A three-dimensional ant colony optimization algorithm for multi-compartment vehicle routing problem considering carbon emissions

A three-dimensional ant colony optimization algorithm (TDACO) is proposed to solve the multi-compartment vehicle routing problem (MCVRP) arising in many industries, such as petrol station replenishment, cold chain logistics, and waste collection. The objective of this problem to be minimized is the total transportation cost including the consideration of carbon emissions (TC_CE). In TDACO, a new three-dimensional pheromone concentration matrix is first presented to learn and accumulate the valuable information from excellent individuals or ants. Then, to make the algorithm have high-quality search in the initial stage, five heuristic rules are designed to initialize the pheromone concentration matrix and construct the initial population or colony. In addition, the vehicle capacity rate and carbon emissions are brought into the state transition rule to reasonably guide the global search towards the promising solutions or regions. Moreover, an adaptive local search with the speed-up search strategy and the first move strategy is devised to perform effective exploitation from the promising regions. Finally, comparative experiments on benchmark problem instances with different scales are conducted, and the superior performance of the proposed TDACO is verified. •The multi-compartment vehicle routing problem considering the carbon emissions is modeled.•Five new heuristic rules are presented to generate high-quality initial individuals.•A three-dimensional pheromone matrix is established.•A sampling method using the newly constructed state transition rule is devised.•An adaptive multi-neighborhood search with two strategies is designed.