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.

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 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.

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.

On Bilevel Optimization with Inexact Follower

2020 ◽  
Vol 17 (1) ◽  
pp. 74-95 ◽  
Author(s):  
M. Hosein Zare ◽  
Oleg A. Prokopyev ◽  
Denis Sauré
Keyword(s):  
Optimization Problems ◽  
Broad Class ◽  
Bilevel Optimization ◽  
Modeling Framework ◽  
Optimization Framework ◽  
Lower Level Problem ◽  
Level Problem ◽  
Potential Impact ◽  
Upper Level ◽  
Optimal Reaction

Traditionally, in the bilevel optimization framework, a leader chooses her actions by solving an upper-level problem, assuming that a follower chooses an optimal reaction by solving a lower-level problem. However, in many settings, the lower-level problems might be nontrivial, thus requiring the use of tailored algorithms for their solution. More importantly, in practice, such problems might be inexactly solved by heuristics and approximation algorithms. Motivated by this consideration, we study a broad class of bilevel optimization problems where the follower might not optimally react to the leader’s actions. In particular, we present a modeling framework in which the leader considers that the follower might use one of a number of known algorithms to solve the lower-level problem, either approximately or heuristically. Thus, the leader can hedge against the follower’s use of suboptimal solutions. We provide algorithmic implementations of the framework for a class of nonlinear bilevel knapsack problem (BKP), and we illustrate the potential impact of incorporating this realistic feature through numerical experiments in the context of defender-attacker problems.

scholarly journals An Evolutionary Algorithm for Solving Bilevel Programming Problems Using Duality Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hecheng Li ◽  
Lei Fang
Keyword(s):  
Evolutionary Algorithm ◽  
Bilevel Programming ◽  
Dual Problem ◽  
Optimization Problems ◽  
Duality Principle ◽  
Single Level ◽  
Nonconvex Functions ◽  
Lower Level Problem ◽  
Level Problem ◽  
Upper Level

Bilevel programming is characterized by two optimization problems located at different levels, in which the constraint region of the upper level problem is implicitly determined by the lower level problem. This paper is focused on a class of bilevel programming with a linear lower level problem and presents a new algorithm for solving this kind of problems by combining an evolutionary algorithm with the duality principle. First, by using the prime-dual conditions of the lower level problem, the original problem is transformed into a single-level nonlinear programming problem. In addition, for the dual problem of the lower level, the feasible bases are taken as individuals in population. For each individual, the values of dual variables can be obtained by taking the dual problem into account, thus simplifying the single-level problem. Finally, the simplified problem is solved, and the objective value is taken as the fitness of the individual. Besides, when nonconvex functions are involved in the upper level, a coevolutionary scheme is incorporated to obtain global optima. In the computational experiment, 10 problems, smaller or larger-scale, are solved, and the results show that the proposed algorithm is efficient and robust.

Constrained design optimization of active magnetic bearings through an artificial immune system

2016 ◽  
Vol 33 (8) ◽  
pp. 2395-2420 ◽  
Author(s):  
Yu-Cheng Chou ◽  
Yi-Hua Fan ◽  
Madoka Nakajima ◽  
Yi-Lin Liao
Keyword(s):  
Design Optimization ◽  
Structural Design ◽  
Optimization Problems ◽  
Clonal Selection ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Artificial Immune ◽  
Content Type ◽  
Structural Design Optimization ◽  
Single Objective

Purpose The purpose of this paper is to present the use of artificial immune systems (AISs) to solve constrained design optimization problems for active magnetic bearings (AMBs). Design/methodology/approach This research applies the AIS approach, more specifically, a representative clonal selection-based AIS called CLONALG, to the single-objective structural design optimization of AMBs. In addition, when compared with a genetic algorithm (GA) developed in the previous work, the CLONALG fails to produce best solutions when a nearly zero feasible ratio occurs in an AMB design problem. Therefore, an AIS called ARISCO (AIS for constrained optimization) is proposed to address the above issue. Findings A total of six AMB design cases are solved by the GA, CLONALG, and ARISCO. Based on the simulation results, in terms of solution quality, the ARISCO is shown to have better overall performance than the CLONALG and GA. In particular, when solving a problem with a nearly zero feasible ratio, the ARISCO and GA perform equally and both outperform the CLONALG. Originality/value In summary, the contributions of this paper include: this research applies the AIS approach, more precisely, the CLONALG, to the single-objective structural design optimization of AMBs; the ARISCO overall produces better AMB designs than the CLONALG and a GA developed in the previous work; in situations where a nearly zero feasible ratio occurs, the ARISCO and GA perform equally, and they both outperform the CLONALG.

Augmented Lagrangian teaching–learning-based optimization for structural design

2017 ◽  
Vol 232 (12) ◽  
pp. 2195-2213
Author(s):  
Hong-Shuang Li ◽  
Qiao-Yue Dong ◽  
Jiao-Yang Yuan
Keyword(s):  
Design Optimization ◽  
Structural Design ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Augmented Lagrangian Function ◽  
Lagrangian Multipliers ◽  
Structural Design Optimization ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning

Stochastic optimization methods have been widely employed to find solutions to structural design optimization problems in the past two decades, especially for truss structures. The primary aim of this study is to introduce a design optimization method combining an augmented Lagrangian function and teaching–learning-based optimization for truss and nontruss structural design optimization. The augmented Lagrangian function serves as a constraint-handling tool in the proposed method and converts a constrained optimization problem into an unconstrained one. On the other hand, teaching–learning-based optimization is employed to resolve the transformed, unconstrained optimization problems. Since the proper values of the Lagrangian multipliers and penalty factors are unknown in advance, the proposed method is implemented in an iterative way to avoid the issue of selecting them, i.e. the Lagrangian multipliers and penalty factors are automatically updated according to the violation level of all constraints. To examine the performance of the proposed method, it is applied on a group of benchmark truss optimization problems and a group of nontruss optimization problems of aircraft wing structures. The computational results obtained by the proposed method are compared to the results produced by both other version of teaching–learning-based optimization and stochastic optimization methods.

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