Max Is More than Min: Solving Maximization Problems with Heuristic Search

Roni Stern; Rami Puzis; Ariel Felner; Scott Kiesel; Wheeler Ruml

Max Is More than Min: Solving Maximization Problems with Heuristic Search

Roni Stern, Rami Puzis, Ariel Felner, Scott Kiesel, Wheeler Ruml

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

Abstract

Most work in heuristic search considers problems where a low cost solution is preferred (MIN problems). In this paper, we investigate the complementary setting where a solution of high reward is preferred (MAX problems). Example MAX problems include finding the longest simple path in a graph, maximal coverage, and various constraint optimization problems. We examine several popular search algorithms for MIN problems — optimal, suboptimal, and bounded suboptimal — and discover the curious ways in which they misbehave on MAX problems. We propose modifications that preserve the original intentions behind the algorithms but allow them to solve MAX problems, and compare them theoretically and empirically. Interesting results include the failure of bidirectional search and a discovered close relationships between Dijkstra’s algorithm, weighted A*, and depth-first search. This work demonstrates that MAX problems demand their own heuristic search algorithms, which are worthy objects of study in their own right.

Original language	English
Title of host publication	Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014
Editors	Stefan Edelkamp, Roman Bartak
Publisher	AAAI press
Pages	148-156
Number of pages	9
ISBN (Electronic)	9781577356769
State	Published - 2014
Externally published	Yes
Event	7th Annual Symposium on Combinatorial Search, SoCS 2014 - Prague, Czech Republic Duration: 15 Aug 2014 → 17 Aug 2014

Publication series

Name	Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014
Volume	2014-January

Conference

Conference	7th Annual Symposium on Combinatorial Search, SoCS 2014
Country/Territory	Czech Republic
City	Prague
Period	15/08/14 → 17/08/14

Bibliographical note

Publisher Copyright:
Copyright © 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

Funding

This research was supported by the Israel Science Foundation (ISF) under grant #417/13 to Ariel Felner.

Funders	Funder number
Israel Science Foundation	417/13

Cite this

Stern, R., Puzis, R., Felner, A., Kiesel, S., & Ruml, W. (2014). Max Is More than Min: Solving Maximization Problems with Heuristic Search. In S. Edelkamp, & R. Bartak (Eds.), Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014 (pp. 148-156). (Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014; Vol. 2014-January). AAAI press.

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title = "Max Is More than Min: Solving Maximization Problems with Heuristic Search",

abstract = "Most work in heuristic search considers problems where a low cost solution is preferred (MIN problems). In this paper, we investigate the complementary setting where a solution of high reward is preferred (MAX problems). Example MAX problems include finding the longest simple path in a graph, maximal coverage, and various constraint optimization problems. We examine several popular search algorithms for MIN problems — optimal, suboptimal, and bounded suboptimal — and discover the curious ways in which they misbehave on MAX problems. We propose modifications that preserve the original intentions behind the algorithms but allow them to solve MAX problems, and compare them theoretically and empirically. Interesting results include the failure of bidirectional search and a discovered close relationships between Dijkstra{\textquoteright}s algorithm, weighted A*, and depth-first search. This work demonstrates that MAX problems demand their own heuristic search algorithms, which are worthy objects of study in their own right.",

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Stern, R, Puzis, R, Felner, A, Kiesel, S & Ruml, W 2014, Max Is More than Min: Solving Maximization Problems with Heuristic Search. in S Edelkamp & R Bartak (eds), Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014. Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014, vol. 2014-January, AAAI press, pp. 148-156, 7th Annual Symposium on Combinatorial Search, SoCS 2014, Prague, Czech Republic, 15/08/14.

Max Is More than Min: Solving Maximization Problems with Heuristic Search. / Stern, Roni; Puzis, Rami; Felner, Ariel et al.
Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014. ed. / Stefan Edelkamp; Roman Bartak. AAAI press, 2014. p. 148-156 (Proceedings of the 7th Annual Symposium on Combinatorial Search, SoCS 2014; Vol. 2014-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Max Is More than Min: Solving Maximization Problems with Heuristic Search

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