scholarly journals A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

1990 ◽  
Author(s):  
Han Tong Loh ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Continuous Variables ◽  
New Approach ◽  
Design Variables ◽  
Nonlinear Design ◽  
Discrete Problems ◽  
Computationally Intensive ◽  
Discrete Values ◽  
Sequential Linearization

Abstract Design optimization models often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

scholarly journals A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

1991 ◽  
Vol 113 (3) ◽  
pp. 325-334 ◽  
Author(s):  
Han Tong Loh ◽  
P. Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Continuous Variables ◽  
New Approach ◽  
Design Variables ◽  
Nonlinear Design ◽  
Discrete Problems ◽  
Computationally Intensive ◽  
Discrete Values ◽  
Sequential Linearization

Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

scholarly journals Improved Quantum-Inspired Evolutionary Algorithm for Engineering Design Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Jinn-Tsong Tsai ◽  
Jyh-Horng Chou ◽  
Wen-Hsien Ho
Keyword(s):  
Evolutionary Algorithm ◽  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Latin Square ◽  
Latin Squares ◽  
Feasible Region ◽  
Continuous Variables ◽  
Nonlinear Design ◽  
Discrete Values

An improved quantum-inspired evolutionary algorithm is proposed for solving mixed discrete-continuous nonlinear problems in engineering design. The proposed Latin square quantum-inspired evolutionary algorithm (LSQEA) combines Latin squares and quantum-inspired genetic algorithm (QGA). The novel contribution of the proposed LSQEA is the use of a QGA to explore the optimal feasible region in macrospace and the use of a systematic reasoning mechanism of the Latin square to exploit the better solution in microspace. By combining the advantages of exploration and exploitation, the LSQEA provides higher computational efficiency and robustness compared to QGA and real-coded GA when solving global numerical optimization problems with continuous variables. Additionally, the proposed LSQEA approach effectively solves mixed discrete-continuous nonlinear design optimization problems in which the design variables are integers, discrete values, and continuous values. The computational experiments show that the proposed LSQEA approach obtains better results compared to existing methods reported in the literature.

On the Performance of the PSP Method for Mixed-Variable Multi-Objective Design Optimization

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Zeeshan Omer Khokhar ◽  
Hengameh Vahabzadeh ◽  
Amirreza Ziai ◽  
G. Gary Wang ◽  
Carlo Menon
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Black Box ◽  
Performance Comparison ◽  
Benchmark Problems ◽  
Continuous Variables ◽  
Multi Objective ◽  
Algorithm Efficiency ◽  
Design Variables ◽  
Mixed Variable

Practical design optimization problems require use of computationally expensive “black-box” functions. The Pareto set pursuing (PSP) method, for solving multi-objective optimization problems with expensive black-box functions, was originally developed for continuous variables. In this paper, modifications are made to allow solution of problems with mixed continuous-discrete variables. A performance comparison strategy for nongradient-based multi-objective algorithms is discussed based on algorithm efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Results using several methods, along with the modified PSP, are given for a suite of benchmark problems and two engineering design ones. The modified PSP is found to be competitive when the total number of function evaluations is limited, but faces an increased computational challenge when the number of design variables increases.

An Active Set Sequential Linearization Algorithm for Nonlinear Design Optimization

1987 ◽  
Author(s):  
N. Tzannetakis ◽  
P. Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Linear Programs ◽  
Chemical Process Design ◽  
Active Set ◽  
Active Set Strategy ◽  
Nonlinear Design ◽  
Working Set ◽  
Sequential Linearization

Abstract Solution of nonlinear design optimization problems via a sequence of linear programs is regaining attention for solving certain model classes, such as in structural design and chemical process design. An active set strategy modification of an algorithm by Palacios-Gomez is presented. A special interior linear programming algorithm with active set strategy is used also for solving the subproblem and generating the working set of the outer iterations. Examples are included.

Study on Mix-Variable Collaborative Design Optimization

2012 ◽  
Vol 215-216 ◽  
pp. 592-596
Author(s):  
Li Gao ◽  
Rong Rong Wang
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Algorithm ◽  
Collaborative Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Collaborative Optimization ◽  
Continuous Variables ◽  
Complex Product ◽  
Divide And Rule

In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Design Optimization of Aircraft Engine-Mount Systems

1993 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Design Optimization ◽  
Vibration Isolation ◽  
Optimization Problems ◽  
Three Dimensional ◽  
Low Frequency ◽  
Aircraft Engine ◽  
Variable Metric ◽  
Design Variables ◽  
Engine Mount ◽  
Optimization Search

Abstract Design optimization of aircraft engine-mount systems for vibration isolation is presented. The engine is modeled as a rigid body connected to a flexible base representing the nacelle. The base is modeled with mass and stiffness matrices and structural damping using finite element modeling. The mounts are modeled as three-dimensional springs with hysteresis damping. The objective is to select the stiffness coefficients and orientation angles of the individual mounts to minimize the transmitted forces from the engine to the base. Meanwhile, the mounts have to be stiff enough not allowing engine deflection to exceed its limits under static and low frequency loadings. It is shown that with an optimal system the transmitted forces may be reduced significantly particularly when mount orientation angles are also treated as design variables. The optimization problems are solved using a Constraint Variable Metric approach. The closed form derivatives of the engine vibrational amplitudes with respect to design variables are derived in order to achieve a more effective optimization search technique.

