DISCRETE STRUCTURAL OPTIMIZATION WITH COMMERCIALLY AVAILABLE SECTIONS

Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables. When a discrete value for such a variable is specified from an allowable set, the values for other variables linked to it must also be used in all the calculations. Optimum design of steel frames using commercially available sections is an example of this class of problems. A general formulation for this type of problems is developed. Approaches for solving such practical optimization problems are described and classified into single and multiple design variable formulations. Many approaches use two phases in their solution process before the final discrete design is obtained: In the first phase, a continuous variable optimum is usually obtained, and in the second phase, the continuous solution is somehow utilized to obtain the final discrete solution. Some of the basic optimization methods used in these approaches are also described.

[1]  C. Fleury.  Structural weight optimization by dual methods of convex programming , 1979 .

[2]  Richard J. Balling,et al.  A filtered simulated annealing strategy for discrete optimization of 3D steel frameworks , 1992 .

[3]  E. Salajegheh,et al.  New Approximation Method for Stress Constraints in Structural Synthesis , 1989 .

[4]  G. Hogg,et al.  UNCONSTRAINED DISCRETE NONLINEAR PROGRAMMING , 1979 .

[5]  J. Arora,et al.  Methods for optimization of nonlinear problems with discrete variables: A review , 1994 .

[6]  A. R. Toakley,et al.  Optimum Design Using Available Sections , 1968 .

[7]  Judith S. Liebman,et al.  Discrete Structural Optimization , 1981 .

[8]  V. Venkayya.  Design of optimum structures , 1971 .

[9]  Robert D. Logcher,et al.  Automated Optimum Design from Discrete Components , 1970 .

[10]  H. Amir,et al.  Nonlinear Mixed-Discrete Structural Optimization , 1989 .

[11]  Min-Wei Huang,et al.  Engineering optimization with discrete variables , 1995 .

[12]  Richard J. Balling,et al.  Optimal Steel Frame Design by Simulated Annealing , 1991 .

[13]  Archibald N. Sherbourne,et al.  Automatic Optimal Design of Tall Steel Building Frameworks , 1995 .

[14]  Jasbir S. Arora,et al.  OPTIMAL DESIGN WITH DISCRETE VARIABLES: SOME NUMERICAL EXPERIMENTS , 1997 .

[15]  Jan Drewes Achenbach,et al.  Direct Search Optimization Method , 1973 .

[16]  Kenneth F. Reinschmidt.  Discrete Structural Optimization , 1970 .

[17]  A. M. Geoffrion.  Integer Programming by Implicit Enumeration and Balas’ Method , 1967 .

[18]  Shih-Fu Ling,et al.  Enhancing Branch-and-Bound Method for Structural Optimization , 1995 .

[19]  Rex K. Kincaid,et al.  Minimizing Distortion and Internal Forces in Truss Structures by Simulated Annealing , 1990 .

[20]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[21]  Lei Xu,et al.  Discrete Optimal Design of 3D Frameworks , 1991 .

[22]  Jasbir S. Arora,et al.  Interactive Design Optimization of Framed Structures , 1987 .

[23]  Donald E. Grierson,et al.  Optimal Synthesis of Steel Frameworks Using Standard Sections , 1984 .

[24]  Donald E. Grierson,et al.  Optimal Synthesis of Frameworks under Elastic and Plastic Performance Constraints Using Discrete Sections , 1986 .

[25]  Richard J. Balling,et al.  New Approach for Discrete Structural Optimization , 1988 .

[26]  Jasbir S. Arora,et al.  Methods for finding feasible points in constrained optimization , 1995 .

[27]  Emile H. L. Aarts,et al.  Simulated annealing and Boltzmann machines. A stochastic approach to combinatorial optimization , 1989 .

[28]  P. Hajela,et al.  GENETIC ALGORITHMS IN OPTIMIZATION PROBLEMS WITH DISCRETE AND INTEGER DESIGN VARIABLES , 1992 .

[29]  R. J. Balling,et al.  Discrete Optimization of 3D Steel Frames , 1989 .

[30]  Jasbir S. Arora,et al.  Optimal design of steel structures using standard sections , 1997 .

[31]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .