Research on Continuous Equilibrium Network Design Model of Stochastic Demand and Supply Based on Genetic Algorithm

12 - Continuous Equilibrium Network Design Problem with Elastic Demand: Derivative-Free Solution Methods

The Robust Model of Continuous Transportation Network Design Problem with Demand and Cost Uncertainties

In this paper, a bi-level programming model based on OD pair travel time reliability is developed to study road network capacity reliability. A user equilibrium traffic assignment model is proposed with a lower problem describing travelers' route choice behavior and an upper problem that maximizes the basic reference OD demand multiplier subject to the corresponding prescribed travel time threshold. An approximation algorithm is introduced to estimate the road network capacity reliability. The algorithm treats the capacity of each link as a discrete random variable and uses the road network most probable states generation method in conjunction with the sensitivity analysis technique to solve the bi-level programming model. Finally, a numerical example of a small road network is used to demonstrate the application of the proposed model and algorithm.

Parameters Sensitive Analyses for Using Genetic Algorithm to Solve Continuous Network Design Problems

This article investigates how to simultaneously optimize both strategic and tactical decisions in the supply chain network design. For this purpose, a bi-level programming model is developed in which supply chain network design problem is considered as a strategic decision in the upper-level model, while the lower-level model contains the assembly line balancing as a tactical decision. In addition, the problem is extended to include push–pull strategy where decisions such as production amount and inventory level of each component in manufacturers are made. Based on the special structure of the model, a heuristic method is proposed to solve the developed bi-level model. A numerical example is employed to show the performance of proposed method in terms of feasibility and convergence. Finally, computational experiments on several problem instances are presented to demonstrate the applications of developed model and the solution method.

The continuous network design problem (CNDP) is known to be difficult to solve due to the intrinsic properties of non-convexity and nonlinearity. Such kinds of CNDP can be formulated as a bi-level programme, in which the upper level represents the designer's decisions and the lower level the travellers' responses. Formulations of this kind can be classified as either Stackelberg approaches or Nash ones according to the relationship between the upper level and the lower level parts. This paper formulates the CNDP for road expansion based on Stackelberg game where leader and follower exist, and allows for variety of travellers' behaviour in choosing their routes. In order to solve the problem by the Stackelberg approach, we need a relation between link flows and design parameters. For this purpose, we use a logit route choice model, which provides this in an explicit closed-form function. This model is applied to two example road networks to test and briefly compare the results between the Stackelberg and Nash approaches to explore the differences between them.

For the current status of e-commerce logistics and distribution terminal node layout,this article considers planners and customers both benefit, while also considering the impact of the end node distribution route for cost.A bi-level programming model of end nodes location was constructed. The upper level model is the smallest in the conditions of transport costs and fixed costs as much as possible to attract customer demand, lower programming model considers the distance, the price of services and quality of service that influence customer choice behavior, and customer demand for the costs of terminal nodes distribution is studied.Finally, a numerical example verifies the feasibility of the model and algorithm.

In order to design the traffic network more accurately, the bi-level programming model for the continuous network design problem based on the paired combinatorial Logit stochastic user equilibrium model is proposed in this study. In the model, the paired combinatorial Logit stochastic user equilibrium model which is used to characterize the route choice behaviors of the users is adopted in the lower level model, and the minimum summation of the system total costs and investment amounts is used in the upper objective function. The route-based self-regulated averaging (SRA) algorithm is designed to solve the stochastic user equilibrium model and the genetic algorithm (GA) is designed to get the optimal solution of the upper objective function. The effectiveness of the proposed combining algorithm which contains GA and SRA is verified by using a simple numerical example. The solutions of the bi-level models which use the paired combinatorial Logit stochastic user equilibrium model in the lower level model with different demand levels are compared. Finally, the impact of the dispersion coefficient parameter which influences the decision results of the network design problem is analyzed.

Considering the impact of informatization condition, vehicles on the road network are divided into connected automated vehicles (CAVs) and human-driven vehicles (HDVs), which follow the principle of system optimization and stochastic user equilibrium, respectively. Taking the road network reserve capacity maximization model under the condition of road capacity constraint as the upper-level programming and the traffic assignment model under heterogeneous flow environment as the lower level programming, then a bilevel programming model is constructed. Among them, the nonuniform demand growth multiplier is adopted for each OD pair to reflect the inconsistency of traffic demand structure growth, and the calculation of link capacity is related to the market penetration of CAVs. The incremental method, method of successive averages, and simulated annealing algorithm are used to solve the model, and the effects of different market penetration on road network capacity, travel time, and saturation are analyzed through a numerical example. The relevant data under different weights are normalized and the optimal deployment scheme of CAVs and HDVs in different periods is obtained by comprehensive evaluation. Meanwhile, the mixed equilibrium flow state is explored under the premise of given market penetration to verify the feasibility of the model and algorithm.

