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.

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.

Structural Optimization of Transmission Line of Steel Poles

2012 ◽  
Vol 166-169 ◽  
pp. 48-51
Author(s):  
Li Qin ◽  
Ya Nan Luo ◽  
Peng Huang
Keyword(s):  
Structural Optimization ◽  
Transmission Line ◽  
Optimization Problems ◽  
Load Condition ◽  
Steel Pipe ◽  
Economic Optimization ◽  
Design Load ◽  
Design Variables ◽  
Load Calculation ◽  
Structural Mass

For the structural optimization of transmission line of steel pipe poles,the structural mass was considered the objective of the economic optimization, the taper of shaft and then the thickness of each wall with the taper of shaft were successively regarded as the design variables, established mathematical modal of transmission line of steel-pipe pole. Various conditions of load calculation were accomplished. Themost unfavorable load condition founded were taken as the design load condition.And LIN-GO is introduced to solve some optimization problems about the design variables. From what has been analysed , it is proved using L INGO on structural optimization of transmission line of steel pipe poles Can significantly reduce the amount of steel used.

Robust Structural Design Optimization Under Non-Probabilistic Uncertainties

2011 ◽  
Author(s):  
Jiantao Liu ◽  
Hae Chang Gea ◽  
Ping An Du
Keyword(s):  
Structural Optimization ◽  
Design Optimization ◽  
Structural Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Optimality ◽  
Worst Case ◽  
Probabilistic Uncertainty ◽  
Structural Design Optimization

Robust structural design optimization with non-probabilistic uncertainties is often formulated as a two-level optimization problem. The top level optimization problem is simply to minimize a specified objective function while the optimized solution at the second level solution is within bounds. The second level optimization problem is to find the worst case design under non-probabilistic uncertainty. Although the second level optimization problem is a non-convex problem, the global optimal solution must be assured in order to guarantee the solution robustness at the first level. In this paper, a new approach is proposed to solve the robust structural optimization problems with non-probabilistic uncertainties. The WCDO problems at the second level are solved directly by the monotonocity analysis and the global optimality is assured. Then, the robust structural optimization problem is reduced to a single level problem and can be easily solved by any gradient based method. To illustrate the proposed approach, truss examples with non-probabilistic uncertainties on stiffness and loading are presented.

Development of a Changeable Airfoil Optimization Model for Use in the Multidisciplinary Design of Unmanned Aerial Vehicles

2009 ◽  
Author(s):  
Scott Ferguson ◽  
Andrew H. Tilstra ◽  
Carolyn C. Seepersad ◽  
Kristin L. Wood
Keyword(s):  
Optimization Problem ◽  
Design Research ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Operating Conditions ◽  
Multidisciplinary Optimization ◽  
System Level ◽  
Airfoil Optimization ◽  
Design Variables ◽  
Subsystem Design

Complex systems need to perform in a variety of functional states and under varying operating conditions. Therefore, it is important to manage the different values of design variables associated with the operating states for each subsystem. The research presented in this paper uses multidisciplinary optimization (MDO) and changeable systems methods together in the design of a reconfigurable Unmanned Aerial Vehicle (UAV). MDO is a useful approach for designing a system that is composed of distinct disciplinary subsystems by managing the design variable coupling between the subsystem and system level optimization problems. Changeable design research addresses how changes in the physical configuration of products and systems can better meet distinct needs of different operating states. As a step towards the development of a realistic reconfigurable UAV optimization problem, this paper focuses on the performance advantage of using a changeable airfoil subsystem. Design principles from transformational design methods are used to develop concepts that determine how the design variables are allowed to change in the mathematical optimization problem. The performance of two changeable airfoil concepts is compared to a fixed airfoil design over two different missions that are defined by a sequence of mission segments. Determining the configurations of the static and changeable airfoils is accomplished using a genetic algorithm. Results from this study show that aircraft with changeable airfoils attain increased performance, and that the manner by which the system transforms is significant. For this reason, the changeable airfoil optimization developed in this paper is ready to be integrated into a complete MDO problem for the design of a reconfigurable UAV.

The Local Approximation Method for Structural Optimization

2014 ◽  
Vol 575 ◽  
pp. 854-858
Author(s):  
Yi Nie ◽  
Yan Wang ◽  
Wei Sun ◽  
Yan He ◽  
Jing Hao ◽  
...  
Keyword(s):  
Structural Optimization ◽  
Approximation Method ◽  
Optimization Problems ◽  
Broad Class ◽  
Local Approximation ◽  
Optimized Design ◽  
Guide Rail ◽  
Original Design ◽  
Design Variables

The local approximation method exhibits many advantage features and it is popular to a broad class of structural optimization problems. In this paper, both the mathematical modeling and case study of the local approximation method were studied. The theoretical analysis indicates that the primary optimization problem can be replaced with a sequence of explicit approximate problems by using the local approximation method. The explicit subproblems are convex and separable, which can be solved efficiently by using a dual method approach. The topology optimization of a guide rail design is then solved to testify the proposed method, which has been coded by Altair OptiStruct. The optimized design of a widely used guide rail with an “I” shape cross section is obtained and compared with the original design. The numerical results have shown that the local approximation method can effectively solve the structure optimization problems, especially the ones with hundreds of design variables or constraints.

