Fundamentals of optimization

The structural design problem is formulated as a general nonlinear optimization problem with constraints. Characteristics of such problems and the solutions are discussed. Methods of solution for constrained as well as unconstrained problems are reviewed, with special emphasis on penalty function methods for constrained problems. A simple example on the solution of a design problem with discrete variables is shown, and a realistic example on the application of optimization methods in midship section design of OBO-carriers is presented.

[1]  K. M. Gisvold,et al.  A Method for Nonlinear Mixed-Integer Programming and its Application to Design Problems , 1972 .

[2]  L. A. Schmit,et al.  An integrated approach to structural synthesis and analysis , 1965 .

[3]  Richard H. Gallagher,et al.  A Procedure for Automated Minimum Weight Structural Design: Part I: Theoretical Basis , 1966 .

[4]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[5]  M. J. Box.  A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems , 1966, Comput. J..

[6]  D. Kavlie,et al.  Application of non‐linear programming to optimum grillage design with non‐convex sets of variables , 1969 .

[7]  Georges Brigham,et al.  An Analog Solution of Programming Problems , 1955, Oper. Res..

[8]  R. Sayer.  Computer aided aircraft structural design , 1968 .

[9]  Fred Moses,et al.  Minimum weight design of structures with application to elastic grillages , 1969 .

[10]  Johannes Moe.  Design of ship structures by means of non-linear programming techniques , 1970 .

[11]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[12]  Fred Moses,et al.  Optimum Structural Design Using Linear Programming , 1964 .

[13]  Richard H. Gallagher,et al.  A Procedure for Automated Minimum Weight Structural Design: Part II: Applications , 1966 .

[14]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[15]  Janusz Kowalik,et al.  Nonlinear programming procedures and design optimization , 1966 .

[16]  Charles W. Carroll.  The Created Response Surface Technique for Optimizing Nonlinear, Restrained Systems , 1961 .

[17]  G. W. Stewart,et al.  A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives , 1967, JACM.

[18]  Daniel M. Brown,et al.  Structural Optimization by Nonlinear Programming , 1966 .

[19]  R. A. Gellatly,et al.  Application of the Created Response Surface Technique to Structural Optimization , 1968 .

[20]  L. A. Schmit,et al.  Structural synthesis 1959-1969 - A decade of progress , 1971 .

[21]  Karl M. Romstad,et al.  Optimum Design of Framed Structures , 1968 .