A review of urban transportation network design problems

Reza Zanjirani Farahani, Elnaz Miandoabchi, W.Y. Szeto, Hannaneh Rashidi
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2fqqu5s6wbgk5gcucpt3wqm3gy" style="color: black;">European Journal of Operational Research</a> </i> &nbsp;
This paper presents a parsimonious review on the definitions, classifications, objectives, constraints, network topology decision variables, and solution methods of the Urban Transportation Network Design Problem (UTNDP), which includes both the Road Network Design Problem (RNDP) and the Public Transit Network Design Problem (PTNDP). The current trend and gap in each class of the problem are discussed and future directions in terms of both modeling and solution approaches are given. This review
more &raquo; ... intends to give a bigger picture of transportation network design problems, allow comparisons of formulation approaches and solution methods of different problems in various classes of UTNDP, and encourage crossfertilization between the RNDP and PTNDP research. Keywords: Transportation; urban transportation network design problem; road network design; transit network design and frequency setting problem; multi modal network design problem Introduction Transportation is important in the sense that it allows people to take part in human activities. With the increasing population, the demand for transportation is increasing. More and more traffic is on roads, which in turn creates more and more mobility related problems such as congestion, air pollution, noise pollution, and accidents, especially in city centers where the level of human activities is high. Governments need to plan transport networks properly and control the urban traffic movements to ensure mobility and mitigate the mobility related problems simultaneously. The higher population also leads to more expensive land especially in the city centre and hence more people living in new towns or suburbs, thereby requiring new transportation infrastructures for serving new towns or improving existing transportation structures to cope with the increasing population in the suburbs. These planning, design and management issues are traditionally addressed in UTNDP. This problem can actually include the design problems in suburban areas in additional to those in urban areas because the methodology involved is basically the same. Moreover, this problem can involve transit networks in addition to road networks since the transportation include both public and private transport. UTNDP has been continuously studied during the last 5 decades, and the number of related publications is growing over time probably because the problem is highly complicated, theoretically interesting, practically important, and multidisciplinary. A number of reviews has also been published by Boyce (and Hao (2008), and recently by Kepaptsoglou and Karlaftis (2009) . Some of these reviews deal with general network design problems but some focus specifically on urban network design or on one part of urban transportation networks. For example, the first five reviews only focus on RNDP while the last three reviews only focus on PTNDP. As a result, the similarities and differences of the formulation approaches and solution methods between the RNDP and PTNDP cannot be addressed in these reviews, which cannot encourage the crossfertilization of the two research areas. Moreover, the problem that considers the interaction between road and public transit network designs has been ignored in these reviews. This paper attempts to provide a holistic view to UTNDP and its classifications by uniting the decisions for * Corresponding. Fax: +44 020 8417 7026; Tel: +44 020 8517 5098; Email: zanjiranireza@gmail.com 2 improving transportation networks. With regard to this, the current paper covers both problem categories, and presents a third problem category for the joint decisions in road and public transit networks with at least two modes, which considers the interactions of these modes. This paper also contains an updated literature for both fields until early 2011. This contrasts to the last review paper on RNDP which published in late 1990s, and the previous reviews of PTNDP which cover the literature until 2007. The main aim of this paper is to cover problems related to urban transportation network topology and its configuration. In this regards, only the strategic level and a number of tactical level decisions related to network topology are covered in this paper; those papers not related to network topology decisions, such as operational level decisions and tactical decisions that are not related to network topology, will not be covered unless they are considered together with network topology decisions. The problems such as the traffic signal setting, parking pricing, toll setting, and the public transit ticket pricing are important sub-problems of UTNDP and even some of these has long history with lots of important features and development. These sub-problems are deserved to be examined and reviewed in a comprehensive manner in future review papers and hence excluded in this paper. Traffic signal setting has the strongest relevancy with network configuration decisions, as the network topology directly affects the flow pattern and the conflict points at intersections. This subproblem has been studied extensively and it has a relatively large body of literature (e.g. Moreover, this review focuses on deterministic transport networks and deterministic travel demand. That is, we focus on papers that assume no supply and demand uncertainty. For example, there is no randomness in travel demand and road capacity considered in the reviewed papers. Nevertheless, we can still identify current trends and gaps as shown later, and bring out new research directions in this field as shown in the last section. Other than reviewing UTNDP, we also review the solution methods. This allows comparisons of solution methods of different problems in various classes of UTNDP and proposes new algorithmic research directions. This algorithmic