A robust algorithm to solve the signal setting problem considering different traffic assignment approaches

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In this paper we extend a stochastic discrete optimization algorithm so as to tackle the signal setting problem. Signalized junctions represent critical points of an urban transportation network, and the efficiency of their traffic signal setting influences the overall network performance. Since road congestion usually takes place at or close to junction areas, an improvement in signal settings contributes to improving travel times, drivers’ comfort, fuel consumption efficiency, pollution and safety. In a traffic network, the signal control strategy affects the travel time on the roads and influences drivers’ route choice behavior. The paper presents an algorithm for signal setting optimization of signalized junctions in a congested road network. The objective function used in this work is a weighted sum of delays caused by the signalized intersections. We propose an iterative procedure to solve the problem by alternately updating signal settings based on fixed flows and traffic assignment based on fixed signal settings. To show the robustness of our method, we consider two different assignment methods: one based on user equilibrium assignment, well established in the literature as well as in practice, and the other based on a platoon simulation model with vehicular flow propagation and spill-back. Our optimization algorithm is also compared with others well known in the literature for this problem. The surrogate method (SM), particle swarm optimization (PSO) and the genetic algorithm (GA) are compared for a combined problem of global optimization of signal settings and traffic assignment (GOSSTA). Numerical experiments on a real test network are reported.

Adacher, L. (2012). A global optimization approach to solve the traffic signal synchronization problem, Procedia-Social and Behavioral Sciences 54: 1270-1277.

Adacher, L. and Cipriani, E. (2010). A surrogate approach for the global optimization of signal settings and traffic assignment problem, 13th International IEEE Conference on Intelligent Transportation Systems (ITSC), Funchal, Portugal, pp. 60-65.

Adacher, L., Cipriani, E. and Gemma, A. (2015). The global optimization of signal settings and traffic assignment combined problem: A comparison between algorithms, Advances in Transportation Studies 36: 35-48.

Adacher, L. and Gemma, A. (2016). An optimizing algorithm to minimize the delay signal setting problem, 3rd International Conference on Mathematics and Computers in Sciences and in Industry (MCSI), Crete, Greece, pp. 197-202.

Allsop, R. and Charlesworth, J. (1977). Traffic in a signal-controlled road network: An example of different signal timings including different routeing, Traffic Engineering & Control 18(5): 262-265.

Cascetta, E., Gallo, M. and Montella, B. (1998). Optimal signal setting on traffic networks with stochastic equilibrium assignment, Proceedings of TRISTAN III, San Juan, Puerto Rico, pp. 17-23.

Ceylan, H. and Bell, M. (2004). Traffic signal timing optimisation based on genetic algorithm approach, including drivers’ routing, Transportation Research B: Methodological 38(4): 329-342.

Chang, T. and Sun, G. (2004). Modeling and optimization of an oversaturated signalized network, Transportation Research B: Methodological 38(8): 687-707.

Chiou, S. (2005). Joint optimization for area traffic control and network flow, Computers & Operations Research 32(11): 2821-2841.

Cohen, S. (1983). Concurrent use of MAXBAND and TRANSYT signal timing programs for arterial signal optimization, Transportation Research Record (906): 81-84.

Cohen, S. and Liu, C. (1986). The bandwidth-constrained TRANSYT signal-optimization program (discussion and closure), Transportation Research Record (1057): 1-7.

Colombaroni, C., Fusco, G., Gemma, A., Demiralp, M., Baykara, N. and Mastorakis, N. (2009). Optimization of traffic signals on urban arteries through a platoon-based simulation model, WSEAS International Conference, Istanbul, Turkey, pp. 450-455.

Fusco, G., Bielli, M., Cipriami, E., Gori, S. and Nigro, M. (2013). Signal settings synchronization and dynamic traffic modelling, European Transport 53, Paper no. 7.

Gokbayrak, K. and Cassandras, C.G. (2002). Generalized surrogate problem methodology for online stochastic discrete optimization, Journal of Optimization Theory and Applications 114(1): 97-132.

