Ar*: a Bounded Suboptimal Search algorithm using Conditional Node Re-expansion Policy

The A* algorithm is a well-known graph search technique widely used in various domains like robotics, games, and logistics. A* combines breadth-first search and heuristics to find optimal paths by evaluating cost and heuristic estimates. However, optimization challenges persist, leading to the need for suboptimal solutions within predefined quality bounds. In the case of Bounded Suboptimal Search, a possible strategy is to reduce unnecessary re-expansions effectively. Existing researches have explored distinct approaches across two primary domains: Never Re-expansion (NR) and Always Re-expansion (AR). In this paper, we introduce an innovative paradigm termed Conditional Re-expansion (CR). This novel algorithm selectively permits re-expansions that yield a considerable decrease in the g-cost value, contingent upon an acceptance error parameter denoted as r. Additionally, we propose an efficient anytime algorithm to rectify the outputs of the algorithm mentioned before. This involves prioritizing the repair of states that were denied reexpansion in the CR phase. Theoretical groundwork and practical demonstrations across diverse benchmarks have been conducted to validate the findings.