An Exact Algorithm for the Shortest Path Problem With Position-Based Learning Effects
研究了带学习效应的最短路径问题，提出一种改进的A*算法（AA*），证明了其可采纳性，并分析了启发函数的一致性与单调性对搜索效率的影响。
The shortest path problems (SPPs) with learning effects (SPLEs) have many potential and interesting applications. However, at the same time they are very complex and have not been studied much in the literature. In this paper, we show that learning effects make SPLEs completely different from SPPs. An adapted A* (AA*) is proposed for the SPLE problem under study. Though global optimality implies local optimality in SPPs, it is not the case for SPLEs. As all subpaths of potential shortest solution paths need to be stored during the search process, a search graph is adopted by AA* rather than a search tree used by A*. Admissibility of AA* is proven. Monotonicity and consistency of the heuristic functions of AA* are redefined and the corresponding properties are analyzed. Consistency/monotonicity relationships between the heuristic functions of AA* and those of A* are explored. Their impacts on efficiency of searching procedures are theoretically analyzed and experimentally evaluated.