Novel derivative of harmony search algorithm for discrete design variables
Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valu...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 199; H. 1; S. 223 - 230 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Elsevier Inc
15.05.2008
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems. |
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| AbstractList | Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems. |
| Author | Geem, Zong Woo |
| Author_xml | – sequence: 1 givenname: Zong Woo surname: Geem fullname: Geem, Zong Woo email: geem@jhu.edu organization: Environmental Planning and Management Program, Johns Hopkins University, 729 Fallsgrove Dr. #6133, Rockville, MD 20850, USA |
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| Cites_doi | 10.1007/978-3-540-71805-5_65 10.1016/j.advwatres.2007.05.009 10.1007/11539902_91 10.1080/03052150500467430 10.1080/03052150500211895 10.3844/ajassp.2005.1552.1557 10.1016/j.ijepes.2007.06.006 10.1007/978-3-540-73007-1_39 10.1016/j.amc.2006.11.033 10.1016/j.cma.2004.09.007 10.1177/003754970107600201 |
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| Keywords | Harmony search Discrete variable Evolutionary algorithm Soft computing Combinatorial optimization Stochastic derivative Meta-heuristics Optimization method Continuous function Search algorithm Numerical analysis Real function Applied mathematics Optimal solution Mathematical programming |
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| References | Lee, Geem (bib10) 2005; 194 Geem, Choi (bib6) 2007; 4448 Mays, Tung (bib14) 1992 Geem (bib5) 2007; 4692 Geem, Kim, Loganathan (bib7) 2001; 76 Geem, Tseng, Park (bib9) 2005; 3612 . Geem (bib2) 2006; 38 Geem (bib4) 2007; 4507 Geem, Lee, Park (bib8) 2005; 2 Ryu, Duggal, Heyl, Geem (bib15) 2007 Lee, Geem, Lee, Bae (bib11) 2005; 37 Mahdavi, Fesanghary, Damangir (bib13) 2007; 188 Ayvaz (bib1) 2007; 30 Li, Chi, Chu (bib12) 2006; 27 Geem (bib3) 2006; 4251 A. Vasebi, M. Fesanghary, S.M.T. Bathaeea, Combined heat and power economic dispatch by harmony search algorithm, International Journal of Electrical Power & Energy Systems, in press Geem (10.1016/j.amc.2007.09.049_bib4) 2007; 4507 Li (10.1016/j.amc.2007.09.049_bib12) 2006; 27 Lee (10.1016/j.amc.2007.09.049_bib11) 2005; 37 Geem (10.1016/j.amc.2007.09.049_bib8) 2005; 2 Mahdavi (10.1016/j.amc.2007.09.049_bib13) 2007; 188 Ryu (10.1016/j.amc.2007.09.049_bib15) 2007 10.1016/j.amc.2007.09.049_bib16 Lee (10.1016/j.amc.2007.09.049_bib10) 2005; 194 Ayvaz (10.1016/j.amc.2007.09.049_bib1) 2007; 30 Geem (10.1016/j.amc.2007.09.049_bib2) 2006; 38 Geem (10.1016/j.amc.2007.09.049_bib5) 2007; 4692 Geem (10.1016/j.amc.2007.09.049_bib7) 2001; 76 Mays (10.1016/j.amc.2007.09.049_bib14) 1992 Geem (10.1016/j.amc.2007.09.049_bib3) 2006; 4251 Geem (10.1016/j.amc.2007.09.049_bib9) 2005; 3612 Geem (10.1016/j.amc.2007.09.049_bib6) 2007; 4448 |
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| SubjectTerms | Calculus of variations and optimal control Combinatorial optimization Combinatorics Combinatorics. Ordered structures Designs and configurations Discrete variable Evolutionary algorithm Exact sciences and technology Harmony search Mathematical analysis Mathematics Meta-heuristics Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Real functions Sciences and techniques of general use Soft computing Stochastic derivative |
| Title | Novel derivative of harmony search algorithm for discrete design variables |
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