits of the bus operators in the total objective function is bigger. Besides, the lower time value that the passengers perceive, the more passengers willing to take bus than metro trains. As the increment of the passenger time value, the combination of feeder bus lines and a longer bus line is better for passengers’ trip demand than the long through-type bus line.
A Y-type urban rail transit is composed of a trunk and a branch, and the passenger demand has the characteristics of multidirectional and unbalanced. It is important to design routing planning of Y-type urban rail transit and provide reasonable service for passengers with acceptable operational cost. In this study, a routing planning design model was proposed for Y-type urban rail transit aimed at minimizing the passenger travel time and train operating distance. The decision variables of the model were the locations of turn-backs and the departure frequencies of the train routings in the multirouting planning. The constraints of passenger demand and line condition were considered. The multi-objective model was turned into a single-objective model by giving weight values to the objectives. Then a genetic algorithm was applied to obtain optimal solutions of the proposed model. Finally, a case study was conducted, and the optimal solutions under different forms of multi-routing planning with different weight values were analyzed. The results showed that when the weight of the passenger travel time increased to a certain level, the optimal solution changed from a two-routing planning to a three-routing planning, and the latter one could better meet the characteristics of the passenger.
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