کاربرد الگوریتم های ژنتیک برای بهینه سازی مشترک پارامترهای تنظیم دهنده سیگنال و تخصیص ترافیک پویا برای داده شبکه واقعی

This paper presents the joint optimization of signal setting parameters and dynamic user equilibrium (DUE) traffic assignment for the congested urban road network. The simulation-based approach is employed to obtain the DUE condition for the case of multiple-origin multiple-destination traffic flows. The dynamic traffic assignment simulation program (DTASP), developed in C language is used to assign the traffic dynamically on the road network, whereas method of successive averages (MSA) is modified and used to arrive at the DUE condition. The artificial intelligence technique of genetic algorithms (GAs) is applied to obtain the optimal signal setting parameters and path flow distribution factor for DUE condition. The methodology developed in such a way that joint optimization of signal setting parameters with DUE is obtained. The proposed method is applied to the real network data of Fort Area of Mumbai city comprising of 17 nodes and 56 unidirectional links with 72 Origin–Destination pairs, where all the 17 nodes are signalized intersections. The traffic flow condition for the optimized signal setting parameters is considerably improved compared to the existing signal settings. The results prove that the GA is an effective technique to solve the joint optimization problem for the real network data.

The performance of a traffic network can be influenced through several types of actions or decision variables. Some of these pertain to changing the load pattern on the network, through demand management actions, including attempts to route vehicles optimally through the network; others pertain to how traffic flow is controlled through signal control (supply management). Conventional methods for traffic signal optimization assume fixed traffic flows; whereas the traffic assignment methods assume fixed signal settings. This separation of traffic control from assignment may lead to inconsistency between traffic flows and signal settings because they are in general inter-dependent. The inter-dependence tends to be more serious in congested networks. The inconsistency may be eliminated by combining signal optimization with an equilibrium assignment. The combined signal optimization and user equilibrium (UE) traffic assignment problem is one in which a traffic engineer tries to optimize the performance of signals while road users choose their routes in a UE manner (Maher & Zhang, 1999). Some of the most important theoretical contributions to the problem of signal control and UE static assignment are made by Smith (1979, 1981), who derived conditions that guarantee the existence of an equilibrium as well as conditions for the uniqueness and stability of the traffic equilibrium when there is interaction between signal setting and users' route choice decisions. Allsop (1974) has proposed an iterative solution procedure for the UE static assignment problem in a pretimed signal-controlled network. Charlesworth (1977) obtained mutually consistent traffic assignment and signal settings through an iterative procedure in which the TRANSYT software is used to optimize the signal settings. In dynamic traffic assignment (DTA) models, a trip may be regarded as a combination of departure time and route choice; consequently departure rates and hence flows and travel times are time dependent. Ghali and Smith (1993) have implemented an iterative procedure using CONTRAM and showed the convergence pattern for DTA. Gartner and Stamatiadis (1997) have presented a general conceptual framework for the implementation of a combined solution for DTA and signal control, but they have not reported implementation of a specific algorithmic procedure. Abdelfatah and Mahmassani (1998: pp. 185–193) have presented a formulation and solution algorithm for the combined system optimal DTA and signal control. Abdelghany, Valdes, Abdelfatah, and Mahmassani (1999) have introduced and illustrated the path-based signal coordination as an example of integrating signal control with network traffic assignment using the real-time DTA. Signal optimization and DUE condition can be carried out as a joint optimization problem or as a bi-level programming problem. The DUE is based on Wardrop's first principle: “no driver can unilaterally reduce his/her travel costs by shifting to another route” (Wardrop, 1952). In the joint optimization problem, decision variables for signal optimization are cycle time, green splits and phase sequence, whereas appropriate path flow distribution is a decision variable for the DUE problem. Both the problems are solved simultaneously. It is easier to identify the convergence to the optimal solution. Whereas, in the bi-level programming problem, signal optimization is the upper-level problem and DUE assignment is the lower-level problem. As the DUE assignment procedure is iterative, bi-level programming approach requires longer time and also it is difficult to identify whether the iterations are converging to the optimal solution. The associated objectives may not always act in tandem. Moreover, looking to the necessity of solving DTA problem for on-line deployment with faster computational tractability, joint optimization approach is more preferable to adopt compared to the bi-level programming. Considering this, in this paper an attempt has been made to solve this problem as a joint optimization problem and that is also using an artificial intelligence technique of GAs. 1.1. Joint optimization problem In this paper predictive dynamic user equilibrium (PDUE) condition is considered (definition is given in Appendix I), in which user chooses a route that minimizes his/her actual travel time along the route to his destination (Tong & Wong, 2000). In the joint optimization problem, for the signal setting parameters, optimum cycle length, green time splits according to flows on the approaches, phasing and phase sequences, offsets between consecutive signalized intersections etc. are required to be set in such a way that delays due to signalized intersections in the network shall be minimum. At the same time proportion of traffic flow on each link/path shall be such that travel cost/actual travel time of users on the used paths of the network shall be equal and minimal. To obtain the optimum cycle length and green splits, any of the available methods like, Webster's formula (1958), Australian Road Capacity Guide Method (ITE, 1982), Highway Capacity Manual Method (1985) is being used generally. These methods are good enough for isolated intersections. Whereas, for the congested network having number of signalized intersections, phase sequences, offsets and management of turning movements are also required to be considered. For this purpose, softwares like TRANSYT, SCOOT for static assignment and CONTRAM, DYNASMART for DTA can be used. In the proposed study genetic algorithm approach is used to select the optimum cycle, green splits and phase sequence simultaneously with the optimal path flow distribution factor (λ) to solve a joint optimization problem. The GAs are stochastic algorithms and can find close to optimal solution of the noisy, discontinuous or complex objective functions faster than the conventional optimization methods (Deb, 1998; Goldberg, 1989). In this proposed study, PDUE condition gives indirect measure of optimal signal setting parameters in the network, because it minimizes the difference of travel cost (actual travel time) between used and shortest path of the users in the system. Actual travel time in both the conditions is not only a function of delay due to signal setting parameters of the signalized intersections, but it also includes delays due to unsignalized intersections and vehicle interactions on links. These delays are the functions of path flow value also. Thus, the minimization of objective function of PDUE problem with the constraints of signal setting parameters will satisfy the signal optimization with PDUE condition. The formulation of joint optimization problem is given as follows: equation(1) View the MathML sourceminimiseZ(f)=∑∀r,s,p,q∫0Tfrsp(t)[ηrsp(t)−ηrsq(t)](F,S)ⅆt Turn MathJax on Subject to, (i) O–D demand flow constraints: equation(2) View the MathML sourcedrs(t)=∑p∈Prs(t)frsp(t)∀r,s,t Turn MathJax on equation(3) View the MathML sourcefrsp(t)≥0∀r,s,t,p∈Prs(t) Turn MathJax on (ii) Constraints of signal setting parameters: equation(4) View the MathML source∑l=1Φnyln(t)=1−Ln(t)/Cn(t)∀n,t Turn MathJax on equation(5) View the MathML sourceyln(t)(Cn(t)−Ln(t))≥glnmin∀n,t Turn MathJax on (The notations, which are used to represent the variables, are shown in Appendix I) The above function is non-linear and non-convex, that makes it difficult to differentiate and to obtain the global minimum using analytical methods. Hence, simulation approach with an appropriate optimization technique can be applied to solve the objective function. In this study, minimization of the above objective function is carried out by deciding signal setting parameters and path flow distribution factor by a GA optimizer, whereas the DTA is carried out by using the developed DTASP and the modified MSA procedure. These procedures are discussed in the following section.

