Parametric Optimization for Structural Design Problems

2019 ◽  
Author(s):  
Krupakaran Ravichandran ◽  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Structural Design ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraint ◽  
Computational Performance ◽  
Design Variables ◽  
Input Parameters ◽  
Parametric Optimization Problem ◽  
Objective Function Values

Abstract Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

scholarly journals Size optimization of single edge folds for cold-formed structural members

2020 ◽  
pp. 73-86
Author(s):  
Serhii Bilyk ◽  
Vitalina Yurchenko
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Structural Members ◽  
Single Edge ◽  
Load Bearing Capacity ◽  
Load Bearing ◽  
Parametric Optimization Problem

Parametric optimization problem for single edge fold size in cold-formed structural members subjected to central compression has been considered by the paper. Determination the load-bearing capacity of the cold-formed structural members has been performed using the geometrical properties calculated based on the constructed “effective” (reduced) cross-sections taking into account local buckling effects in the section as well as distortional buckling effects. Single edge fold size in cold-formed C-profile has been considered as design variable. Linear convolution of criteria, namely minimization criterion of design area of stiffener cross-section and maximization criterion effective area of stiffener cross-section which defines it reduced load-bearing capacity due to flexural buckling has been used as optimization criterion. The parametric optimization problem has been solved using the method of objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations. In order to realize the formulated optimization problem, software OptCAD intended to solve parametric optimization problems for steel structural systems has been used. Optimization results of the single edge folds for the cold-formed С-profiles manufactured by «Blachy Pruszyński» company, «BF FACTORY» company as well as «STEELCO» company have been presented by the paper. The results of the performed investigation can be used as recommendations for companies-manufacturers of the cold-formed profiles, as well as a guide for creation the national assortment base of the effective cold-formed profiles promoting wider implementation of cold-formed steel structures in building practice.

Solution of a parametric optimization problem

Cybernetics ◽  
1975 ◽  
Vol 10 (1) ◽  
pp. 166-170
Author(s):  
V. L. Tiskin
Keyword(s):  
Optimization Problem ◽  
Parametric Optimization ◽  
Parametric Optimization Problem

scholarly journals Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Shu-qiang Shan ◽  
Yu Han ◽  
Nan-jing Huang
Keyword(s):  
Nash Equilibria ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Upper Semicontinuity ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Quasiequilibrium Problems ◽  
Parametric Variational Inequality ◽  
Parametric Optimization Problem ◽  
Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.

A Two Level Parallel Evolution Strategy for Solving Mixed-Discrete Structural Optimization Problems

1995 ◽  
Author(s):  
Georg Thierauf ◽  
Jianbo Cai
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Parallel Evolution ◽  
Evolution Strategy ◽  
Parallel Computer ◽  
Computing Architecture ◽  
Design Variables

Abstract A method for the solution of mixed-discrete structural optimization problems based on a two level parallel evolution strategy is presented. On the first level, the optimization problem is divided into two subproblems with discrete and continuous design variables, respectively. The two subproblems are solved simultaneously on a parallel computing architecture. On the second level, each subproblem is further parallelized by means of a parallel sub-evolution-strategy. Periodically, the design variables in the two groups axe exchanged. Examples are included to demonstrate the implementation of this method on a 8 nodes parallel computer.

scholarly journals An Exact Algorithm for Bilevel 0-1 Knapsack Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Raid Mansi ◽  
Cláudio Alves ◽  
J. M. Valério de Carvalho ◽  
Saïd Hanafi
Keyword(s):  
Optimization Problem ◽  
Original Problem ◽  
Parametric Optimization ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Decision Makers ◽  
Knapsack Problems ◽  
Hierarchical Decision ◽  
Parametric Optimization Problem

We propose a new exact method for solving bilevel 0-1 knapsack problems. A bilevel problem models a hierarchical decision process that involves two decision makers called the leader and the follower. In these processes, the leader takes his decision by considering explicitly the reaction of the follower. From an optimization standpoint, these are problems in which a subset of the variables must be the optimal solution of another (parametric) optimization problem. These problems have various applications in the field of transportation and revenue management, for example. Our approach relies on different components. We describe a polynomial time procedure to solve the linear relaxation of the bilevel 0-1 knapsack problem. Using the information provided by the solutions generated by this procedure, we compute a feasible solution (and hence a lower bound) for the problem. This bound is used together with an upper bound to reduce the size of the original problem. The optimal integer solution of the original problem is computed using dynamic programming. We report on computational experiments which are compared with the results achieved with other state-of-the-art approaches. The results attest the performance of our approach.

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