Abstract

The objective of any transit system is to provide good level of service to its users with the available resources. Waiting time of the passengers during their journey is good measure of level of service. Total waiting time on a transit system includes the transfer time of passengers transferring between different routes and the initial waiting time of the passengers waiting to board a bus, at their point of origin. The overall waiting time can be minimized through proper scheduling of the transit system. In this study, the scheduling problem for a transit system, in which capacities of vehicles (say buses) are limited (i.e., may not be able to accommodate all the passengers who are waiting for that bus at that station) is considered. First a mathematical programming (MP) formulation for this problem is presented. However, due to the large number of variables and non-linearity, it is difficult to solve the MP formulation by traditional methods. Hence, a Genetic Algorithm (Genetic Algorithms are powerful search and optimization methods) based procedure is developed and used to solve the problem. Function based declarations and coding of variables possible in GA-based algorithms allow an efficient reformulation of the original problem. The revised formulation of the problem is computationally much simpler than the original formulation of the problem (it may be noted that one can revise the formulation because of certain features present in GAs). Results from a number of test cases show that the proposed procedure is able to find optimal schedules with reasonable computational resource.