In this paper PDUE problem is formulated along with constraints of signal setting parameters. The developed traffic simulator (DTASP) is used to load the traffic flows on the network dynamically. The PDUE problem is solved using modified MSA and GA with the optimization of signal setting parameters on a real network data of Fort Area, Mumbai. The conclusions are as follows: • A few researchers have used GA either to solve the DTA problem or to optimize the signal timings in the network, but not for both. Whereas, in this study GAs are successfully used to obtain the PDUE condition along with the optimization of signal setting parameters. • Simulation approach to load the traffic dynamically on the network gives better flexibility than the complex mathematical approach to reflect close to real traffic conditions, particularly for the networks with signalized intersections. • GA has emerged as an efficient technique to solve the non-linear and non-convex PDUE traffic assignment problem along with optimization of signal setting parameters, as it permits the relaxation of many of the assumptions necessary to solve the problem analytically by traditional techniques. • Optimization of signal setting parameters can drastically reduce the travel time of users in the network. Optimization of not only the signal cycle time and green splits, but also of the phase sequence and phase offset is significant to reduce the travel time in the network. Joint optimization of signal setting parameters and PDUE condition is found better using GA and DTASP with modified MSA as it converges very close to the optimal solution (Convergence gap of 2.835%). • Comparison between PDUE condition for existing signal settings and optimized signal settings for the selected network (for the simulation of evening peak 2 h' traffic flow data) shows that by joint optimization – (i) the value of objective function of PDUE is reduced by 11.48%, (ii) convergence gap is reduced by 20.41%, (iii) average travel time of platoons is reduced by 0.59%, and (iv) total system's travel cost is reduced by 1.65%. • Joint optimization using GA may be useful as an off-line application for deciding better signal settings at the network level during peak hours. • On-line application of joint optimization with GA can be made possible by – (i) decreasing simulation time from 2 h to the half an hour, (ii) decreasing pool size and number of generations in GA, and (iii) using higher capacity computer system.