{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848710,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix $F$, we say a (0,1)-matrix $A$ avoids $F$ (as a configuration) if there is no submatrix of $A$ which is a row and column permutation of $F$. Let $\\|{A}\\|$ denote the number of columns of $A$. We define $\\mathrm{forb}(m,F)=\\max\\{\\|{A}\\|\\ : A$ is an $m$-rowed simple matrix that avoids $F \\}$. Define an extremal matrix as an $m$-rowed simple matrix $A$ with that avoids $F$ and $\\|{A}\\|=\\mathrm{forb}(m,F)$. We describe the use of Local Search Algorithms (in particular a Genetic Algorithm) for finding extremal matrices. We apply this technique to two forbidden configurations in turn, obtaining a guess for the structure of an $m\\times\\mathrm{forb}(m,F)$ simple matrix avoiding $F$ and then proving the guess is indeed correct. The Genetic Algorithm was also helpful in finding the proof.<\/jats:p>","DOI":"10.37236\/717","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:39:11Z","timestamp":1578713951000},"source":"Crossref","is-referenced-by-count":0,"title":["Genetic Algorithms Applied to Problems of  Forbidden Configurations"],"prefix":"10.37236","volume":"18","author":[{"given":"R. P.","family":"Anstee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Raggi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,12,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p230\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p230\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:58:28Z","timestamp":1579301908000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p230"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/717","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,12,5]]},"article-number":"P230"}}