In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation techniques for the lower level nonlinear complementarity, the original bilevel formulation can be converted to a single level nonlinear programming problem. We show that certain reformulations are more effective than others to solve the proposed MPCC model. Recommendations are thus provided on how to choose a reformulation of the continuous network design problem that can be solved effectively and/or efficiently.

The model of the multi-objective optimal allocation of water resources with government system of water rights is a bi-level programming model. The function of water trade price is difficult to determine, and some factors are interactive such as water price, coefficient of water-saving and objective function, whose relationships are rather complex, so that it is attractive to study the model solution. In this paper, the solution to the bi-level programming model of the optimal allocation of water resources is put forward, in which the upper-level programming is solved by genetic algorithm and the lower-level programming is solved by simplex method, the values about water trade price and coefficient of water-saving are assigned via random-points in a certain range. The results show that the solution is reasonable, and it has been made great progress in ideas and methods to solve this model.

Mixed Transportation Network Design Based on Immune Clone Annealing Algorithm

In recent years, with the global energy shortage and severe environmental deterioration, railway transport has begun to attract great interest as a green transportation mode. One of the vital means to realize social sustainable development is to improve railway transportation systems, in which providing a demand-oriented train timetable with a higher service level is the most viable method. A demand-oriented train timetable problem generally deals with passengers’ train-choice decisions according to the queue principle, but it is not adapted to rail systems, such as China’s, where passengers usually book tickets a few days in advance by telephone or online instead of going to stations. This paper is devoted to modeling and solving the demand-oriented train timetabling problem integrated with passengers’ train-booking decisions. Firstly, a bi-level programming model is formulated for their integrated optimization on a rail network. Its upper-level model is to optimize train arrival and departure times at each visited station with the aim of reducing passengers’ total travel cost, while its lower-level model aims to determine passengers’ train-booking behavior using the user equilibrium theory. Then, a priority-based heuristic algorithm is designed to solve this model. It has two main steps at each iteration: one is to determine the number of passengers booking each train with a given train timetable, and the other is to improve the current train timetable based on the valuable information of passenger train-booking decisions. The performance, convergence, and practicability of the proposed method were analyzed based on the Changsha–Zhuzhou–Xiangtan intercity rail in China. Experimental results show the proposed method can effectively reduce the travel cost for passengers, creating a greater passenger demand for railway travel, which is beneficial to the sustainable development of railway systems and even society.

To enhance the resilience of urban rail transit networks in dealing with interference events and facilitating rapid network recovery, this paper focuses on studying damaged urban rail transit networks and proposes comprehensive resilience evaluation indexes for urban rail transit networks that take into account two dimensions: network topology and passenger travel path selection. A bi-level programming model is constructed to maximize the comprehensive toughness, where the upper-level model is an integer planning model for determining the optimal recovery sequence of the affected stations under interference events that result in station closure or inoperability. The lower-level model is a passenger flow allocation model aiming to minimize travelers’ impedance. A genetic algorithm and Dijkstra’s labeling algorithm are used to solve the upper model as well as the shortest path of the lower model, respectively. Using a real-world urban rail transit network as an example, this research applies different recovery strategies, random recovery, node importance-based recovery, and comprehensive toughness-based recovery, across five common interference scenarios to analyze the recovery sequence of stations in each scenario. The modeling results show that the comprehensive toughness-based restoration strategy yields the most favorable results for the rail transportation network, followed by the node importance-based restoration strategy. In addition, the network’s toughness varies more significantly when employing different restoration strategies during target interference, as compared to the random and range interference scenarios.

To ensure the equity of exclusive bus lane (EBL) allocation under multimodal traffic conditions, a bi-level programming model is first constructed. The upper-level model is the minimum total system cost considering the Gini coefficient and the lower-level model constructed a stochastic user equilibrium (SUE) model based on logit loading. Secondly, a heuristic algorithm combining an improved genetic algorithm (GA) and a method of the successive average method (MSA) is designed. Finally, the Nguyen and Dupuis networks are used as examples to verify and analyze the effectiveness, superiority and sensitivity of the model and algorithm. The results show that the method can effectively obtain the optimal solution of the upper-level model as 15,004 RMB, the Gini coefficient is 0.31, and the equity is at a relatively reasonable level. Compared with the different allocation schemes, the proposed scheme has a higher bus sharing rate and lower Gini coefficient. At the same time, when the actual demand is twice the basic demand, the bus share rate is the largest, 65%, and the Gini coefficient is the smallest at 0.3. The bus share rate decreases with the increase in the proportion of high time value travelers, which fully verifies the sensitivity of the model to the type of traveler.