Document Zbl 1507.68351

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Comput. Sci.</a> <a href="/?q=in%3A494065" title="Articles in this Issue">950, Article ID 113757, 24 p. (2023)</a>. </div> <div class="abstract">Summary: Most runtime analyses of randomised search heuristics focus on the expected number of function evaluations to find a unique global optimum. We ask a fundamental question: if additional search points are declared optimal, or declared as desirable target points, do these additional optima speed up evolutionary algorithms? More formally, we analyse the expected hitting time of a target set $\mathrm{OPT} \cup S$ where $S$ is a set of non-optimal search points and OPT is the set of optima and compare it to the expected hitting time of OPT. We show that the answer to our question depends on the number and placement of search points in $S$. For all black-box algorithms and all fitness functions with polynomial expected optimisation times we show that, if additional optima are placed randomly, even an exponential number of optima has a negligible effect on the expected optimisation time. Considering Hamming balls around all global optima gives an easier target for some algorithms and functions and can shift the phase transition with respect to offspring population sizes in the $(1, \lambda )$ EA on <span class="zbmathjax-textsc">OneMax</span>. However, for the one-dimensional Ising model the time to reach Hamming balls of radius $(1 / 2 - \varepsilon) n$ around optima does not reduce the asymptotic expected optimisation time in the worst case. Finally, on functions where search trajectories typically join in a single search point, turning one search point into an optimum drastically reduces the expected optimisation time.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7664332">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W50" title="MSC2020">68W50</a> </td> <td class="space"> Evolutionary algorithms, genetic algorithms (computational aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W20" title="MSC2020">68W20</a> </td> <td class="space"> Randomized algorithms </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W40" title="MSC2020">68W40</a> </td> <td class="space"> Analysis of algorithms </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C59" title="MSC2020">90C59</a> </td> <td class="space"> Approximation methods and heuristics in mathematical programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aevolutionary+algorithms">evolutionary algorithms</a>; <a href="/?q=ut%3Apseudo-Boolean+functions">pseudo-Boolean functions</a>; <a href="/?q=ut%3Aruntime+analysis">runtime analysis</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1507.68351" data-ciurl="/ci/07664332" data-biburl="/bibtex/07664332.bib" data-amsurl="/amsrefs/07664332.bib" data-xmlurl="/xml/07664332.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07664332.pdf" title="Zbl 1507.68351 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.tcs.2023.113757" aria-label="DOI for “Do additional target points speed up evolutionary algorithms?”" title="10.1016/j.tcs.2023.113757">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Neumann, F.; Witt, C., Bioinspired Computation in Combinatorial Optimization - Algorithms and Their Computational Complexity (2010), Springer · <a href="/1223.68002" class="nowrap">Zbl 1223.68002</a></td> </tr><tr> <td>[2]</td> <td class="space">(Auger, A.; Doerr, B., Theory of Randomized Search Heuristics - Foundations and Recent Developments. 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