Ant Colony Optimization Approach for Optimizing Traffic Signal Timings

Abstract

In urban networks, traffic signals are used to control vehicle movements so as to reduce congestion, improve safety, and enable specific strategies such as minimizing delays, improving environmental pollution, etc (Teklu et al., 2007). Due to the increasing in the number of cars and developing industry, finding optimal traffic signal parameters has been an important task in order to use the network capacity optimally. Through the last decade, developments in communications and information technologies have improved the classical methods for optimising the traffic signal timings toward the intelligent ones. There is an important interaction between the signal timings and the routes chosen by individual road users in road networks controlled by fixed time signals. The mutual interaction leads to the framework of a leader-follower or Stackelberg game, where the supplier is the leader and the user is the follower (Fisk, 1984). Network design problem (NDP) that it may contain the signal setting problem is characterized by the so called bilevel structure. Bi-level programming problems generally are difficult to solve, because the evaluation of the upper-level objective involves solving the lower level problem for every feasible set of upper level decisions (Sun et al., 2006). On the upper level, a transport planner designs the network. Road users respond to that design in the lower level. This problem is known to be one of the most attractive mathematical problems in the optimization field because of non-convexity of feasible region that it has multiple local optima (Baskan, 2009). Moreover, the driver’s behaviours on the network should be taken into account when the traffic signal timings are optimised. When drivers follow the Wardrop’s (1952) first principle, the problem is called the “user equilibrium” (UE). On the other hand, it turns to the stochastic user equilibrium (SUE) in the case that the users’ face with the decision of route choice between the each Origin-Destination (O-D) pair for a given road network according to perceived travel time. The difference between SUE and UE approaches is that in SUE models each driver is meant to define ‘travel costs’ individually instead of using a single definition of costs applicable to all drivers. SUE traffic assignment takes into account the variability in driver’s perception of cost. This is done by treating the perceived cost on