Multi-modal urban transit network design considering reliability: multi-objective bi-level optimization

Highlights

• Expansion of link capacity in the urban transportation network investigated.

• The upper level of the bi-level optimization is a multi-objective problem.

• The reliability of travel time and capacity are considered in the bimodal network.

• Proposed solution method which can update the parameters of PSO adaptively.

Abstract

Due to the presence of transportation infrastructure in metropolitan areas, authorities often seek to modify the capacity of existing urban transportation links. Therefore, to meet travel demands, it is necessary to consider public transport (PT) modes and carry out systematic planning. In this research, assuming the existence of urban transportation infrastructure, we develop a mathematical model to determine the amount of link capacity increase for the dual-mode PT network. Such an increase in capacity can improve the network capacity and travel time reliabilities under both normal and peak traffic conditions. To investigate this issue, travel demand is assumed to follow a lognormal distribution under normal conditions. Then, the total travel time and flow through the links are calculated and applied to the model using the Monte Carlo method. In this study, we assume that the links of both transport modes forming a path are interdependent. Moreover, due to NP-hardness, we propose the PSO algorithm with dynamic parameters to solve the multi-objective bi-level model. Considering two public transport modes, we develop the algorithm for a part of the urban transportation network in Tehran, Iran.

Introduction

One of the major issues facing people and managers in urban life, especially in metropolitan areas, is traffic problems or, more generally, urban transportation problems. As the population grows and the number of vehicles increases, it becomes more and more difficult for citizens in large cities to travel. This leads to problems such as waste of effective time of citizens, fatigue, nervousness, noise and environmental pollution, loss of energy, and urban warming. Several solutions have been proposed to resolve these problems, such as culture building, management, deterrence (e.g., different traffic schedules and bans on vehicles on different days), etc. However, the prerequisite for all these solutions is the creation or improvement of transportation infrastructure so that it could provide the necessary and adequate capacity for the population of each city or region. Otherwise, from the transportation engineering perspective, if the appropriate basic infrastructure is not provided, none of the solutions will be able to solve the traffic problems. The preparation of the infrastructure required for the urban transportation system is commonly referred to as the urban transportation network design problem (UTNDP). UTNDPs cover a wide range but can be divided into two broad categories. In the first category, all or part of the urban transportation network is created. In the second category, some modifications are made to existing urban transportation networks, for instance, by increasing the capacity of links, converting two-way links into one-way links, etc. This paper focuses on changing the capacity of existing transportation networks to solve traffic problems by increasing the capacity of some links in urban transportation networks.

The main advantage of modeling in this research is to be able to design the urban transportation network of metropolitan areas, because urban transportation networks were mostly designed before the transformation into metropolitan areas and their network was traditionally expanded. Therefore, the redesign of the transportation network changes the residential, commercial, administrative, and other urban fabrics, and staggering costs are imposed on the transportation management. Hence, it is inevitable to make some decisions to solve the traffic dilemma, as the capacity of streets and roads does not meet the demand or traffic flow. In this way, not only the traffic problem will be solved under normal conditions, but also the congestion and heavy traffic will be prevented during the peak transport demand.

Transportation and traffic organizations in metropolitan areas are constantly trying to solve the problem of street and road traffic, because it has very serious consequences for the economy, culture, and society in a direct or indirect manner. One strategy is to build culture for transporting people by public transport. In any case, increasing the capacity of existing streets and roads is undeniable. Therefore, transportation management should increase the capacity of roads to meet the network demand and thus minimize the cost of this increase. In addition, the capacity of roads should not exceed a certain level.

To analyze the real-world problems, the functional results are obtained if the problem hypotheses can be defined close to the real world. One of the most important hypotheses is to consider different transport modes. In the real world, there are several modes whose demands are interrelated. The multi-modal network design problem (MMNDP) can well refer to the problems with at least two different modes for the UTNDP. The MMNDP can cover cars, taxis, trucks, buses, bicycles, motorcycles, subways, etc. The multi-modal problems in urban transportation networks often occur in the following forms [26]:

(a) Absence of interactions between flows of different modes; (b) Presence of interactions only between flows of different modes; (c) Presence of interactions between flows and decisions.

Another dimension of the MMNDP is the number of modes involved in the travel between two points. In this dimension, there are two cases: (a) The modes involved in the travel of passengers can be only one; (b) The modes involved in the travel of passengers can be more than one.

Certainty or uncertainty is among the effective hypotheses for bringing the problems closer to the real world. In the real world, there is no certainty, and this is also the case with urban transportation networks. In UTNDPs, there is uncertainty surrounding various problems, including travel time, demand, flow, and link capacity, which leads to uncertainty in the network and is called the reliability of urban transportation networks. There are three criteria for assessing the reliability of a transportation network: connectivity reliability, travel time reliability, and capacity reliability [15].

This was a brief description of urban transportation problems. These problems are essentially modeled at two levels, since there are two major decision-makers, namely the citizens and the urban transportation management. It is difficult to solve a bi-level network design problem by the exact solution method because the problem has NP-hardness. One of the initial studies on the bi-level problems was performed by Ben-Ayed and Blair [7] who concluded that even a simple bi-level problem with both linear up and down levels is still NP-hard. Another reason is the non-convexity of the bi-level network design problem. Even though both the up and down levels in the bi-level problems are convex, this does not guarantee the convexity of the bi-level problem [44].

Considering the nature of urban transportation problems, this paper considers two types of decision-makers for modeling. The first decision-maker is the management of the urban transportation network, which seeks to increase the capacity of the network links considering both public transport modes. This can improve the travel time reliability and network capacity reliability by increasing the capacity of the links. These modes of transport are completely independent in terms of flow through links, and passengers can use a combination of modes for their travel and switch transport modes at intersection nodes. The management also seeks to minimize the cost of increased capacity of the links. The result of reliability maximization is overall satisfaction, reduction in traffic, and reduction in travel time or time spent on travel. The second decision-maker in this problem is the passengers who choose a path with minimum average total travel time and maximum capacity reliability according to the management decisions. This problem considers uncertainty in total travel time, flow through links, and travel demand. The modeling also assumes that the decision-makers of the low-level problem are the passengers who want to travel during peak traffic in addition to the normal demand. Another important point to note in this paper is the correlation between all the links forming the path. In the real world, the links forming a path have a correlation due to the passing flow, which should be considered in the calculations. However, according to the hypotheses, there is no correlation between the links with different modes, because they have completely independent movement flows.

This paper consists of 7 sections. Section 2 presents the literature review on the subject of this paper. Section 3 describes a multi-level dual-mode model for the problem presented in this study. Then, Section 4 presents a meta-heuristic solution using the particle swarm optimization (PSO) algorithm for the model presented in Section 3. To apply the proposed model and algorithm, Section 5 examines part of urban transportation network in the metropolitan area of Tehran. Finally, Section 6 draws conclusions and makes suggestions for future research.