review and the new directions are particularly important given that these methods are required to solve practical design problems, and their problem sizes become larger and larger. Real case scenarios are also reviewed to give insight about the size of the networks for each problem catalogues currently considered and give some hints on the future requirement of the solution methods for practical problems. The rest of the paper is organized as follows. Section 2 explains the key definitions, classifications, and general formulations of UTNDP. Section 3 reviews the specific problem studied in the literature. Section 4 depicts the solution methods used in the literature. Section 5 describes the application to real case scenario. Section 6 presents an overall of the research development of UTNDP. Finally, the summary and further research directions are presented in Section 7. Definitions, general formulations and classifications of UTNDP Definitions of UTNDP There are at least three different definitions of UTNDP in the literature: 1. UTNDP is concerned with building new streets or expanding the capacity of existing streets (Dantzig et al., 1979) . This definition is quite common in the literature, but most studies use other names for this problem catalog such as the Road Network Design Problem (RNDP), the transportation network design problem, and the network design problem. 2. UTNDP is to determine the optimal locations of facilities to be added into a transportation network, or determine the optimal capacity enhancements of existing facilities in the network (Friesz, 1985) . In this definition, the facilities may be represented by either nodes or links. Therefore, this definition is wider than the F and u are, respectively, the objective function and (network design) decision variable vector of the upper level problem (U0), and G is a vector function in the upper level constraint. f and v are, respectively, the objective function and decision variable (flow) vector of the lower level problem (L0), and g is a vector function in the lower level constraint. v(u) is called the reaction or response function, which depicts the user reaction in terms of a flow pattern for each network design u. Since v(u) is an implicit function that cannot be shown explicitly, it is depicted by L0. In each network design problem, v(u) is an optimal solution of L0. In fact, the objective of the bi-level network design problem is to find an optimal decision vector u to optimize the objective function F subject to the network design constraint (2) as well as the user reaction constraints (3)-(4). The above lower-level problem can be expressed as a variational inequality; in this case the bi-level network design problem can be formulated as a mathematical program with equilibrium constraints. UTNDP then becomes single-level but conceptually, it is bi-level with two different types of games involved, namely the leader-follower game and the non-cooperative Nash game. Solving a bi-level network design problem using exact solution methods is very difficult because the problem is NP-hard. Ben-Ayed et al. (1988) studied bi-level problems and concluded that even a simple bi-level problem with both linear upper-level and lower-level problems is also NP-hard. Another reason is the non-convexity of bi-level network design problems. Even if both the upper and lower level problems be convex, the convexity of the bi-level problem cannot be guaranteed (Luo et al., 1996) . The presented mathematical model mostly corresponds to RNDPs, while due to the complexity of TNDSPs only in some cases formulating the TNDSP as a bi-level network design problem is possible. Most of the TNDP are single level problems where the reactions of users are simplified. As mentioned by Chakroborty (2003) it is difficult to formulate TNDSP as a mathematical problem, since it is inherently discrete and concepts such as transfers and route continuity are hard to represent. Finally, Baaj and Mahmassani (1991) discussed the complexity of this problem arised from its combinatorial, nonlinearity, non-convexity and multi-objective nature. They also depicted the difficulties in formulating as a mathematical model, and in defining acceptable spatial route layouts. Classifications of Upper Level Problems or Design Problems in UTNDP UTNDP can be classified into problems which arise from variety of possible network design policies and decisions. Traditionally, UTNDP is separately considered in two main catalogues, namely RNDP and TNDSP. RNDP mainly Studies of the Road Network Design Problem (RNDP) Generally, the inputs of RNDP are as follows: (1) The network topology, (2) The travel demand between each origin-destination pair for a specific time interval in terms of a matrix or a function, (3) The characteristics of streets such as the capacity, the number of lanes, the free flow travel time, and the specifications of the travel time function, (4) The upper and lower bounds of decision variables for handling physical or political considerations such as the maximum allowable increase in capacity and the maximum toll level, (5) The set of candidate projects for network improvement, (6) The available budget, and (7) The cost of each candidate project. For some problems such as scheduling traffic light and determining road tolls, inputs (4)-(7) are not necessary. The upper level constraints of RNDP may include the following: (1) The simple upper and lower bound constraints for the decision variables, (2) The budget constraint, and (3) The definitional constraints such as
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejor.2013.01.001">doi:10.1016/j.ejor.2013.01.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yrqqmh5i7bhllblcaldpjy3rca">fatcat:yrqqmh5i7bhllblcaldpjy3rca</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171130013042/https://core.ac.uk/download/pdf/38030803.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/63/3563756c96c4ad3f749ddc298437279eaaade5a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejor.2013.01.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>