Читать книгу Optimization and Machine Learning - Patrick Siarry - Страница 26

Moura (2008) presented three objectives organized as follows, to minimize the number of vehicles and the total distance and to maximize the volume used, respectively. Moura and Oliveira (2009) developed a sequential approach (using LS and GRASP heuristics) and a hierarchical approach (using constructive; post constructive; and local search phase) to solve the 3L-CVRPTW. The objectives are to minimize the number of vehicles and the total route time. In the hierarchical approach, the loading problem is seen as a sub-problem of the routing problem.

Bortfeldt and Homberger (2013) described two steps: the first one is to pack items into vehicles with respect to the capacity of each vehicle and the second one consists of designing a route sequence.

Zhang et al. (2017) proposed a hybrid approach by combining TS and the artificial bee colony (ABC) algorithm to solve a VRP with pallet loading and time window constraints.

The problem considers the LIFO constraint; fragility and orientation are not considered. Moura et al. (2019) presented a MILP model. The model allows all boxes to rotate in 3D and they may also have fixed or limited orientation. The boxes could be loaded in multiple layers formed by different sized and shaped boxes.

Vega et al. (2019) studied VRP with 3D loading constraints and additional constraints such as time windows and capacity constraints. They proposed a nonlinear mixed integer program (NLMIP). Pace et al. (2015) considered a constraint of a heterogeneous fleet of vehicles for the 3L-CVRPTW. Iterated local search (ILS) and simulated annealing (SA) are proposed to solve the problem.