Local Search: Simple, Successful, But Sometimes Sluggish

• Published in: Automata, Languages and Programming pp. 1 - 17
• Main Authors: Monien, Burkhard, Dumrauf, Dominic, Tscheuschner, Tobias
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Delay Function; Local Search; Nash Equilibrium; Simplex Algorithm; Travel Salesman Problem
• ISBN: 3642141641; 9783642141645
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-14165-2_1

In this paper, we survey the research on the complexity of computing locally optimal solutions. We revisit well-known and successful local search heuristics and present results on the complexity of the frequently used standard local search algorithm for various problems. Here, our focus in on worst case, average case, and smoothed complexity along with the existence of sequences of improving steps of exponential length. For a more theoretical investigation, we revisit the framework of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{PLS}$\end{document} and mostly concentrate on the research on CongestionGames, which sparked the interconnection between local search and game theory. We conclude by stating various open problems.