Packing unequal circles into a strip of minimal length with a jump algorithm
The paper considers a problem of packing unequal circles into a rectangular strip with fixed width and minimal length. We develop the idea of increasing the dimension of the solution space by assuming radii of circles to be variables. A mathematical model of the problem is constructed and its charac...
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| Published in | Optimization letters Vol. 8; no. 3; pp. 949 - 970 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-013-0646-1 |
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| Abstract | The paper considers a problem of packing unequal circles into a rectangular strip with fixed width and minimal length. We develop the idea of increasing the dimension of the solution space by assuming radii of circles to be variables. A mathematical model of the problem is constructed and its characteristics are investigated. Taking into account the characteristics we offer a solution strategy of the problem including a number of non-linear programming subproblems of packing circles of variable radii. The solution strategy involves special ways of construction of starting points, calculation of local minima, jump from one local extremum to another, decrease of the problem dimension and rearrangement of pairs of circles. For calculating local extrema an interior point optimizer together with the concept of active inequalities are used. We compare 146 numerical benchmark examples and give seven new ones for 125, 150, 175, 225, 250, 275 and 300 circles. |
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| AbstractList | The paper considers a problem of packing unequal circles into a rectangular strip with fixed width and minimal length. We develop the idea of increasing the dimension of the solution space by assuming radii of circles to be variables. A mathematical model of the problem is constructed and its characteristics are investigated. Taking into account the characteristics we offer a solution strategy of the problem including a number of non-linear programming subproblems of packing circles of variable radii. The solution strategy involves special ways of construction of starting points, calculation of local minima, jump from one local extremum to another, decrease of the problem dimension and rearrangement of pairs of circles. For calculating local extrema an interior point optimizer together with the concept of active inequalities are used. We compare 146 numerical benchmark examples and give seven new ones for 125, 150, 175, 225, 250, 275 and 300 circles. |
| Author | Stoyan, Yu Yaskov, G. |
| Author_xml | – sequence: 1 givenname: Yu surname: Stoyan fullname: Stoyan, Yu email: ystoyan@mail.ru, stoyan@ipmach.kharkov.ua organization: Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine – sequence: 2 givenname: G. surname: Yaskov fullname: Yaskov, G. organization: Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine |
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| Cites_doi | 10.1016/j.cie.2011.02.009 10.1016/S0305-0548(03)00020-0 10.1016/S0166-218X(01)00359-6 10.1111/1475-3995.00404 10.1016/j.ejor.2005.12.047 10.1016/j.cor.2009.09.017 10.1111/j.1475-3995.2008.00655.x 10.1007/s10107-004-0559-y 10.1057/palgrave.jors.2601836 10.1016/0377-2217(95)00032-L 10.1016/j.ejor.2007.01.054 10.1007/s10100-009-0103-5 10.1007/s10898-011-9716-z 10.1155/2009/150624 10.1007/BF01071258 10.1007/s10898-012-9948-6 10.1007/BF01885707 |
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| Keywords | Rectangle Circle Jump algorithm Packing Optimization |
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| References | Rudnev (CR13) 2009; 16 CR14 Stoyan, Yaskov (CR22) 2004; 156 CR10 Birgin, Gentil (CR19) 2010; 37 Wächter, Biegler (CR28) 2006; 106 Szabó, Markót, Csendes, Specht, Casado, García (CR25) 2007; 6 Huang, Li, Akeb, Li (CR4) 2005; 56 Hifi, M’Hallah (CR12) 2004; 31 Hifi, M’Hallah (CR3) 2003; 10 Akeb, Hifi (CR5) 2008; 15 CR2 CR6 Wäscher, Hausner, Schumann (CR1) 2007; 183 CR8 CR7 George, George, Lamar (CR11) 1995; 84 CR9 Stoyan, Yaskov (CR27) 2012; 52 Hifi, Paschos, Zissimopoulos (CR15) 2004; 159 CR24 Locatelli, Raber (CR26) 2002; 122 CR23 CR21 Stoyan, Yaskov (CR20) 1998; 5 Akeb, Hifi, Negre (CR17) 2011; 61 Castillo, Kampas, Pintér (CR18) 2008; 191 Kubach, Bortfeldt, Gehring (CR16) 2009; 17 JA George (646_CR11) 1995; 84 PG Szabó (646_CR25) 2007; 6 WQ Huang (646_CR4) 2005; 56 H Akeb (646_CR17) 2011; 61 646_CR7 G Wäscher (646_CR1) 2007; 183 646_CR6 646_CR9 646_CR8 646_CR23 646_CR22 646_CR21 646_CR20 I Castillo (646_CR18) 2008; 191 646_CR24 M Hifi (646_CR3) 2003; 10 M Hifi (646_CR12) 2004; 31 Yu Stoyan (646_CR27) 2012; 52 EG Birgin (646_CR19) 2010; 37 646_CR2 A Wächter (646_CR28) 2006; 106 T Kubach (646_CR16) 2009; 17 H Akeb (646_CR5) 2008; 15 646_CR10 646_CR15 646_CR14 646_CR13 M Locatelli (646_CR26) 2002; 122 |
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