# A-MHA*: Anytime Multi-Heuristic A*

## TL;DR

This paper introduces A-MHA*, an extension of Multi-Heuristic A* that operates as an anytime algorithm, quickly finding and continually improving suboptimal solutions in complex path planning and puzzle domains.

## Contribution

It extends MHA* to an anytime framework inspired by ARA*, maintaining guarantees while enabling iterative solution improvement.

## Key findings

- A-MHA* finds feasible solutions rapidly in tested domains.
- It outperforms original MHA* and other anytime algorithms in efficiency.
- The approach preserves suboptimality and completeness guarantees.

## Abstract

Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space but these may not be admissible throughout the domain thereby affecting the optimality guarantees of the search. Bounded suboptimal search using several such partially good but inadmissible heuristics was developed in Multi-Heuristic A* (MHA*). Although MHA* leverages multiple inadmissible heuristics to potentially generate a faster suboptimal solution, the original version does not improve the solution over time. It is a one shot algorithm that requires careful setting of inflation factors to obtain a desired one time solution. In this work, we tackle this issue by extending MHA* to an anytime version that finds a feasible suboptimal solution quickly and continually improves it until time runs out. Our work is inspired from the Anytime Repairing A* (ARA*) algorithm. We prove that our precise adaptation of ARA* concepts in the MHA* framework preserves the original suboptimal and completeness guarantees and enhances MHA* to perform in an anytime fashion. Furthermore, we report the performance of A-MHA* in 3-D path planning domain and sliding tiles puzzle and compare against MHA* and other anytime algorithms.