Optimizing a public transportation system by a vector-evaluated particle swarm optimization algorithm - A case study in an urban bus organization

Expanding cities and population causes an increase of travel demands. Private vehicles cannot cope with responding to the travel demand of the large urban population. Therefore, it is interesting and unavoidable issue to use different urban public transportation systems for commuters in cities. Different parameters are involved in the public transportation system development. Some parameters are as follows: travel time, walking time to bus stop, travel convening, utility cost resulted from a public transportation system and maximum routes covering and crossing the downtown and the like. However, the most important parameters that causes in increasing the use of the public transportation system is travel time and travel cost for commuters. For this purpose, a multi-objective mathematical model is presented to minimize the travel time and travel cost while covering the routes with the minimum number of buses. Due to the NP-hardness of such a hard routing problem, a vector-evaluated particle swarm optimization (VEPSO) algorithm is proposed to solve a real case problem for the current routes of the Ardabil urban bus system. The associated results are compared with the multi-objective particle swarm optimization (MOPSO) algorithm. The comparison of the obtained results shows the efficiency of the VEPSO algorithm for the considered case study.