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Bu çalışmada optimum bağ kapasite genişletme değerlerinin belirlenmesi sürekli ulaşım ağ tasarım problemi olarak formüle edilmiştir. Emisyon salınım miktarlarının dikkate alınarak optimum bağ kapasite genişletmelerinin hesaplanabilmesi için diferansiyel gelişim algoritması tabanlı iki seviyeli programlama modeli geliştirilmiştir. Problemin çözümü için geliştirilen iki seviyeli modelde üst seviyedeki amaç fonksiyonu, ağdaki toplam seyahat süresi, bağ kapasitesi genişletmelerinin toplam yatırım maliyeti ve kirleticilerin oluşturduğu emisyon salınım maliyeti olarak tanımlanmıştır. Alt seviyede ise deterministik trafik atama problemi çözülmüştür.Geliştirilen modelin etkinliğini gösterebilmek için Sioux-Falls karayolu ağında model test edilmiştir. Emisyon salınım maliyetinin sürekli ulaşım ağ tasarım problemine eklenmesinin etkilerinin daha iyi görülebilmesi için dört adet senaryo analiz edilmiştir. Senaryo 1’de amaç fonksiyonu olarak sadece emisyon salınımlarının oluşturduğu maliyet dikkate alınmıştır. İkinci senaryoda amaç fonksiyonu hesaplanırken emisyon salınımlarına ait maliyet ve ağdaki kapasite genişletmesine ilişkin yatırım maliyeti dikkate alınmıştır. Senaryo3’te toplam seyahat maliyeti ve yatırım maliyetleri amaç fonksiyonuna dahil edilmiş ve son senaryoda ise bu maliyetlere ek olarak emisyon salınım maliyetleri de göz önüne alınmıştır. Senaryolar karşılaştırıldığında emisyon salınım maliyetinin dikkate alınması durumunda elde edilen optimum bağ kapasite genişletmeleri değerlerinin sadece seyahat ve yatırım maliyetlerinin dikkate alındığı durumda elde edilen sonuçlara göre yaklaşık olarak %3,5 fazla olduğu bulunmuştur. In this study, determining of optimum link capacity expansions is formulated as a continuous transportation network design problem. To calculate the optimum link capacity expansions by considering the emission, a bi-level programming model based on the differential evaluation algorithm has been developed. In the bi-level model, the upper-level objective function is defined as the total travel time in the network, the total investment cost of link capacity expansions, and the emission cost. The deterministic traffic assignment problem is solved at the lower level.To demonstrate the effectiveness of the developed model, the model has been tested in the Sioux-Falls transportation network. Four scenarios are analysed to better understand the effect of adding the emission cost to the continuous transportation network design problem. In Scenario 1, only the emission cost is considered as the objective function. In the second scenario, the emission and the investment costs of link capacity expansions in the network are taken into account while calculating the objective function. In scenario 3, total travel costs and investment costs are included in the objective function, and in the last scenario, emission cost is also considered in addition to these costs. When the scenarios are compared, it was found that the optimum link capacity expansions obtained when the emission cost is considered, are approximately 3.5% higher than the results obtained when only travel and investment costs are taken into account.

Since the bilevel formulation of the Continuous Network Design Problem (CNDP) has the characteristic of a non- convex optimization problem, heuristic methods are usually the preferred option for solving it. On the other hand, the computation time is crucial importance for solving the CNDP because the algorithms implemented on real sized networks require solving traffic assignment model many times, in which algorithms spend more time in comparison with the other parts of the solution process. Therefore, solving the CNDP with less number of traffic assignments can be assessed as one of the most important topics in the transportation field. Thus, the paper deals with analyzing the performance of recently developed heuristic methods in solving the CNDP. In this study, the capability of Harmony Search (HS), Artificial Bee Colony (ABC) and Differential Evolution (DE) algorithms for solving the CNDP is evaluated, and numerical calculations are performed on example test networks. The results obtained through the HS, ABC and DE algorithms on 18-link network are compared with those generated by two different heuristic methods, which are available in a previous study. Additionally, the performance of the proposed heuristics is compared on Sioux Falls city network with other major algorithms available in the literature. Numerical examples have clearly indicated that the DE shows good performance in comparison with the proposed algorithms in terms of both objective function value and required computational effort.

The Continuous Network Design Problem (CNDP) is recognized to be one of the most difficult problems in transportation field since the bilevel formulation of the CNDP is nonconvex. On the other hand, the computation time is crucial importance for solving the CNDP because the algorithms implemented on real sized networks require solving traffic assignment model many times, which is the most time consuming part of the solution process. Although the methods developed so far are capable of solving the CNDP, an efficient algorithm, which is able to solve the CNDP with less number of User Equilibrium (UE) assignments, is still needed. Therefore, this paper deals with solving the CNDP using MOdified Differential Evolution (MODE) algorithm with a new local search and mutation operators. For this purpose, a bilevel model is proposed, in which the upper level problem deals with minimizing the sum of total travel time and investment cost of link capacity expansions, while at the lower level problem, UE link Bows are determined by Wardrop's first principle. A numerical example is presented to compare the proposed MODE algorithm with some existing methods. Results showed that the proposed algorithm may effectively be used in order to reduce the number of UE assignments in solving the CNDP. (C) 2013 The Authors. Published by Elsevier Ltd.

Route guidance and information systems are developed and popularly applied to help travelers to make route decisions today. Such devices can present information or give recommendations, so they have influence on the travelers' travel choice in the traffic network. In this sense, the influence of the guidance system on travelers’ route choice should be considered when the scenario of traffic network design is developed. However, few existing traffic network design problem models consider the effect, and this motivates the authors to develop a Continuous Network Design Problem (CNDP) model under a traffic network with guidance system. This study is based on the research of Jahn et al. (2005) to develop a single level program for CNDP under the traffic network with guidance system. The guidance system gives advice to travelers based on system optimal rules with user constrains. From the result of simulation, it can be inferred that if the tolerance factor φ is properly chosen in the CNDP model, travelers all can decrease their travel time after network design than that they experienced at user equilibrium before network enhancement. That is to say, every traveler can profit from this CNDP scenario for proper tolerance factor φ.