Global optimization of truss topology with discrete bar areas-Part II: Implementation and numerical results

Computational Optimization and Applications

Volumn 44, Issue 2, 2009, Pages 315-341

  Achtziger, Wolfgang ^a   Stolpe, Mathias ^b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Branch and bound; Global optimization; Truss topology optimization

Indexed keywords

ALGORITHMIC FRAMEWORK; BAR AREA; BRANCH AND BOUNDS; BRANCH-AND-BOUND; CLASSICAL PROBLEMS; CONVEX RELAXATION; CROSS SECTIONAL AREA; DESIGN PROBLEMS; DESIGN VARIABLES; DISCRETE PROBLEMS; DISCRETE TOPOLOGY; FEASIBLE SET; FINITE CONVERGENCE; GLOBAL OPTIMIZER; MIXED INTEGER; NUMERICAL EXAMPLE; NUMERICAL RESULTS; OBJECTIVE FUNCTIONS; PROBLEM FORMULATION; QUADRATIC PROGRAMS; STATIC LOADS; THEORETICAL RESULT; TRUSS DESIGN; TRUSS TOPOLOGY OPTIMIZATION;

GLOBAL OPTIMIZATION; RELAXATION PROCESSES; STRUCTURAL DESIGN; STRUCTURAL OPTIMIZATION; TOPOLOGY; TRUSSES;

BRANCH AND BOUND METHOD;

EID: 70449523712     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9152-7     Document Type: Article

References (22)

1. Achtziger, W.: Topology optimization of discrete structures: An introduction in view of computational and nonsmooth aspects. In: Rozvany, G.I.N. (ed.) Topology Optimization in Structural Mechanics, pp. 57-100. Springer, Vienna (1997)
2. W. Achtziger M. Stolpe 2007 Global optimization of truss topology with discrete bar areas-Part I: Theory of relaxed problems Comput. Optim. Appl. 10.1007/s10589-007-9138-5
3. W. Achtziger M. Stolpe 2007 Truss topology optimization with discrete design variables-guaranteed global optimality and benchmark examples Struct. Multidiscip. Optim. 34 1 1 20 10.1007/s00158-006-0074-2 2330689 (Pubitemid 46828874)
4. A. Ben-Tal A. Nemirovski 1994 Potential reduction polynomial time method for truss topology design SIAM J. Optim. 4 3 596 612 10.1137/0804033 1884919
5. A. Ben-Tal A. Nemirovski 1997 Robust truss topology design via semidefinite programming SIAM J. Optim. 7 4 991 1016 10.1137/S1052623495291951 1479611
6. Ben-Tal, A., Nemirovski, A.: Structural design. In: Handbook of Semidefinite Programming, pp. 443-467. Kluwer Academic, Dordrecht (2000)
7. Bendsøe, M.P., Sigmund, O.: Topology Optimization-Theory, Methods and Applications. Springer, Berlin (2003)
8. S. Bollapragada O. Ghattas J.N. Hooker 2001 Optimal design of truss structures by logical-based branch and cut Oper. Res. 49 1 42 51 10.1287/opre.49.1.42.11196 1814608
9. P.E. Gill W. Murray M.A. Saunders 2002 SNOPT: An SQP algorithm for large-scale constrained optimization SIAM J. Optim. 12 4 979 1006 10.1137/S1052623499350013 1922505
10. A.A. Groenwold N. Stander J.A. Snyman 1996 A pseudo-discrete rounding method for structural optimization Struct. Optim. 11 218 227 10.1007/BF01197037
11. P. Hajela E. Lee 1995 Genetic algorithms in truss topology optimization Int. J. Solids Struct. 32 22 3341 3357 10.1016/0020-7683(94)00306-H 1349952
12. Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches. Springer, Berlin (1993)
13. ILOG Inc.: ILOG Cplex 9.0 user's manual and reference manual. (2004) http://www.ilog.com
14. C. Kane M. Schoenauer 1996 Topological optimum design using genetic algorithms Control Cybern. 25 5 1059 1087 1464037 (Pubitemid 126489871)
15. A.H. Land A.G. Doig 1960 An automatic method for solving discrete programming problems Econometrica 28 497 520 10.2307/1910129 115825
16. The MathWorks: Matlab user guides. http://www.mathworks.com (2005)
17. Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. Wiley, New York (1999)
18. U. Ringertz 1986 A branch and bound algorithm for topology optimization of trusses Eng. Optim. 10 111 124 10.1080/03052158608902532
19. U. Ringertz 1988 On methods for discrete structural optimization Eng. Optim. 13 44 64
20. M. Stolpe 2007 On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs Optim. Eng. 8 163 192 10.1007/s11081-007-9005-3 2327162 (Pubitemid 47322198)
21. M. Stolpe A. Kawamoto 2005 Design of planar articulated mechanisms using branch and bound Math. Program. 103 2 357 398 10.1007/s10107-005-0586-3 2146384 (Pubitemid 40878754)
22. M. Stolpe K. Svanberg 2003 Modeling topology optimization problems as linear mixed 0-1 programs Int. J. Numer. Methods Eng. 57 5 723 739 10.1002/nme.700 1982308 (Pubitemid 36761896)