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Packing circles in the smallest circle: an adaptive hybrid algorithm / I. Al-Mudahka in Journal of the operational research society (JORS), Vol. 62 N° 11 (Novembre 2011) 

Public ISBD [article]  in Journal of the operational research society (JORS) > Vol. 62 N° 11 (Novembre 2011) . - pp. 1917–1930 Titre : Packing circles in the smallest circle: an adaptive hybrid algorithm Type de document : texte imprimé Auteurs : I. Al-Mudahka, Auteur ; M. Hifi, Auteur ; R. M'Hallah, Auteur Année de publication : 2011 Article en page(s) : pp. 1917–1930 Note générale : Recherche opérationnelle Langues : Anglais (eng) Mots-clés : Heuristics  Tabu  search  Non-linear  programming  Circular  packing  Nested  partitioning Index. décimale : 001.424 Résumé : The circular packing problem (CPP) consists of packing n circles Ci of known radii ri, i∈N={1, …, n}, into the smallest containing circle ℂ. The objective is to determine the coordinates (xi, yi) of the centre of Ci, i∈N, as well as the radius r and centre (x, y) of ℂ. CPP, which is a variant of the two-dimensional open-dimension problem, is NP hard. This paper presents an adaptive algorithm that incorporates nested partitioning within a tabu search and applies some diversification strategies to obtain a (near) global optimum. The tabu search is to identify the n circles’ ordering, whereas the nested partitioning is to determine the n circles’ positions that yield the smallest r. The computational results show the efficiency of the proposed algorithm. DEWEY : 001.424 ISSN : 0160-5682 En ligne : http://www.palgrave-journals.com/jors/journal/v62/n11/abs/jors2010157a.html [article] Packing circles in the smallest circle: an adaptive hybrid algorithm [texte imprimé] / I. Al-Mudahka, Auteur ; M. Hifi, Auteur ; R. M'Hallah, Auteur . - 2011 . - pp. 1917–1930. Recherche opérationnelle Langues : Anglais (eng) in Journal of the operational research society (JORS) > Vol. 62 N° 11 (Novembre 2011) . - pp. 1917–1930 Mots-clés : Heuristics  Tabu  search  Non-linear  programming  Circular  packing  Nested  partitioning Index. décimale : 001.424 Résumé : The circular packing problem (CPP) consists of packing n circles Ci of known radii ri, i∈N={1, …, n}, into the smallest containing circle ℂ. The objective is to determine the coordinates (xi, yi) of the centre of Ci, i∈N, as well as the radius r and centre (x, y) of ℂ. CPP, which is a variant of the two-dimensional open-dimension problem, is NP hard. This paper presents an adaptive algorithm that incorporates nested partitioning within a tabu search and applies some diversification strategies to obtain a (near) global optimum. The tabu search is to identify the n circles’ ordering, whereas the nested partitioning is to determine the n circles’ positions that yield the smallest r. The computational results show the efficiency of the proposed algorithm. DEWEY : 001.424 ISSN : 0160-5682 En ligne : http://www.palgrave-journals.com/jors/journal/v62/n11/abs/jors2010157a.html