Document Zbl 1257.90050

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Glob. Optim.</a> <a href="/?q=in%3A309916" title="Articles in this Issue">54, No. 4, 745-764 (2012)</a>. </div> <div class="abstract">Summary: Heuristic algorithms, especially hill-climbing algorithms, are prone to being trapped by local optimization. Many researchers have focused on analyzing convergence and runtime of some heuristic algorithms on SAT-solving problems. However, there is rare work on analyzing success ratio (the ratio of the number of runs that find the global maxima of optimization versus the total runs) and expected fitness at each generation. Expected fitness at each generation could lead us to better understand the expected fitness of a heuristic algorithm could find on the problem to be solve at a certain generation. Success ratio help us understand with what a probability a heuristic algorithm could find the global optimization of the problem to be solved. So, this paper analyzed expected fitness and success ratio of two hill-climbing algorithms on two bimodal MaxSAT problems by using Markov chain. The theoretical and experimental results showed that though hill-climbing algorithms (both hill-climbing RandomWalk and Local ($1+1$)EA) converged faster, they could not always find global maxima of bimodal SAT-solving problems. The success ratios of hill-climbing algorithms usually have their own limits. The limit of success ratio is dependent on the SAT-solving problem itself and the expected distribution of initial bit string, and independent on whether hill-climbing RandomWalk or Local ($1+1$)EA is used.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C09" title="MSC2020">90C09</a> </td> <td class="space"> Boolean programming </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%3Asuccess+ratio">success ratio</a>; <a href="/?q=ut%3Aexpected+fitness">expected fitness</a>; <a href="/?q=ut%3AMarkov+chain">Markov chain</a>; <a href="/?q=ut%3Asatisfiability">satisfiability</a></div> <div class="software"> <h3>Software:</h3><a href="/software/993">UnitWalk</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 1257.90050" data-ciurl="/ci/06121316" data-biburl="/bibtex/06121316.bib" data-amsurl="/amsrefs/06121316.bib" data-xmlurl="/xml/06121316.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06121316.pdf" title="Zbl 1257.90050 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/10.1007/s10898-011-9790-2" aria-label="DOI for “The analysis of expected fitness and success ratio of two heuristic optimizations on two bimodal MaxSat problems”" title="10.1007/s10898-011-9790-2">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">Cook, S.A.: The complexity of theorem-proving procedures. 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