Solving the Public Transportation Problem Using Linear Programming and hybrid PS-ACO Meta-heuristic Method

Bus urban public transport is one of the most considered systems and the buses have received more attention because of their special privileges compared to other systems. In most cities, the bus system is responsible due to the lack of advanced transportation systems such as subways, trams, and light-rail. Due to the positive attributes and advantages of this system, the improvement of their capabilities needs planning and consulting with experts. In this paper, a linear programming model for optimizing the public bus transportation system is proposed to minimize the total cost of setting up the lines, maintenance costs and fuel consumption as well as minimizing the bus arrival times in order to increase the welfare of the passengers. The proposed model is simulated in GAMS software and the sensitivity analysis is performed over the parameters. Due to the time complexity of the proposed model, a hybrid meta-heuristic method based on the Ant Colony Optimization (ACO) and Particle Swarm Intelligence (PSO) name PS-ACO is also developed and simulated in Matlab for solving the proposed model. The computational results show that the fuel cost and distance between stations have the most effect on operational cost, and the time distance between the stations is the most effective parameter on the passenger's welfare. Besides, the number of the stations highly affects the model complexity and solution time.