Evaluating Meta-heuristic Algorithms for Dynamic Capacitated Arc Routing Problems Based on a Novel Lower Bound Method

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.