Towards effective multi-valued heuristics for bi-objective shortest-path algorithms via differential heuristics

Han Zhang, Oren Salzman, Ariel Felner, T. K. Satish Kumar, Shawn Skyler, Carlos Hernández Ulloa, Sven Koenig

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


In bi-objective graph search, each edge is annotated with a cost pair, where each cost corresponds to an objective to optimize. We are interested in finding all undominated paths from a given start state to a given goal state (called the Pareto front). Almost all existing works of bi-objective search use single-valued heuristics, which use one number for each objective, to estimate the cost between any given state and the goal state. However, single-valued heuristics cannot reflect the trade-offs between the two costs. On the other hand, multi-valued heuristics use a set of pairs to estimate the Pareto front between any given state and the goal state and are more informed than single-valued heuristics. However, they are rarely studied and have yet to be investigated in explicit state spaces by any existing work. In this paper, we are interested in using multi-valued heuristics to improve bi-objective search algorithms in explicit state spaces. More specifically, we generalize Differential Heuristics (DHs), a class of memorybased heuristics for single-objective search, to bi-objective search, resulting in Bi-objective Differential Heuristics (BODHs). We propose several techniques to reduce the memory usage and computational overhead of BO-DHs significantly. Our experimental results show that, with suggested improvement and tuned parameters, BO-DHs can reduce the node expansion and runtime of a bi-objective search algorithm by up to an order of magnitude, paving the way for more effective multi-valued heuristics.

Original languageEnglish
Pages (from-to)101-109
Number of pages9
JournalThe International Symposium on Combinatorial Search
Issue number1
StatePublished - 2023
Externally publishedYes
Event16th International Symposium on Combinatorial Search, SoCS 2023 - Prague, Czech Republic
Duration: 14 Jul 202316 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023, Association for the Advancement of Artificial Intelligence (


The research at the University of Southern California was supported by the National Science Foundation (NSF) under grant numbers 1409987, 1724392, 1817189, 1837779, 1935712, 2121028, and 2112533. The research was also supported by the United States-Israel Binational Science Foundation (BSF) under grant number 2021643 and Centro Nacional de Inteligencia Artificial CENIA, FB210017, BASAL, ANID. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organizations, agencies, or any government.

FundersFunder number
Centro Nacional de Inteligencia Artificial CENIAFB210017
National Science Foundation1409987, 1724392, 1935712, 2121028, 1837779, 1817189, 2112533
Bloom's Syndrome Foundation2021643
United States-Israel Binational Science Foundation
Agencia Nacional de Investigación y Desarrollo


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