@article{dcae45bfa97a4d54b336dee039fa3dc8, title = "The two-dimensional vector packing problem with general costs", abstract = "The two-dimensional vector packing problem with general costs (2DVPP-GC) arises in logistics where shipping items of different weight and volume are packed into cartons before being transported by a courier company. In practice, the delivery cost of a carton of items is usually retrieved from a cost table. The costs may not preserve any known mathematical function since it could specify arbitrary price at any possible weight. Such a general pricing scheme meets a majority of real-world bin packing applications, where the price of delivery service is determined by many complicated and correlated factors. Compared to the classical bin packing problem and its variants, the 2DVPP-GC is more complex and challenging. To solve the 2DVPP-GC with minimizing the total cost, we propose a memetic algorithm to compute solutions of high quality. Fitness functions and improved operators are proposed to achieve effectiveness. Computational experiments on a variety of test instances show that the algorithm is competent to solve the 2DVPP-GC. In particular, optimal solutions are found in a second for all the test instances that have a known optimal solution.", keywords = "Application, Bin packing, General costs, Memetic algorithm, Two-dimensional vector packing", author = "Qian Hu and Lijun Wei and Andrew Lim", year = "2018", month = jan, doi = "10.1016/j.omega.2017.01.006", language = "English", volume = "74", pages = "59--69", journal = "Omega", issn = "0305-0483", publisher = "Pergamon Press", }