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Bidirectional Bounded-Suboptimal Heuristic Search with Consistent Heuristics

Shahaf S. Shperberg, Natalie Morad, Lior Siag, Ariel Felner, Dor Atzmon

TL;DR

This work extends bidirectional heuristic search to bounded-suboptimal settings by integrating WA*-style inflation with the BAE* framework, resulting in Weighted BAE* (WBAE*) variants that incorporate a tunable heuristic-error term. The authors prove bounded-suboptimality for WBAE* when the consistency condition holds and analyze how the lambda parameter governs the trade-off between tightening lower bounds and finding solutions. They also introduce tighter lower-bound techniques (ALB and gcd-based bounds) and demonstrate, across diverse domains, that tuned lambda values and stronger lower bounds yield substantial reductions in node expansions and runtime in many scenarios. The study provides practical guidance on parameter selection and termination criteria, and suggests avenues for extending BiHS beyond WA*-based approaches. Overall, WBAE* offers a flexible, principled way to balance optimality guarantees with computational efficiency in complex search spaces, with tangible benefits for pathfinding and planning applications.

Abstract

Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms. While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.

Bidirectional Bounded-Suboptimal Heuristic Search with Consistent Heuristics

TL;DR

This work extends bidirectional heuristic search to bounded-suboptimal settings by integrating WA*-style inflation with the BAE* framework, resulting in Weighted BAE* (WBAE*) variants that incorporate a tunable heuristic-error term. The authors prove bounded-suboptimality for WBAE* when the consistency condition holds and analyze how the lambda parameter governs the trade-off between tightening lower bounds and finding solutions. They also introduce tighter lower-bound techniques (ALB and gcd-based bounds) and demonstrate, across diverse domains, that tuned lambda values and stronger lower bounds yield substantial reductions in node expansions and runtime in many scenarios. The study provides practical guidance on parameter selection and termination criteria, and suggests avenues for extending BiHS beyond WA*-based approaches. Overall, WBAE* offers a flexible, principled way to balance optimality guarantees with computational efficiency in complex search spaces, with tangible benefits for pathfinding and planning applications.

Abstract

Recent advancements in bidirectional heuristic search have yielded significant theoretical insights and novel algorithms. While most previous work has concentrated on optimal search methods, this paper focuses on bounded-suboptimal bidirectional search, where a bound on the suboptimality of the solution cost is specified. We build upon the state-of-the-art optimal bidirectional search algorithm, BAE*, designed for consistent heuristics, and introduce several variants of BAE* specifically tailored for the bounded-suboptimal context. Through experimental evaluation, we compare the performance of these new variants against other bounded-suboptimal bidirectional algorithms as well as the standard weighted A* algorithm. Our results demonstrate that each algorithm excels under distinct conditions, highlighting the strengths and weaknesses of each approach.

Paper Structure

This paper contains 22 sections, 5 theorems, 27 equations, 2 figures, 21 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Bidirectional Heuristic Search: Definitions
  3. Background: BiHS Algorithms
  4. WA* and Bidirectional WA*
  5. Meet in the middle (MM) and WMM
  6. Weighted MM.
  7. BS* and its BSS variant
  8. BAE*
  9. Weighted BAE*
  10. Theoretical analysis
  11. The Role of $\lambda$
  12. Obtaining Stronger Lower Bounds
  13. Alternative Termination Criteria
  14. Utilizing Information on Edge Costs
  15. Empirical Evaluation
  16. ...and 7 more sections

Key Result

Lemma 1

It holds that $\hbox{$b_{W_D}$}(n) \leq W \cdot \hbox{$b_D$}(n)$ for every node $n$ and any $\lambda \leq W$.

Figures (2)

  • Figure 1: An example demonstrating the role of $\lambda$
  • Figure 2: Comparison of the methods for strengthening the lower bound on STP

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Theorem 3
  • proof