scholarly journals Global Optimization for Mixed–Discrete Structural Design

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1529
Author(s):  
Jung-Fa Tsai ◽  
Ming-Hua Lin ◽  
Duan-Yi Wen
Keyword(s):  
Structural Design ◽  
Design Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Computational Time ◽  
Optimization Approach ◽  
Global Optimality ◽  
Discrete Variables ◽  
Beam Design ◽  
Continuous And Discrete Variables

Several structural design problems that involve continuous and discrete variables are very challenging because of the combinatorial and non-convex characteristics of the problems. Although the deterministic optimization approach theoretically guarantees to find the global optimum, it usually leads to a significant burden in computational time. This article studies the deterministic approach for globally solving mixed–discrete structural optimization problems. An improved method that symmetrically reduces the number of constraints for linearly expressing signomial terms with pure discrete variables is applied to significantly enhance the computational efficiency of obtaining the exact global optimum of the mixed–discrete structural design problem. Numerical experiments of solving the stepped cantilever beam design problem and the pressure vessel design problem are conducted to show the efficiency and effectiveness of the presented approach. Compared with existing methods, this study introduces fewer convex terms and constraints for transforming the mixed–discrete structural problem and uses much less computational time for solving the reformulated problem to global optimality.

Non-Probabilistic Based Structural Design Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2012 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Limei Xu
Keyword(s):  
Design Optimization ◽  
Structural Design ◽  
External Load ◽  
Optimization Problems ◽  
Global Optimum ◽  
Global Optimality ◽  
Lower Level Problem ◽  
Structural Design Optimization ◽  
Level Problem ◽  
Upper Level

The non-probabilistic-based structural design optimization problems with external load uncertainties are often solved through a two-level approach. However there are several challenges in this method. Firstly, to assure the reliability of the design, the lower level problem must be solved to its global optimality. Secondly, the sensitivity of the upper level problem cannot be analytically derived. To overcome these challenges, a new method based on the Eigenvalue-Superposition of Convex Models (ESCM) is proposed in this paper. The ESCM method replaces the global optimum of the lower level problem by a confidence bound, namely the ESCM bound, and with which the two-level problem can be formulated into a single level problem. The advantages of the ESCM method in efficiency and stability are demonstrated through numerical examples.

Taguchi-Particle Swarm Optimization for Numerical Optimization

2012 ◽  
pp. 44-59
Author(s):  
T. O. Ting ◽  
H. C. Ting ◽  
T. S. Lee
Keyword(s):  
Particle Swarm Optimization ◽  
Taguchi Method ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Particle Swarm ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Swarm Optimization ◽  
Continuous And Discrete Variables

In this work, a hybrid Taguchi-Particle Swarm Optimization (TPSO) is proposed to solve global numerical optimization problems with continuous and discrete variables. This hybrid algorithm combines the well-known Particle Swarm Optimization Algorithm with the established Taguchi method, which has been an important tool for robust design. This paper presents the improvements obtained despite the simplicity of the hybridization process. The Taguchi method is run only once in every PSO iteration and therefore does not give significant impact in terms of computational cost. The method creates a more diversified population, which also contributes to the success of avoiding premature convergence. The proposed method is effectively applied to solve 13 benchmark problems. This study’s results show drastic improvements in comparison with the standard PSO algorithm involving continuous and discrete variables on high dimensional benchmark functions.

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.

scholarly journals Self-Directed Online Machine Learning for Topology Optimization

2021 ◽  
Author(s):  
Changyu Deng ◽  
Yizhou Wang ◽  
Can Qin ◽  
Wei Lu
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Region Of Interest ◽  
Global Optimum ◽  
Training Data ◽  
Computational Time ◽  
Minimization Problems ◽  
Design Variables

Abstract Topology optimization by optimally distributing materials in a given domain requires gradient-free optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by compliance minimization problems and fluid-structure optimization problems. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

A new hybrid particle swarm optimization approach for structural design optimization in the automotive industry

