Product Optimization Incorporating Discrete Design Variables Based on Decomposition of Performance Characteristics

2006 ◽  
Author(s):  
Masataka Yoshimura ◽  
Yu Yoshimura ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Optimization Problems ◽  
Optimization Method ◽  
Design Solution ◽  
Hierarchical Optimization ◽  
Design Variables ◽  
Design Alternatives ◽  
Hierarchical Levels ◽  
Discrete Design Variables ◽  
Product Optimization ◽  
Alternative Designs

In order to obtain superior design solutions, the largest possible number of design alternatives, often expressed as discrete design variables, should first of all be considered, and the best design solution should then be selected from this wide set of alternative designs. Also, product designs should be initiated from the earliest possible stages, such as the conceptual and fundamental design stages, when discrete rather than continuous design variables have primacy. Although the use of discrete design variables is fundamentally important, this has implications in terms of computational demands and the accuracy of the optimized solution. This paper proposes an optimization method for product designs incorporating discrete design variables, in which hierarchical product optimization methodologies are constructed based on decomposition of characteristics and/or extraction of simpler characteristics. The optimizations are started at the lowest levels of the hierarchical optimization structure, and proceed to the higher levels. The discrete design variables are efficiently selected and optimized as smaller sub-optimization problems at the lowest hierarchical levels, while the optimum solutions for the entire problem are obtained by conventional mathematical programming methods. Practical optimization procedures for machine product optimization problems having several types of discrete design variables are constructed, and some applied examples demonstrate their effectiveness.

Product Optimization Incorporating Discrete Design Variables Based on Decomposition of Performance Characteristics

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Masataka Yoshimura ◽  
Yu Yoshimura ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Mathematical Programming ◽  
Optimization Problems ◽  
System Optimization ◽  
Optimization Method ◽  
Hierarchical Optimization ◽  
Standard Material ◽  
Design Variables ◽  
Hierarchical Levels ◽  
Discrete Design Variables ◽  
Product Optimization

This paper proposes a system optimization method for product designs incorporating discrete design variables, in which hierarchical product optimization methodologies are constructed based on decomposition of characteristics and/or extraction of simpler characteristics from original characteristics. The method is constructed to take advantage of hierarchical optimization procedures, enabling the incorporation of discrete design variables. The proposed method can be applied to machine product designs that include discrete design variables such as material types, machining methods, standard material forms, and specifications. The optimizations begin at the lowest levels of the hierarchical optimization structure and proceed to the higher levels. Discrete design variables are efficiently selected and optimized in the form of small suboptimization problems at the lowest hierarchical levels, and optimum solutions for the entire problem are ultimately obtained using conventional mathematical programming methods. Practical optimization procedures for machine product optimization problems that include several types of discrete design variables are constructed, and applied examples are provided to demonstrate their effectiveness.

scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

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.

Optimization Method Based on a Mix Strategy

2013 ◽  
Vol 816-817 ◽  
pp. 1154-1157
Author(s):  
Xu Yin ◽  
Ai Min Ji
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Local Solution ◽  
Collaborative Optimization ◽  
Design Variables ◽  
Gradient Optimization ◽  
Local Optimal Solution ◽  
Optimal Values ◽  
Low Efficiency

To solve problems that exist in optimal design such as falling into local optimal solution easily and low efficiency in collaborative optimization, a new mix strategy optimization method combined design of experiments (DOE) with gradient optimization (GO) was proposed. In order to reduce the effect on the result of optimization made by the designers decision, DOE for preliminary analysis of the function model was used, and the optimal values obtained in DOE stage was taken as the initial values of design variables in GO stage in the new optimization method. The reducer MDO problem was taken as a example to confirm the global degree, efficiency, and accuracy of the method. The results show the optimization method could not only avoid falling into local solution, but also have an obvious superiority in treating the complex collaborative optimization problems.

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jianhua Zhou ◽  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Quadratic Programming ◽  
Robust Optimization ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Critical Role ◽  
Interval Uncertainty ◽  
Design Solution ◽  
Novel Approach ◽  
Design Variables ◽  
Feasibility Robustness

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, sequential quadratic programming for robust optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

Study on Vibration Reduction Design of Steel-Composite Material Hybrid Mounting for Ship Based on Material Selection Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 415-424
Author(s):  
Wei Wang ◽  
Lu Yun Chen ◽  
Yu Fang Zhang
Keyword(s):  
Power Flow ◽  
Optimization Problems ◽  
Material Selection ◽  
Vibration Reduction ◽  
Optimization Method ◽  
Optimization Approach ◽  
Structural Dynamic ◽  
Level Difference ◽  
Design Variables ◽  
Steel Composite

The material selection optimization for vibration reduction design is studied present article. By introducing the stacking sequence hypothesis of metal material, taking into account the power flow level difference and vibration level difference parameter, the mechanical parameters of the material and plies number are defined as design variables, and the mathematical model of structural dynamic optimization based on material selection optimization approach is established. Finally, a naval hybrid steel-composite mounting structure for example, by introducing genetic algorithm, the optimization problems is solved. The numerical results show that the optimization method is effective and feasible.

