{"type":"ScholarlyArticle","title":"Extending Weighted Heuristic Search to Bi-Objective Search Problems","authors":[{"name":"Hans Kühn Leiva","slug":"hans-kuhn-leiva","given":"Hans","family":"Kühn Leiva","affiliation":""},{"name":"Jorge A. Baier","slug":"jorge-a-baier","given":"Jorge A.","family":"Baier","affiliation":""},{"name":"Carlos Hernández Ulloa","slug":"carlos-hernandez-ulloa","given":"Carlos","family":"Hernandez Ulloa","affiliation":""},{"name":"Oren Salzman","slug":"oren-salzman","given":"Oren","family":"Salzman","affiliation":""},{"name":"Ariel Felner","slug":"ariel-felner","given":"Ariel","family":"Felner","affiliation":""},{"name":"Sven Koenig","slug":"sven-koenig","given":"Sven","family":"Koenig","affiliation":""}],"abstract":"In heuristic search, a well-known technique to speed up search while providing a suboptimality guarantee is to multiply the heuristic function by a weight w > 1. In this paper, we study the theoretical and practical implications of using such a technique in bi-objective heuristic search, a natural academic exercise that has remained unexplored. We introduce Weighted BOA∗ϵ (WBOA∗\r\nϵ ), a weighted version of the BOA* algorithm, which uses two real parameters: a weight w for the heuristic and an approximation factor ϵ. Higher values of w and ϵ allow for faster computation of approximate Pareto-optimal solution sets. We prove that WBOA∗ ϵ returns a representative solution set containing (w − 1, ϵ)-approximate solutions. We empirically compare it to A*pex, the state-of-the-art approximate bi-objective search algorithm. We find that WBOA∗ ϵ is competitive with A*pex: when using perfect heuristic functions, in road maps WBOA∗ϵ is faster for higher approximation factors, while in grid maps WBOA∗ϵ dominates A*pex. With imperfect heuristic functions, WBOA∗ϵ performs better than A*pex for lower approximation factors, while the opposite is true for larger approximation factors.","doi":"10.24963/ijcai.2026/700","url":"https://ijcai.org/proceedings/2026/700","pdf":"https://ijcai.org/proceedings/2026/0700.pdf","markdown":"https://ijcai.org/proceedings/2026/700.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/700","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Search","track":"Main Track","number":700,"pages":{"first":6291,"last":6298},"keywords":["Search: Heuristic search","Search: Combinatorial search and optimisation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}