2012 ◽  
Vol 226 (10) ◽  
pp. 1340-1351 ◽  
Author(s):  
Ali R Yildiz
Keyword(s):  
Particle Swarm Optimization ◽  
Design Optimization ◽  
Automotive Industry ◽  
Structural Design ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimization Approach ◽  
Swarm Optimization ◽  
Hybrid Particle Swarm Optimization ◽  
Structural Design Optimization

This paper presents an innovative optimization approach to solve structural design optimization problems in the automotive industry. The new approach is based on Taguchi’s robust design approach and particle swarm optimization algorithm. The proposed approach is applied to the structural design optimization of a vehicle part to illustrate how the present approach can be applied for solving design optimization problems. The results show the ability of the proposed approach to find better optimal solutions for structural design optimization problems.

An Efficient Strategy for the Robust Optimization of Large Scale Nonlinear Design Problems

1994 ◽  
Author(s):  
Balaji Ramakrishnan ◽  
S. S. Rao
Keyword(s):  
Robust Optimization ◽  
Design Problem ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Effort ◽  
Geometric Constraints ◽  
Connecting Rod ◽  
Linear System Of Equations ◽  
Beam Design ◽  
Nonlinear Design

Abstract The application of the concept of robust design, based on Taguchi’s design philosophy, in formulating and solving large, computationally intensive, nonlinear optimization problems whose analysis is based on a linear system of equations is investigated. The design problem is formulated using a robust optimization procedure that utilizes the expected value of Taguchi’s loss function as the objective. An efficient solution scheme that uses approximate expressions for the gradients and employs a fast reanalysis technique for their evaluation is introduced. This approach is validated by solving a simple minimum cost welded beam design problem; where the dimensions of the weldment and the beam are found without exceeding the limitations stated on the shear stress in the weld, normal stress in the beam, buckling load on the beam and tip deflection of the beam. The method is then used to obtain the optimal shape of an engine connecting rod, that minimizes its weight when subject to geometric constraints on the shape variables, and behavioral constraints such as stress and buckling loads. The results obtained by solving the conventional and robust formulations of this problem, and the considerable savings in time that result by virtue of using the fast reanalysis technique are presented. The methodology presented in this work is expected to be useful in reducing the computational effort in obtaining insensitive designs of large structures and machines.

A Robust Optimization Approach Using Taguchi’s Loss Function for Solving Nonlinear Optimization Problems

1991 ◽  
Author(s):  
Balaji Ramakrishnan ◽  
S. S. Rao
Keyword(s):  
Nonlinear Optimization ◽  
Loss Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Beam Design ◽  
Robust Formulation ◽  
Machining Parameter ◽  
Machining Characteristics ◽  
Taguchi’S Loss Function

Abstract The application of the concept of robust design, based on Taguchi’s loss function, in formulating and solving nonlinear optimization problems is investigated. The effectiveness of the approach is illustrated with two examples. The first example is a machining parameter optimization problem wherein the production cost, tool life and production rate are optimized with limitations on machining characteristics such as cutting power, cutting tool temperature and surface finish. The second example is a welded beam design problem where the dimensions of the weldment and the beam are found without exceeding the limitations stated on the shear stress in the weld, normal stress in the beam, buckling load on the beam and tip deflection of the beam. The results are highlighted by comparing the solutions of the robust formulation with those obtained from the conventional formulation. The methodology presented in this work is expected to be useful in the design of products and processes which are least sensitive to the noises and which reflect in higher quality.

DISTURBANCE CHAOTIC ANT SWARM

2011 ◽  
Vol 21 (09) ◽  
pp. 2597-2622 ◽  
Author(s):  
FANGZHEN GE ◽  
ZHEN WEI ◽  
YANG LU ◽  
LIXIANG LI ◽  
YIXIAN YANG
Keyword(s):  
Computational Complexity ◽  
Optimization Problems ◽  
Search Space ◽  
Global Optimum ◽  
Global Optimality ◽  
High Dimensions ◽  
Original Algorithm ◽  
Intelligence Theory ◽  
Optimum Solution ◽  
Solution Accuracy