scholarly journals Application of evolutionary algorithms to optimize cooling channels

2019 ◽  
Vol 10 ◽  
pp. A4 ◽  
Author(s):  
Narasimha R. Nagaiah ◽  
Christopher D. Geiger
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Simulation Method ◽  
Optimization Method ◽  
Composite Function ◽  
Cooling Channels ◽  
Design Variables ◽  
Evolutionary Simulation ◽  
Conventional Methods ◽  
Cooling Passage

The design and development is a complex, repetitive, and more often difficult task, as design tasks comprising of restraining and conflicting relationships among design variables with more than one design objectives. Conventional methods for solving more than one objective optimization problems is to build one composite function by scalarizing the multiple objective functions into a single objective function with one solution. But, the disadvantages of conventional methods inspired scientists and engineers to look for different methods that result in more than one design solutions, also known as Pareto optimal solutions instead of one single solution. Furthermore, these methods not only involved in the optimization of more than one objectives concurrently but also optimize the objectives which are conflicting in nature, where optimizing one or more objective affects the outcome of other objectives negatively. This study demonstrates a nature-based and bio-inspired evolutionary simulation method that addresses the disadvantages of current methods in the application of design optimization. As an example, in this research, we chose to optimize the periodic segment of the cooling passage of an industrial gas turbine blade comprising of ribs (also known as turbulators) to enhance the cooling effectiveness. The outlined design optimization method provides a set of tradeoff designs to pick from depending on designer requirements.

An Approach to Identify Six Sigma Robust Solutions of Multi/Many-Objective Engineering Design Optimization Problems

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Tapabrata Ray ◽  
Md Asafuddoula ◽  
Hemant Kumar Singh ◽  
Khairul Alam
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Product Family ◽  
Latin Hypercube Sampling ◽  
General Aviation ◽  
Design Variables ◽  
Engineering Design Optimization ◽  
The Face ◽  
And Performance

In order to be practical, solutions of engineering design optimization problems must be robust, i.e., competent and reliable in the face of uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this study focuses on problems where uncertainties emanate from the design variables. While approaches to identify robust optimal solutions of single and multi-objective optimization problems have been proposed in the past, we introduce a practical approach that is capable of solving robust optimization problems involving many objectives building on authors’ previous work. Two formulations of robustness have been considered in this paper, (a) feasibility robustness (FR), i.e., robustness against design failure and (b) feasibility and performance robustness (FPR), i.e., robustness against design failure and variation in performance. In order to solve such formulations, a decomposition based evolutionary algorithm (DBEA) relying on a generational model is proposed in this study. The algorithm is capable of identifying a set of uniformly distributed nondominated solutions with different sigma levels (feasibility and performance) simultaneously in a single run. Computational benefits offered by using polynomial chaos (PC) in conjunction with Latin hypercube sampling (LHS) for estimating expected mean and variance of the objective/constraint functions has also been studied in this paper. Last, the idea of redesign for robustness has been explored, wherein selective component(s) of an existing design are altered to improve its robustness. The performance of the strategies have been illustrated using two practical design optimization problems, namely, vehicle crash-worthiness optimization problem (VCOP) and a general aviation aircraft (GAA) product family design problem.

An efficient discrete optimization algorithm for performance-based design optimization of steel frames

2019 ◽  
Vol 23 (3) ◽  
pp. 411-423 ◽  
Author(s):  
Xingfeng Wang ◽  
Qing Zhang ◽  
Xianrong Qin ◽  
Yuantao Sun
Keyword(s):  
Design Optimization ◽  
Discrete Optimization ◽  
Optimization Algorithm ◽  
Computational Efficiency ◽  
Steel Frames ◽  
Performance Based Design ◽  
Cross Sectional ◽  
Performance Constraints ◽  
Design Variables ◽  
Computationally Intensive

Performance-based design optimization of steel frames, with element sections selected from standard sections, is a computationally intensive task. In this article, an efficient discrete optimization algorithm is proposed for performance-based design optimization of steel frames. The computational efficiency is improved by searching in a sensible manner, guided by the deformation information of structural elements. To include all standard sections in the design space, the cross-sectional area ( Area) and moment of inertia ( Ix) are selected as the design variables. Based on different relationships between Area and Ix, a twofold strategy is put forward, which includes a quick exploration and an elaborate exploitation. For comparison, a similar algorithm is also proposed, using Area as the only design variable. A fixed relationship between Area and other sectional properties is used. Two numerical examples are presented to minimize the structural weight while satisfying performance constraints. The results indicate that the proposed discrete algorithm can achieve lighter structural designs than the area-only algorithm. Furthermore, the convergence history proves that a high computational efficiency can be realized by using the proposed algorithm.

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