Читать книгу Optimization and Machine Learning - Patrick Siarry - Страница 15

The 2L-CVRP is an NP-hard problem, it is solved by exact, heuristic and metaheuristic algorithms:

Iori et al. (2007) use the first exact algorithm for solving small-scale instances of the 2L-CVRP and only for the sequential variant. They proposed a branch-and-cut approach for the routing problem and branch-and-bound for the packing problem.

Gendreau et al. (2008) use a Tabu search (TS) metaheuristic algorithm. They considered two loading heuristics for the sequential and unrestricted case, known as the LH2S L and the LH2U L.

Zachariadis et al. (2009) propose another metaheuristic algorithm which integrates TS and guided local search, referred to as GTS. For the loading problem, they used five packing heuristics and three neighborhood searches to generate the initial solution, namely: customer relocation, route exchange and route interchange.

Fuellerer et al. (2009) present an algorithm based on ant colony optimization (ACO) while bottom-left-fill and touching perimeter algorithms are proposed for solving the packing problem.

Leung et al. (2011) propose an extended guided Tabu search (EGTS) algorithm for the routing problem and a lowest line best-fit heuristic (LBFH) to solve 2D-BPP.

Duhamel et al. (2011) use the greedy randomized adaptive search procedure and the evolutionary local search algorithm, denoted GRASP-ELS.

Leung et al. (2013) study the heterogeneous fleet vehicle routing problem (2L-HFVRP). They propose six packing heuristics to check the feasibility of loading (presented in Table 1.1) and simulated annealing with a heuristic local search (SA-HLS) for the routing problem.

Zacharidis et al. (2013) present a static move description algorithm.

Dominguez et al. (2016) study the 2L-CVRP with a heterogeneous fleet using the multi-start biased randomized algorithm and the touching perimeter algorithm for the packing problem.

Wei et al. (2015) propose a variable neighborhood search (VNS) approach for solving the 2L-CVRP and adapt the skyline heuristic to examine loading constraints.

Wei et al. (2017) propose the simulated annealing (SA) algorithm to solve 2 |SO| L, 2 |SR| L, 2 |UO| L and 2 |UR| L versions of the 2L-CVRP.

Sbai et al. (2017) propose a new heuristic based on an adaptive genetic algorithm (GA) for solving the 2L-CVRP, considering only the unrestricted loading case.

Sabar et al. (2020) present a heterogeneous fleet 2L-CVRP, denoted as 2L-HFVRP. They propose a two-stage method: the routing stage and the packing stage. The problem is solved using MA for the routing stage and five heuristics (presented in Table 1.1) for the packing stage.

Coté et al. (2020) introduce a stochastic variant of the 2L-CVRP, known as the S2L-CVRP, where the size of some items is uncertain at the time the vehicle routes are planned. They use a lower bounding functional, called L-cuts, to solve the problem.

Figure 1.1. An example of a 2L-CVRP solution