The capacitated location-routing problem involves determining the depots from
a set of candidate capacitated depot locations and finding the required routes
from the selected depots to serve a set of customers whereas minimizing a cost
function that includes the cost of opening the chosen depots, the fixed
utilization cost per vehicle used, and the total cost (distance) of the routes.
This paper presents a multi-population integrated framework in which a
multi-depot edge assembly crossover generates promising offspring solutions
from the perspective of both depot location and route edge assembly. The method
includes an effective neighborhood-based local search, a feasibility-restoring
procedure and a diversification-oriented mutation. Of particular interest is
the multi-population scheme which organizes the population into multiple
subpopulations based on depot configurations. Extensive experiments on 281
benchmark instances from the literature show that the algorithm performs
remarkably well, by improving 101 best-known results (new upper bounds) and
matching 84 best-known results. Additional experiments are presented to gain
insight into the role of the key elements of the algorithm.

该研究提出了一个多种群综合框架，通过多个仓库配置生成有效的子代解决方案，包括一个有效的基于邻域的局部搜索、一个可行性恢复过程和一个多样化的突变方法，在 281 个基准实例的广泛实验中得到了明显的改进，并匹配了 84 个已知的最佳结果。