a vehicle routing problem with minimizing fuel consumption and number of vehicles by improved particle swarm optimization

in recent years, reducing emissions has become an important issue. besides reducing the economic costs, reducing the fuel consumption decreases emissions, pollutant impact and increases society health as well. green vehicle routing problem are a major key to reduce hazardous effects of transportation such as air pollution, greenhouse gas (ghg) emissions, noise and the like. generally, the amount of pollution emitted by a vehicle over an arc  depends on many factors like vehicle load, travel speed, travel distance, road slop and etc. vehicle load has a major effect among other factors on amount of emissions and influences the route selection. some works were completed on the estimation of the cost of the ghg emissions. therefore, the effect of the carried load in fuel consumption is contributed in the model by minimizing a weighted load function. this paper presents a new method for vehicle routing problem with minimizing fuel consumption and number of vehicles. distributing managers are often interested in minimizing fuel consumption caused by two reasons: 1) reducing fuel consumption caused to reduce the service cost, economic costs and increasing customer’s satisfaction, and 2) reducing fuel consumption is a way for reducing pollutant negative impact on our environment and increasing society health. also, minimizing the number of vehicles is caused the reducing in fixed and other related cost. it is proven that vrps belong to the category of np-hard problems thus due to the complexity of vrp with exact methods in large-scale problems, a meta-heuristic method based on particle swarm optimization is proposed, so called improved particle swarm optimization (ipso). in addition, to show the efficiency of the proposed ipso, a number of test problems in small and large sizes are proposed and solved by the ipso. then, the obtained results are evaluated with the results obtained by lingo.