Optimality and Constrained Derivatives in Two-Level Design Optimization

1990 ◽  
Vol 112 (4) ◽  
pp. 563-568 ◽  
Author(s):  
S. Azarm ◽  
W.-C. Li
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Simple Approach ◽  
Problem Structure ◽  
Before And After ◽  
Level Problem ◽  
Level Design ◽  
Identification Of Active Constraints ◽  
Optimality Test

The objective of this paper is twofold. First, an optimality test is presented to show that the optimality conditions for a separable two-level design optimization problem before and after its decomposition are the same. Second, based on identification of active constraints and exploitation of problem structure, a simple approach for calculating the gradient of a “second-level” problem is presented. This gradient is an important piece of information which is needed for solution of two-level design optimization problems. Three examples are given to demonstrate applications of the approach.

Optimality and Constrained Derivatives in Two-Level Design Optimization

1989 ◽  
Author(s):  
S. Azarm ◽  
W.-C. Li
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Simple Approach ◽  
Problem Structure ◽  
Before And After ◽  
Level Problem ◽  
Level Design ◽  
Identification Of Active Constraints ◽  
Optimality Test

Abstract The objective of this paper is twofold. First, an optimality test is presented to show that the optimality conditions for a two-level design optimization problem before and after its decomposition are the same. Second, based on identification of active constraints and exploitation of problem structure, a simple approach for calculating the gradient of a “second-level” problem is presented. This gradient is an important piece of information which is needed for solution of two-level design optimization problems. Three examples are given to demonstrate applications of the approach.

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
A. Almansoori
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Test Results ◽  
Robust Solution ◽  
Multi Objective ◽  
Function Calls ◽  
Level Problem ◽  
Upper Level

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

Evolutionary Algorithm Embedded With Bump-Hunting for Constrained Design Optimization

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Kamrul Hasan Rahi ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Computational Cost ◽  
Search Space ◽  
Bump Hunting ◽  
Simulation Based ◽  
Engineering Problems ◽  
Turbine Design

Abstract Real-world design optimization problems commonly entail constraints that must be satisfied for the design to be viable. Mathematically, the constraints divide the search space into feasible (where all constraints are satisfied) and infeasible (where at least one constraint is violated) regions. The presence of multiple constraints, constricted and/or disconnected feasible regions, non-linearity and multi-modality of the underlying functions could significantly slow down the convergence of evolutionary algorithms (EA). Since each design evaluation incurs some time/computational cost, it is of significant interest to improve the rate of convergence to obtain competitive solutions with relatively fewer design evaluations. In this study, we propose to accomplish this using two mechanisms: (a) more intensified search by identifying promising regions through “bump-hunting,” and (b) use of infeasibility-driven ranking to exploit the fact that optimal solutions are likely to be located on constraint boundaries. Numerical experiments are conducted on a range of mathematical benchmarks and empirically formulated engineering problems, as well as a simulation-based wind turbine design optimization problem. The proposed approach shows up to 53.48% improvement in median objective values and up to 69.23% reduction in cost of identifying a feasible solution compared with a baseline EA.

Hierarchical Arrangement of Characteristics in Product Design Optimization Problems for Deeper Insight Into Optimized Results

2004 ◽  
Author(s):  
Masataka Yoshimura ◽  
Masahiko Taniguchi ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimum Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Method ◽  
Hierarchical Level ◽  
Hierarchical Arrangement ◽  
Insight Into

This paper proposes a design optimization method for machine products that is based on the decomposition of performance characteristics, or alternatively, extraction of simpler characteristics, to accommodate the specific features or difficulties of a particular design problem. The optimization problem is expressed using hierarchical constructions of the decomposed and extracted characteristics and the optimizations are sequentially repeated, starting with groups of characteristics having conflicting characteristics at the lowest hierarchical level and proceeding to higher levels. The proposed method not only effectively enables achieving optimum design solutions, but also facilitates deeper insight into the design optimization results, and aids obtaining ideas for breakthroughs in the optimum solutions. An applied example is given to demonstrate the effectiveness of the proposed method.

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.

A Framework of Multi-Fidelity Topology Design and its Application to Optimum Design of Flow Fields in Battery Systems

2019 ◽  
Author(s):  
Kentaro Yaji ◽  
Shintaro Yamasaki ◽  
Shohji Tsushima ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Flow Fields ◽  
Design Solution ◽  
Design Parameters ◽  
High Fidelity ◽  
Topology Optimization Problem ◽  
Battery Systems

Abstract We propose a novel framework based on multi-fidelity design optimization for indirectly solving computationally hard topology optimization problems. The primary concept of the proposed framework is to divide an original topology optimization problem into two subproblems, i.e., low- and high-fidelity design optimization problems. Hence, artificial design parameters, referred to as seeding parameters, are incorporated into the low-fidelity design optimization problem that is formulated on the basis of a pseudo-topology optimization problem. Meanwhile, the role of high-fidelity design optimization is to obtain a promising initial guess from a dataset comprising topology-optimized design candidates, and subsequently solve a surrogate optimization problem under a restricted design solution space. We apply the proposed framework to a topology optimization problem for the design of flow fields in battery systems, and confirm the efficacy through numerical investigations.

A PENALTY METHOD FOR SOLVING BILEVEL LINEAR FRACTIONAL/LINEAR PROGRAMMING PROBLEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 207-224 ◽  
Author(s):  
HERMINIA I. CALVETE ◽  
CARMEN GALÉ
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Fractional Linear Programming ◽  
Linear Programming Problems ◽  
Level Problem ◽  
The Relationship ◽  
Planning Problems

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.

Significant Factors Identification for Particle Swarm Optimization Algorithm to Solving the Design Optimization Problem of a Four-Bar Linkage for Path Generation

2012 ◽  
Vol 249-250 ◽  
pp. 1180-1187 ◽  
Author(s):  
Cheng Kang Lee ◽  
Yung Chang Cheng
Keyword(s):  
Particle Swarm Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Population Based ◽  
Path Generation ◽  
Swarm Optimization ◽  
Control Factors ◽  
Four Bar Linkage

Particle swarm optimization (PSO) is a well-known population-based searching algorithm to solving optimization problems. This paper aims at identifying significant control factors for PSO to solving the design optimization problem of a four-bar linkage for path generation. Control factors considered herein are inertial weight, acceleration coefficients, breeding operation, and the number of population. A full factorial design of experiments is used to construct a set of experiments. Experimental results are analyzed with the analysis of variance method. According to the results obtained in this paper, breeding operation and the interaction between breeding operation and acceleration coefficients are significant. Inertial weight, acceleration coefficients, the number of population, and the other interactions are not significant. For the design optimization problem discussed herein, it is suggested to adopt breeding operation strategy and apply constant acceleration coefficients to increase significantly PSO’s performance and robustness. Type of inertial weight and the number of population do not affect PSO’s performance and robustness significantly.

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.

scholarly journals Proximal Gradient Method for Solving Bilevel Optimization Problems

2020 ◽  
Vol 25 (4) ◽  
pp. 66
Author(s):  
Seifu Endris Yimer ◽  
Poom Kumam ◽  
Anteneh Getachew Gebrie
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Split Feasibility Problem ◽  
Bilevel Optimization ◽  
Feasibility Problem ◽  
Proximal Gradient Method ◽  
Level Problem ◽  
Upper Level ◽  
The Split Feasibility Problem

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.

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