#### Nicolás Rivera, Jorge A. Baier, Carlos Hernández, **Incorporating weights into real-time heuristic search**, Artificial Intelligence, Volume 225, August 2015, Pages 1-23, ISSN 0004-3702, DOI: 10.1016/j.artint.2015.03.008.

Multiplying the heuristic function by a weight greater than one is a well-known technique in heuristic search. When this technique is applied to A* with an admissible heuristic it yields substantial runtime savings, at the expense of sacrificing solution optimality. Its applicability to real-time heuristic search, a search approach that builds upon heuristic search, however, has only been explored by a few studies. In this article we present two new approaches to using weights in real-time heuristic search, applicable to a wide range of algorithms. The first one, weighted lookahead, is a variant of an existing approach by Shimbo and Ishida, and utilizes the weight while the algorithm performs lookahead search. The second one, weighted update, incorporates the weight to the edges of the search graph during the learning phase. We implemented both techniques within LSS-LRTA* and evaluated them in path-planning benchmarks. We show that weighted lookahead outperforms an existing approach by Shimbo and Ishida but that it does not improve over existing approaches that do not use weights. Weighted update, on the other hand, yields performance improvements of up to one order of magnitude both in solution cost and total search time. To illustrate further the generality of weighted update, we incorporate the technique in two other well-known real-time heuristic search algorithms: LRTA*-LS and daLSS-LRTA*, and we empirically show significant improvements for LRTA*-LS and modest but still important improvements for daLSS-LRTA*. We analyze the properties of weighted update in depth, showing, among other things, that it guarantees termination. Convergence behavior of LSS-LRTA*, modified to use weighted update, is also analyzed. In such a setting, we prove solutions are w-optimal, and provide additional bounds on solution quality that in practice are tighter than w-optimality.