Differential evolution algorithms for scheduling raw milk transportation

• The heterogeneous fleet with many tanks is considered to collect raw milk.
• Raw milk from different centers cannot be transferred into the same compartment.
• Both traveling costs and cleaning costs are considered as the objective function.
• Five modified DEs were proposed including reincarnation and survival processes.
• Skipped customer and multi-route processes were developed in the decoding process.

This paper focuses on determining routes for raw milk collection from collection centers to dairy factories with the objective of minimizing the total costs, considering fuel costs and costs of cleaning and sanitizing raw milk tanks on vehicles. This problem is considered to be a special case of the vehicle routing problem (VRP) but it is complex compared to the general VRP, especially since each vehicle contains more than one tank with heterogeneous capacity to collect raw milk and raw milk from different collection centers cannot be transferred into the same compartment. In this paper, a DE metaheuristic was used to solve the problem. In order to improve the solution quality, five modified DE algorithms with two additional steps, reincarnation and survival processes, were proposed. In addition, the skipped customer and multi-route attributes are also developed in the decoding process in order to obtain a shorter traveling distance and lower truck usage in the system, especially if they are used together with the reincarnation and survival processes. The computational results reveal that the modified DE algorithms yield higher relative improvement (RI) on the total costs and also the RI on the number of vehicles used.