Meta-heuristic algorithms, especially evolutionary algorithms, have been frequently used to find near optimal solutions to combinatorial optimization problems. The evaluation of such algorithms is often conducted through comparisons with other algorithms on a set of benchmark problems. However, even if one algorithm is the best among all those compared, it still has difficulties in determining the true quality of the solutions found because the true optima are unknown, especially in dynamic environments. It would be desirable to evaluate algorithms not only relatively through comparisons with others, but also in absolute terms by estimating their quality compared to the true global optima. Unfortunately, true global optima are normally unknown or hard to find since the problems being addressed are NP-hard. In this paper, instead of using true global optima, lower bounds are derived to carry out an objective evaluation of the solution quality. In particular, the first approach capable of deriving a lower bound for dynamic capacitated arc routing problem (DCARP) instances is proposed, and two optimization algorithms for DCARP are evaluated based on such a lower bound approach. An effective graph pruning strategy is introduced to reduce the time complexity of our proposed approach. Our experiments demonstrate that our approach provides tight lower bounds for small DCARP instances. Two optimization algorithms are evaluated on a set of DCARP instances through the derived lower bounds in our experimental studies, and the results reveal that the algorithms still have room for improvement for large complex instances.

中文翻译：

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基于新型下界方法评估动态电容圆弧路由问题的元启发式算法


元启发式算法，尤其是进化算法，经常被用来寻找组合优化问题的近乎最优的解决方案。此类算法的评估通常是通过与一组基准问题上的其他算法进行比较来进行的。然而，即使一种算法是所有比较算法中最好的，它仍然难以确定找到的解的真实质量，因为真正的最优值是未知的，尤其是在动态环境中。最好不仅通过与其他算法的比较来相对地评估算法，而且通过估计它们与真正的全局最优值相比的质量来绝对评估算法。不幸的是，真正的全局最优通常是未知的或难以找到的，因为所解决的问题是 NP 困难的。在本文中，没有使用真正的全局最优值，而是推导出了下限来对解质量进行客观评估。特别地，提出了第一种方法能够推导出动态电容电弧路由问题 （DCARP） 实例的下界，并基于该下界方法评估了两种 DCARP 优化算法。引入了一种有效的图修剪策略来降低我们提出的方法的时间复杂性。我们的实验表明，我们的方法为小型 DCARP 实例提供了严格的下限。在我们的实验研究中，通过推导的下界在一组 DCARP 实例上评估了两种优化算法，结果表明，对于大型复杂实例，这些算法仍有改进的空间。