A meta‐heuristic algorithm for heterogeneous fleet vehicle routing problems with two‐dimensional loading constraints

The two‐dimensional loading heterogeneous fleet vehicle routing problem (2L‐HFVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles. These vehicles have different capacities, fixed and variable operating costs, length and width in dimension, and two‐dimensional loading constraints. The objective of this problem is to minimize transportation cost of designed routes, according to which vehicles are used, to satisfy the customer demand. In this study, we proposed a simulated annealing with heuristic local search (SA_HLS) to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints in 2L‐HFVRP. To speed up the search process, a data structure was used to record the information related to loading feasibility. The effectiveness of SA_HLS was tested on benchmark instances derived from the two‐dimensional loading vehicle routing problem (2L‐CVRP). In addition, the performance of SA_HLS was also compared with three other 2L‐CVRP models and four HFVRP methods found in the literature.