Heuristics used for solving hard real-time search problems have regions with depressions. Such regions are bounded areas of the search space in which the heuristic function is inaccurate compared to the actual cost to reach a solution. Early real-time search algorithms, like LRTA~*, easily become trapped in those regions since the heuristic values of their states may need to be updated multiple times, which results in costly solutions. State-of-the-art real-time search algorithms, like LSS-LRTA~* or LRTA~*(k), improve LRTA~*'s mechanism to update the heuristic, resulting in improved performance. Those algorithms, however, do not guide search towards avoiding depressed regions. This paper presents depression avoidance, a simple real-time search principle to guide search towards avoiding states that have been marked as part of a heuristic depression. We propose two ways in which depression avoidance can be implemented: mark-and-avoid and move-to-border. We implement these strategies on top of LSS-LRTA~* and RTAA~*, producing 4 new real-time heuristic search algorithms: aLSS-LRTA~*, daLSS-LRTA~*, aRTAA~*, and daRTAA~*. When the objective is to find a single solution by running the real-time search algorithm once, we show that daLSS-LRTA~* and daRTAA~* outperform their predecessors sometimes by one order of magnitude. Of the four new algorithms, daRTAA~* produces the best solutions given a fixed deadline on the average time allowed per planning episode. We prove all our algorithms have good theoretical properties: in finite search spaces, they find a solution if one exists, and converge to an optimal after a number of trials.
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