Modeling without categorical variables: A mixed-integer nonlinear program for the optimization of thermal insulation systems

Optimization and Engineering

Volumn 11, Issue 2, 2010, Pages 185-212

  Abhishek, Kumar ^a   Leyffer, Sven ^b   Linderoth, Jeffrey T ^c  

^a Enterprise Optimization   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

^c University of Wisconsin Madison   (United States)

Author keywords

Categorical variables; Mixed integer nonlinear programming; Modeling with binary variables; Thermal insulation systems

Indexed keywords

BINARY VARIABLES; BLACK-BOX MODELING; CATEGORICAL VARIABLES; COLD SURFACE; CONTINUOUS RELAXATION; DESIGN DECISIONS; HEAT FLOWS; HOT SURFACE; LOAD-BEARING; MIXED INTEGER NONLINEAR PROGRAM; MIXED-INTEGER NONLINEAR PROGRAMMING; MODELING TECHNIQUE; NEW MODEL; NONLINEAR MODELING; OPTIMAL DESIGN; THERMAL INSULATION SYSTEMS;

COMPUTER SIMULATION LANGUAGES; INTEGER PROGRAMMING; NONLINEAR PROGRAMMING; OPTIMIZATION;

THERMAL INSULATION;

EID: 77952543296     PISSN: 13894420     EISSN: 15732924     Source Type: Journal    
DOI: 10.1007/s11081-010-9109-z     Document Type: Article

References (18)

1. Abhishek K, Leyffer S, Linderoth JT (2006) FilMINT: an outer-approximation-based solver for nonlinear mixed integer programs. Preprint ANL/MCS-P1374-0906, Mathematics and Computer Science Division, Argonne National Lab.
2. Abramson MA (2004) Mixed variable optimization of a load-bearing thermal insulation system using a filter pattern search algorithm. Optim Eng 5: 157-177.
3. Abramson MA, Audet C, Dennis JE (2007) Filter pattern search algorithms for mixed variable constrained optimization problems. Pac J Optim 3(3): 477-500.
4. Audet C, Dennis J (2004) A pattern search filter method for nonlinear programming without derivatives. SIAM J Optim 14(4): 980-1010.
5. Audet C, Dennis JE (2000) Pattern search algorithms for mixed variable programming. SIAM J Optim 11(3): 573-594.
6. Beal JM, Shukla A, Brezhneva OA, Abramson MA (2008) Optimal sensor placement for enhancing sensitivity to change in stiffness for structural health monitoring. Optim Eng 9: 119-142.
7. Bonami P, Biegler LT, Conn AR, Cornuéjols G, Grossmann IE, Laird CD, Lee J, Lodi A, Margot F, Sawaya N, Wächter A (2008) An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optim 5: 186-204.
8. Dakin RJ (1965) A tree search algorithm for mixed programming problems. Comput J 8: 250-255.
9. Fletcher R, Leyffer S, Toint P (2002) On the global convergence of a Filter-SQP algorithm. SIAM J Optim 13: 44-59.
10. Fourer R, Gay DM, Kernighan BW (2003) AMPL: a modelling language for mathematical programming, 2nd edn. Books/Cole-Thomson Learning, Florence.
11. Grossmann IE (2002) Review of nonlinear mixed-integer and disjunctive programming techniques. Optim Eng 3: 227-252.
12. Gupta OK, Ravindran A (1985) Branch and bound experiments in convex nonlinear integer programming. Manag Sci 31: 1533-1546.
13. Kokkolaras M, Audet C, Dennis JE (2001) Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system. Optim Eng 2: 5-29.
14. Leyffer S (1998a) User manual for MINLP. University of Dundee, Dundee.
15. Leyffer S (1998b) User manual for MINLP-BB. University of Dundee, Dundee.
16. Nemhauser GL, Savelsbergh MWP, Sigismondi GC (1994) MINTO, a mixed INTeger optimizer. Oper Res Lett 15: 47-58.
17. Quesada I, Grossmann IE (1992) An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems. Comput Chem Eng 16: 937-947.
18. Zhao Z, Meza J, van Hove M (2006) Using pattern search methods for surface structure determination of nanostructures. J Phys, Condens Matter 18: 8693-8706.