scholarly journals Hierarchical Optimization Method for Energy Scheduling of Multiple Microgrids

2019 ◽  
Vol 9 (4) ◽  
pp. 624 ◽  
Author(s):  
Tao Rui ◽  
Guoli Li ◽  
Qunjing Wang ◽  
Cungang Hu ◽  
Weixiang Shen ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Stackelberg Game ◽  
Optimization Method ◽  
Economic Benefits ◽  
Power Grids ◽  
Mixed Integer ◽  
Hierarchical Optimization ◽  
Load Demand ◽  
Control Framework ◽  
Two Stages

This paper proposes a hierarchical optimization method for the energy scheduling of multiple microgrids (MMGs) in the distribution network of power grids. An energy market operator (EMO) is constructed to regulate energy storage systems (ESSs) and load demands in MMGs. The optimization process is divided into two stages. In the first stage, each MG optimizes the scheduling of its own ESS within a rolling horizon control framework based on a long-term forecast of the local photovoltaic (PV) output, the local load demand and the price sent by the EMO. In the second stage, the EMO establishes an internal price incentive mechanism to maximize its own profits based on the load demand of each MG. The optimization problems in these two stages are solved using mixed integer programming (MIP) and Stackelberg game theory, respectively. Simulation results verified the effectiveness of the proposed method in terms of the promotion of energy trading and improvement of economic benefits of MMGs.

Exploring the Effectiveness of Using Graveyard Data When Generating Design Alternatives

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Garrett Foster ◽  
Scott Ferguson
Keyword(s):  
Design Space Exploration ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Computational Cost ◽  
Beam Design ◽  
Design Alternatives ◽  
Alternative Generation ◽  
Alternative Identification ◽  
Alternative Designs ◽  
Future Work

The objective of this paper is to demonstrate that unique alternative designs can be efficiently found by searching the discarded data (or graveyard) from a multiobjective genetic algorithm (MOGA). Motivation for using graveyard data to generate design alternatives arises from the computational cost associated with real-time design space exploration of multiobjective optimization problems. The effectiveness of this approach is explored by comparing (1) the uniqueness of alternatives found using graveyard data and those generated using an optimization-based search, and (2) how alternative generation near the Pareto frontier is impacted. Two multiobjective case study problems are introduced—a two bar truss and an I-beam design optimization. Results from these studies indicate that using graveyard data allows for the discovery of alternative designs that are at least 70% as unique as alternatives found using an optimization-based alternative identification approach, while saving a significant number of functional evaluations. Additionally, graveyard data are shown to be better suited for alternative generation near the Pareto frontier than standard sampling techniques. Finally, areas of future work are also discussed.

Vibration Isolator Design for Space Application Based on Multiobjective Optimization Method

2013 ◽  
Vol 365-366 ◽  
pp. 77-81
Author(s):  
Zhi Wei Feng ◽  
Qian Gang Tang ◽  
Qing Bin Zhang
Keyword(s):  
Multiobjective Optimization ◽  
High Frequency ◽  
Optimization Problems ◽  
Optimization Method ◽  
Resonant Peak ◽  
Space Application ◽  
Vibration Isolator ◽  
Peak Reduction ◽  
Space Applications ◽  
Design Variables

A multiobjective optimization based vibration isolator design for space application is described. It is common to use passive isolator and isolate the platform noise in space applications. The design of a passive isolator involves a trade-off between the resonant peak reduction and the high frequency attenuation. The equation of motion and transfer function model for single-stage and two-stage connector model is derived by using basic principle. The multiobjective optimization model is proposed, where the design variables are the damping coefficients and stiffness coefficients, the objective functions are the resonant peak reduction and the high frequency attenuation, and the constraints are the natural frequency of the connector. The multiobjective optimization problems for the design of the passive isolator are solved by using the multiobjective evolutionary algorithm based on decomposition (MOEA/D). The Pareto front obtained can provide multiple candidate solutions for the designer. The method is effective for the design process of the passive isolator.

scholarly journals An Improved Genetic Algorithm for the Optimization of Composite Structures

2006 ◽  
Author(s):  
Vladimir Gantovnik ◽  
Georges Fadel ◽  
Zafer Gu¨rdal
Keyword(s):  
Genetic Algorithm ◽  
Composite Structures ◽  
Optimization Problems ◽  
Multivariate Approximation ◽  
Approximation Procedure ◽  
Continuous Variables ◽  
Improved Genetic Algorithm ◽  
Design Variables ◽  
Discrete Design Variables ◽  
Proposed Modification

This paper describes a new approach for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed modification improves the efficiency of the memory constructed in terms of the continuous variables. The work presents the algorithmic implementation of the proposed memory scheme and demonstrates the efficiency of the proposed multivariate approximation procedure for the weight optimization of a segmented open cross section composite beam subjected to axial tension load. Results are generated to demonstrate the advantages of the proposed improvements to a standard genetic algorithm.

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