A hybrid discrete artificial bee colony for the green pickup and delivery problem with time windows

Abstract

This paper formulates a new optimization pickup and delivery problem with time windows which take into account CO2 emissions. This new NP-hard combinatorial optimization problem is called green pickup and delivery problem with time windows (GPDPTW), the recent development in the vehicle routing problem and its variants, which extends PDP and PDPTW with respect to several constraints. The objective is to find a set of routes for a fleet of vehicles in order to serve given transportation requests with a minimization of fuel consumption and CO2 emission to ensure the preservation of a clean and green environment. This paper presents a mathematical formulation and proposes a hybrid discrete artificial bee colony algorithm (HDABC) as a meta-heuristic algorithm which combines a discrete artificial bee colony with neighborhood operators to solve the GPDPTW model. To the best of our knowledge, this is the first time that an emission of CO2 for the PDPTW is proposed. We performed computational experiments to evaluate the effectiveness of the proposed method, which provides the best result and can effectively find an optimal tour. Our results show that, (1) the shortest route is not necessarily the route that consumes the least fuel; (2) the fuel consumption is affected by the load and the number of vehicles.