Chaotic Ant Swarm (CAS) is an optimization algorithm based on swarm intelligence theory, which has been applied to find the global optimum solution in search space. However, it often loses its effectiveness and advantages when applied to large and complex problems, e.g. those with high dimensions. To resolve the problems of high computational complexity and low solution accuracy existing in CAS, we propose a Disturbance Chaotic Ant Swarm (DCAS) algorithm to significantly improve the performance of the original algorithm. The aim of this paper is achieved by three strategies which include modifying the method of updating ant's best position, neighbor selection method and establishing a self-adaptive disturbance strategy. The global convergence of the DCAS algorithm is proved in this paper. Extensive computational simulations and comparisons are carried out to validate the performance of the DCAS on two sets of benchmark functions with up to 1000 dimensions. The results show clearly that DCAS substantially enhances the performance of the CAS paradigm in terms of computational complexity, global optimality, solution accuracy and algorithm reliability for complex high-dimensional optimization problems.

scholarly journals Gaussian Perturbation Specular Reflection Learning and Golden-Sine-Mechanism-Based Elephant Herding Optimization for Global Optimization Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Yuxian Duan ◽  
Changyun Liu ◽  
Song Li ◽  
Xiangke Guo ◽  
Chunlin Yang
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Specular Reflection ◽  
Search Space ◽  
Global Optimum ◽  
Initial Population ◽  
Engineering Problems ◽  
Gaussian Perturbation ◽  
Set Up ◽  
Solution Accuracy

Elephant herding optimization (EHO) has received widespread attention due to its few control parameters and simple operation but still suffers from slow convergence and low solution accuracy. In this paper, an improved algorithm to solve the above shortcomings, called Gaussian perturbation specular reflection learning and golden-sine-mechanism-based EHO (SRGS-EHO), is proposed. First, specular reflection learning is introduced into the algorithm to enhance the diversity and ergodicity of the initial population and improve the convergence speed. Meanwhile, Gaussian perturbation is used to further increase the diversity of the initial population. Second, the golden sine mechanism is introduced to improve the way of updating the position of the patriarch in each clan, which can make the best-positioned individual in each generation move toward the global optimum and enhance the global exploration and local exploitation ability of the algorithm. To evaluate the effectiveness of the proposed algorithm, tests are performed on 23 benchmark functions. In addition, Wilcoxon rank-sum tests and Friedman tests with 5% are invoked to compare it with other eight metaheuristic algorithms. In addition, sensitivity analysis to parameters and experiments of the different modifications are set up. To further validate the effectiveness of the enhanced algorithm, SRGS-EHO is also applied to solve two classic engineering problems with a constrained search space (pressure-vessel design problem and tension-/compression-string design problem). The results show that the algorithm can be applied to solve the problems encountered in real production.

scholarly journals Advanced arithmetic optimization algorithm for solving mechanical engineering design problems

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255703
Author(s):  
Jeffrey O. Agushaka ◽  
Absalom E. Ezugwu
Keyword(s):  
Engineering Design ◽  
Optimization Algorithm ◽  
Beta Distribution ◽  
Optimization Problems ◽  
Global Optimum ◽  
Natural Logarithm ◽  
Beam Design ◽  
Efficient Performance ◽  
Engineering Design Problems ◽  
Addition And Subtraction

The distributive power of the arithmetic operators: multiplication, division, addition, and subtraction, gives the arithmetic optimization algorithm (AOA) its unique ability to find the global optimum for optimization problems used to test its performance. Several other mathematical operators exist with the same or better distributive properties, which can be exploited to enhance the performance of the newly proposed AOA. In this paper, we propose an improved version of the AOA called nAOA algorithm, which uses the high-density values that the natural logarithm and exponential operators can generate, to enhance the exploratory ability of the AOA. The addition and subtraction operators carry out the exploitation. The candidate solutions are initialized using the beta distribution, and the random variables and adaptations used in the algorithm have beta distribution. We test the performance of the proposed nAOA with 30 benchmark functions (20 classical and 10 composite test functions) and three engineering design benchmarks. The performance of nAOA is compared with the original AOA and nine other state-of-the-art algorithms. The nAOA shows efficient performance for the benchmark functions and was second only to GWO for the welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD).

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