{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1037","name":"Runtime Analysis of a Simple Multi-Objective Evolutionary Algorithm","abstract":"Practical knowledge on the design and \r\napplication of multi-objective evolutionary\r\nalgorithms (MOEAs) is available but well-founded\r\ntheoretical analyses of the runtime are rare.\r\nLaumanns, Thiele, Zitzler, Welzel and Deb (2002)\r\nhave started such an analysis for two simple\r\nmutation-based algorithms including SEMO.\r\nThese algorithms search locally in the\r\nneighborhood of their current population by\r\nselecting an individual and flipping one \r\nrandomly chosen bit. Due to its local search \r\noperator, SEMO cannot escape from local optima,\r\nand, therefore, has no finite expected runtime \r\nin general.\r\n\r\nIn this talk, we investigate the runtime of \r\na variant of SEMO whose mutation operator \r\nflips each bit independently. It is proven\r\nthat its expected runtime is O(n^n) for all\r\nobjective functions f: {0,1}^n -> R^m, and\r\nthat there are bicriteria problems among the\r\nhardest problem for this algorithm. Moreover, \r\nfor each d between 2 and n, a bicriteria \r\nproblem with expected runtime Theta(n^d) is \r\npresented. This shows that bicriteria problems \r\ncover the full range of potential runtimes of \r\nthis variant of SEMO. For the problem LOTZ \r\n(Leading-Ones-Trailing Zeroes), the runtime \r\ndoes not increase substantially if we use the \r\nglobal search operator. Finally, we consider\r\nthe problem MOCO (Multi-Objective-Counting-Ones). \r\nWe show that the conjectured bound O((n^2)log n) \r\non the expected runtime is wrong for both \r\nvariants of SEMO. In fact, MOCO is almost a \r\nworst case example for SEMO if we consider \r\nthe expected runtime; however, the runtime is \r\nO((n^2)log n) with high probability. Some \r\nideas from the proof will be presented.","keywords":["Runtime analysis","multi-objecive evolutionary algorithms"],"author":{"@type":"Person","name":"Giel, Oliver","givenName":"Oliver","familyName":"Giel"},"position":19,"pageStart":1,"pageEnd":4,"dateCreated":"2005-11-10","datePublished":"2005-11-10","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Giel, Oliver","givenName":"Oliver","familyName":"Giel"},"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04461.19","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume551","volumeNumber":4461,"name":"Dagstuhl Seminar Proceedings, Volume 4461","dateCreated":"2005-08-10","datePublished":"2005-08-10","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1037","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume551"}}}