Bridging the Evaluation Gap: Standardized Benchmarks for Multi-Objective Search

Multi-objective shortest-path (MOSP) algorithms traditionally rely on single-valued heuristics (SVHs), which associate each state with a single admissible cost vector. While SVHs provide safe lower bounds, they fail to capture the trade-off structure of the Pareto frontier and often yield weak search guidance. Multi-valued heuristics (MVHs) address this limitation by mapping states to sets of cost estimates, enabling a richer approximation of possible trade-offs. Modern MOSP algorithms are highly dependent on dimensionality reduction (DR) techniques to efficiently perform dominance checks. However, integrating MVHs with DR introduces subtle correctness challenges. We show that naively combining DR with MVHs destroys the ordering invariants required for DR, leading to unsound and incomplete search. To address this issue, we develop the first theoretical frameworks for safely integrating MVHs with DR. First, we introduce $\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}$, a theoretical baseline that restores search correctness by enforcing heuristic consistency. Recognizing the practical limitations of this approach, we then introduce our primary contribution, $\text{L}\text{-}\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}$. This algorithm employs a "lazy," optimistic approach to DR, preserving exact correctness with only an admissible MVH by dynamically detecting and repairing local ordering violations. Across a range of benchmarks, $\text{L}\text{-}\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}$ matches or improves over state-of-the-art MOSP algorithms, and achieves speedups of over 10x in instances where the additional guidance provided by the MVH translates into stronger pruning.

Robotic planning often involves multiple objectives with complex priority relationships, such as safety, efficiency, and regulatory compliance. Rulebooks formalize these relationships, allowing partial ordering of objectives that generalizes both Pareto and lexicographic dominance. Computing the full set of rulebook-optimal solutions, however, is computationally expensive. To address this challenge, we introduce the concept of epsilon-rule-dominance, a principled notion of approximate dominance under rulebooks, and propose RApex, a best-first search algorithm that efficiently computes a compact set of epsilon-approximate rulebook-optimal solutions. RApex leverages dimensionality reduction, a technique used to speed up existing multi-objective search algorithms, while respecting rule hierarchies by maintaining separate closed sets and performing dominance checks over truncated and residual rule sets. We provide a formal analysis of RA*pex, proving that every rulebook-optimal solution is epsilon-rule-dominated (a generalization of approximate dominance we introduce) by at least one solution in the returned set. Empirical results demonstrate that our approach achieves computation times over two orders of magnitude faster than existing methods.

Benchmarking shortest-path algorithms is commonly based on aggregate performance over heterogeneous graph sets, which limits insight into how different search paradigms react to instance structure. We adopt an instance-landscape view of graph benchmarking by embedding graphs into a low-cost structural feature space and clustering them into regions of similar structure. Three benchmark suites are studied: weighted Erdős--Rényi graphs, random geometric (wireless) graphs, and real-world road networks. We evaluate four representative shortest-path solvers spanning uninformed exact search (Dijkstra), bidirectional exact search (bidirectional Dijkstra), heuristic-guided exact search (A$^{*}$), and deque-based strategies (DEQ). Clustering robustness is analyzed under multiple feature-selection schemes, and runtime distributions are compared across landscape regions using non-parametric tests. While generator parameters induce stable structural regions, we find that feature-space similarity does not necessarily imply performance similarity: significant runtime shifts are frequently observed even within the same landscape region. A merged-suite analysis further shows that different benchmark families occupy largely disjoint regions. These results highlight both the potential and the limits of structural landscapes for the structure-aware benchmarking of shortest-path algorithms.