scholarly journals Harris Hawks Optimization for Optimum Design of Truss Structures with Discrete Variables

2021 ◽  
Vol 6 (4) ◽  
pp. 1157-1173
Author(s):  
Mustafa Al-Bazoon
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Population Based ◽  
Truss Structures ◽  
Discrete Variables ◽  
Structural Problems ◽  
Collaborative Behavior ◽  
Design Variables ◽  
Predatory Birds ◽  
The Mathematical Model

This article investigates the use of Harris Hawks Optimization (HHO) to solve planar and spatial trusses with design variables that are discrete. The original HHO has been used to solve continuous design variables problems. However, HHO is formulated to solve optimization problems with discrete variables in this research. HHO is a population-based metaheuristic algorithm that simulates the chasing style and the collaborative behavior of predatory birds Harris hawks. The mathematical model of HHO uses a straightforward formulation and does not require tuning of algorithmic parameters and it is a robust algorithm in exploitation. The performance of HHO is evaluated using five benchmark structural problems and the final designs are compared with ten state-of-the-art algorithms. The statistical outcomes (average and standard deviation of final designs) show that HHO is quite consistent and robust in solving truss structure optimization problems. This is an important characteristic that leads to better confidence in the final solution from a single run of the algorithm for an optimization problem.

Large Scale Structural Optimization With Linear Goal Programming

1990 ◽  
Author(s):  
Mohamed E. M. El-Sayed ◽  
T. S. Jang
Keyword(s):  
Structural Optimization ◽  
Goal Programming ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Design Tool ◽  
Linear Goal Programming ◽  
Programming Techniques ◽  
Structural Optimization Problem

Abstract This paper presents a method for solving large scale structural optimization problems using linear goal programming techniques. The method can be used as a multicriteria optimization tool since goal programming removes the difficulty of having to define an objective function and constraints. It also has the capacity of handling rank ordered design objectives or goals. The method uses finite element analysis, linear goal programming techniques and successive linearization to obtain the solution for the nonlinear goal optimization problems. The general formulation of the structural optimization problem into a nonlinear goal programming form is presented. The successive linearization method for the nonlinear goal optimization problem is discussed. To demonstrate the validity of the method, as a design tool, the solution of the minimum weight structural optimization problem with stress constraints for 10, 25 and 200 truss problems are included.

Parallelization of Evolution Strategy on a Workstation-Cluster and its Application to Discrete Structural Optimization

1994 ◽  
Author(s):  
Jianbo Cai ◽  
Georg Thierauf
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Biological Evolution ◽  
Computing Environment ◽  
Design Point ◽  
Workstation Cluster ◽  
Conventional Optimization ◽  
Discrete Optimization Problems

Abstract Evolution strategies (ESs) imitate biological evolution and have two characteristics that differ from other conventional optimization algorithms: (a) ESs use randomized operators instead of the usual deterministic ones; (b) instead of a single design point, the ESs work simultaneously with a population of design points in the space of variables. The second characteristic allows for an implementation in a parallel computing environment. In this paper the application of ESs for the solution of discrete optimization problems and its parallelization are described.

Two-Level Structural Optimization Method for Multi-Processor Environment

1990 ◽  
Author(s):  
Ching-Kuo Hsiung ◽  
Mohamed E. M. El-Sayed
Keyword(s):  
Structural Optimization ◽  
Lower Bounds ◽  
Optimization Problem ◽  
Optimization Method ◽  
Global Constraints ◽  
Optimization Approach ◽  
Final Solution ◽  
Local Constraints ◽  
Numerical Examples ◽  
Design Variables

Abstract In this paper a two-level structural optimization approach is presented. At the first level, the objective of the optimization problem is to minimize the total weight of the whole structure subject to the global constraints. At the second level, the optimization problem is divided into several subproblems, each subproblem represents a substructure. The objective of each subproblem is to minimize the weight of the assigned substructure subject to its local constraints. To assure that the final solution will not violate the global constraints, the optimum values of the design variables from the first level are used to update the lower bounds on these variables at the second level. Two numerical examples are included to demonstrate the approach and its application in a multi-processor environment.

Structural Optimization With Nonlinear Goal Programming Using Powell’s Method

1991 ◽  
Author(s):  
Mohamed E. M. El-Sayed ◽  
T. S. Jang
Keyword(s):  
Structural Optimization ◽  
Goal Programming ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Numerical Test ◽  
Design Tool ◽  
Test Cases ◽  
Programming Techniques ◽  
Ordered Design

Abstract This paper presents a method for solving structural optimization problems using nonlinear goal programming techniques. The developed method removes the difficulty of having to define an objective function and constraints. It also has the capacity of handling rank ordered design objectives or goals. The formulation of the structural optimization problem into a goal programming form is discussed. The resulting optimization problem is solved using Powell’s conjugate direction search algorithm. To demonstrate the effectiveness of the method, as a design tool, the solutions of some numerical test cases are included.

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