Goliya, H. and Jain, N. (2012). Synchronization of traffic signals: “A case study-eastern ring road, Indore”, International Journal of Advanced Technology in Civil Engineering 1(2): 1-7.

Góngora, P.A. and Rosenblueth, D.A. (2015). A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria, International Journal of Applied Mathematics and Computer Science 25(3): 577-596, DOI: 10.1515/amcs-2015-0043.

Hadi, M. and Wallace, C. (1993). Algorithm to optimize signal phasing and transportation research record, Transportation Research Record (1421): 104-112.

Khaki, A. and Pour, P. (2014). The impacts of traffic signal timings optimization on reducing vehicle emissions and fuel consumption by aimsun and synchro software’s (Case study: Tehran intersections), International Journal of Civil and Structural Engineering 5(2): 144.

Klaučo, M., Blažek, S. and Kvasnica, M. (2016). An optimal path planning problem for heterogeneous multi-vehicle systems, International Journal of Applied Mathematics and Computer Science 26(2): 297-308, DOI: 10.1515/amcs-2016-0021.

Köhler, E., Möhring, R., Nökel, K. and Wünsch, G. (2008). Optimization of signalized traffic networks, in H.J. Krebs and W. J¨ager (Eds.), Mathematics-Key Technology for the Future, Springer, Berlin/Heidelberg, pp. 179-188.

Malakapalli, M.M. (1993). Enhancements to the PASSER II-90 delay estimation procedures, Transportation Research Record (1421): 94-103.

Nagel, K. and Flötteröd, G. (2012). Agent-based traffic assignment: Going from trips to behavioural travelers, 12th International Conference on Travel Behaviour Research, Jaipur, Rajasthan, India, pp. 261-294.

Park, B., Messer, C. and Urbanik, T. (1999). Traffic signal optimization program for oversaturated conditions: Genetic algorithm approach, Transportation Research Record (1683): 133-142.

Robertson, D. (1969). Transyt: A traffic network study tool ministry of transport, RRL Report LR253, Crowthorne, Berkshire.

Smith, M. (2006). Bilevel optimisation of prices and signals in transportation models, in S. Lawphongpanich et al. (Eds.), Mathematical and Computational Models for Congestion Charging, Springer, Boston, MA, pp. 159-199.

Smith, M. (2015). Traffic signal control and route choice: A new assignment and control model which designs signal timings, Transportation Research C: Emerging Technologies 58: 451-473.

Stevanovic, A., Stevanovic, J., Zhang, K. and Batterman, S. (2009). Optimizing traffic control to reduce fuel consumption and vehicular emissions: Integrated approach with VISSIM, CMEM, and VISGAOST, Transportation Research Record: Journal of the Transportation Research Board (2128): 105-113.

Sun, D., Benekohal, R.F. and Waller, S. (2006). Bi-level programming formulation and heuristic solution approach for dynamic traffic signal optimization, Computer-Aided Civil and Infrastructure Engineering 21(5): 321-333.

Szeto, W. and Lo, H. (2006). Dynamic traffic assignment: Properties and extensions, Transportmetrica 2(1): 31-52.

Teklu, F., Sumalee, A. and Watling, D. (2007). A genetic algorithm approach for optimizing traffic control signals considering routing, Computer-Aided Civil and Infrastructure Engineering 22(1): 31-43.

Van den Berg, M., De Schutter, B., Hellendoorn, J. and Hegyi, A. (2008). Influencing route choice in traffic networks: A model predictive control approach based on mixed-integer linear programming, IEEE International Conference on Control Applications, CCA 2008, San Antonio, TX, USA, pp. 299-304.

Xiaojian, H., Jian, L.,Wang, W. and Zhirui, Y. (2015). Research article traffic signal synchronization in the saturated high-density grid road, Computational Intelligence and Neuroscience 2015, Article ID: 532960.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

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