An Exact Algorithm for the Shortest Path Problem With Position-Based Learning Effects

[EN] 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.This work was supported in part by the National Natural Science Foundation of China under Grant 61572127 and Grant 61272377, and in part by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20120092110027. The work of R. Ruiz was supported in part by the Spanish Ministry of Economy and Competitiveness under Project "RESULT-Realistic Extended Scheduling Using Light Techniques" under Grant DPI2012-36243-C02-01, and in part by the FEDER.Wang, Y.; Li, X.; Ruiz García, R. (2017). An Exact Algorithm for the Shortest Path Problem With Position-Based Learning Effects. IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans. 47(11):3037-3049. https://doi.org/10.1109/TSMC.2016.2560418S30373049471

Short-Sighted Stochastic Shortest Path Problems

Two extreme approaches can be applied to solve a probabilistic planning problem, namely closed loop algorithms and open loop (a.k.a. replanning) algorithms. While closed loop algorithms invest significant computational effort to generate a closed form solution, open loop algorithms compute open form solutions and interact with the environment in order to refine the computed solution. In this paper, we introduce short-sighted Stochastic Shortest Path (SSP), a new model in which solutions computed based on it can be executed for at least t steps as a closed form solution. Using short-sighted SSPs, we present a novel probabilistic planner called Short-sighted Open Loop Planner (SOLP) that bridges the gap between open and closed loop planners by varying the parameter t: as t increases, more actions can be executed without replanning and, for t sufficiently large, a closed form solution is obtained. We prove that SOLP is asymptotically optimal. To the best of our knowledge, SOLP is the unique probabilistic planner that at the same time provides both replanning and optimality guarantees. We empirically compare SOLP with the winners of the previous probabilistic planning competitions and SOLP outperforms all of them in 33.3% of the problems and ties with the best planner in 48.3% of the problems

Depth-based Short-sighted Stochastic Shortest Path Problems

Stochastic Shortest Path Problems (SSPs) are a common representation for probabilistic planning problems. Two approaches can be used to solve SSPs: (i) consider all probabilistically reachable states and (ii) plan only for a subset of these reachable states. Closed policies, the solutions obtained in the former approach, require significant computational effort, and they do not require replanning, i.e., the planner is never re-invoked. The second approach, employed by replanners, computes open policies, i.e., policies for a subset of the probabilistically reachable states. Therefore, when a state is reached in which the open policy is not defined, the replanner is reinvoked to compute a new open policy. In this article, we introduce a special case of SSPs, the depth-based short-sighted SSPs, in which every state has a nonzero probability of being reached using at most t actions. We also introduce the novel algorithm Short-Sighted Probabilistic Planner (SSiPP), which solves SSPs through depth-based short-sighted SSPs and guarantees that at least t actions can be executed without replanning. Therefore, SSiPP can compute both open and closed policies: as t increases, the returned policy approaches the behavior of a closed policy, and for t large enough, the returned policy is closed. Moreover, we present two extensions to SSiPP: Labeled-SSiPP and SSiPP-FF. The former extension incorporates a labeling mechanism to avoid revisiting states that have already converged. The latter extension combines SSiPP and determinizations to improve the performance of SSiPP in problems without dead ends. We also performed an extensive empirical evaluation of SSiPP and its extensions in several problems against state-of-the-art planners. The results show that (i) Labeled-SSiPP outperforms SSiPP and the considered planners in the task of finding the optimal solution when the problems have a low percentage of relevant states; and (ii) SSiPP-FF outperforms SSiPP in the task of quickly finding suboptimal solutions to problems without dead ends while performing similarly in problems with dead ends.</p