Robust Optimization in Uncertain Capacitated Arc Routing Problems: Progresses and Perspectives [Review Article

Abstract

The capacitated arc routing problem is an important NP-hard problem with numerous real-world applications. The capacitated arc routing problem with uncertainties refers to those instances where there are uncertainties in decision variables, objective functions and/or constraints. The capacitated arc routing problem with uncertainties captures real-world situations much better than a static capacitated arc routing problem because few real-world problems are static and certain. Uncertainties in the capacitated arc routing problem pose new research challenges. Algorithms that work well for a static and certain capacitated arc routing problem may not work on the version with uncer-tainties. There have been increasing progresses in studying the capacitated arc routing problem with uncertainties during the past two decades. However, the papers on the capacitated arc rout-ing problem with uncertainties have been scattered around in different journals and conferences in artificial intelligence, computer science, and operational research. Different defini-tions and formulations of capacitated arc routing problem with uncertainties are used by different papers, making comparisons difficult. In order to better understand the state-of-the-art in solv-ing the capacitated arc routing problem with uncertainties, this paper presents a comprehensive review of the problem and its key research issues. Not only has the paper summarized the progresses so far, key research issues are identified, including scalability of the algorithms, performance measures, common benchmarks, etc. Future research direc-tions are also identified at the end of this review.