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Andres Guerra(aguerramines.edu) Abstract: We present a mixedinteger nonlinear programming (MINLP) formulation to achieve minimumcost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the crosssection dimensions for each element and relative sizes of crosssection dimensions of elements within the structure. Other restrictions define a stiffness and displacement correlation among all structural elements via finite element analysis. The design of minimum cost RC structures introduces a new class of optimization problems, namely, mixedinteger nonlinear programs with complementarity constraints. The complementarity constraints are used to model RC element strength and ACI coderequired safety factors. We reformulate the complementarity constraints as nonlinear equations and show that the resulting illconditioned MINLPs can be solved by using an offtheshelf MINLP solver. Our work provides discretevalued design solutions for an explicit representation of a process most often performed implicitly with iterative calculations. We demonstrate the capabilities of a mixedinteger nonlinear algorithm, MINLPBB, to find optimal sizing and reinforcing for castinplace beam and column elements in multistory RC structures. Problem instances contain up to 678 variables, of which 214 are integer, and 844 constraints, of which 582 are nonlinear. We solve problems to local optimality within a reasonable amount of computational time, and we find an average cost savings over typicalpractice design solutions of 13 percent. Keywords: complementarity problems, applications in optimization, mixed integer programming Category 1: Applications  Science and Engineering (Civil and Environmental Engineering ) Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 3: Complementarity and Variational Inequalities Citation: Mathematics and Computer Science Division Preprint ANL/MCSPnnnn1109, Argonne National Laboratory, November 2009 Download: [PDF] Entry Submitted: 11/26/2009 Modify/Update this entry  
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