An Alternative Formulation of Collaborative Optimization Based on Geometric Analysis

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Xiang Li ◽  
Changan Liu ◽  
Weiji Li ◽  
Teng Long
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Geometric Analysis ◽  
Equality Constraints ◽  
Collaborative Optimization ◽  
System Level ◽  
Alternative Formulation ◽  
Linear Approximations ◽  
Engineering Design Problems ◽  
Level Problem

Collaborative optimization (CO) is a multidisciplinary design optimization (MDO) method with bilevel computational structure, which decomposes the original optimization problem into one system-level problem and several subsystem problems. The strategy of decomposition in CO is a useful way for solving large engineering design problems. However, the computational difficulties caused by the system-level consistency equality constraints hinder the development of CO. In this paper, an alternative formulation of CO called CO with combination of linear approximations (CLA-CO) is presented based on the geometric analysis of CO, which is more intuitive and direct than the previous algebraic analysis. In CLA-CO, the consistency equality constraints in CO are replaced by linear approximations to the subsystem responses. As the iterative process goes on, more linear approximations are added into the system level. Consequently, the combination of these linear approximations makes the system-level problem gradually approximate the original problem. In CLA-CO, the advantages of the decomposition strategy are maintained while the computational difficulties of the conventional CO are avoided. However, there are still difficulties in applying the presented CLA-CO to problems with nonconvex constraints. The application of CLA-CO to three optimization problems, a numerical test problem, a composite beam design problem, and a gear reducer design problem, illustrates the capabilities and limitations of CLA-CO.

Multidisciplinary collaborative optimization based on relaxation method for solving complex problems

2020 ◽  
Vol 28 (4) ◽  
pp. 280-289
Author(s):  
Hamda Chagraoui ◽  
Mohamed Soula
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Relaxation Method ◽  
Multidisciplinary Optimization ◽  
Collaborative Optimization ◽  
System Level ◽  
Dynamic Relaxation ◽  
Dynamic Relaxation Method ◽  
Feasible Solutions ◽  
The Impact

The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.

Probability Collectives with Collaborative Optimization (PCCO): A Novel Framework for Handling Complex Optimization Problems

2013 ◽  
Vol 373-375 ◽  
pp. 1036-1044
Author(s):  
Wei Zhao ◽  
Nan Wang
Keyword(s):  
Optimization Problems ◽  
Level Structure ◽  
Collaborative Optimization ◽  
System Level ◽  
Coordination Ability ◽  
Complex Optimization ◽  
Pc Method

In this paper, a novel framework as a combination of Probability Collectives (PC) and Collaborative Optimization (CO) is proposed and detailed illustrated. The framework has a two-level structure which is similar to that of CO, but with the system level replaced by distributed PC based agents. This formulation maintains the advantage of CO while enhances the optimization and coordination ability at the system level. For better implementation, some adaption and improvement has been made to the origin PC method. The resultant PCCO framework shows satisfied performance in handling complex optimization problems with both efficiency and accuracy.

scholarly journals Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Debiao Meng ◽  
Xiaoling Zhang ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Huanwei Xu
Keyword(s):  
Interaction Design ◽  
Large Scale ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Design Parameters ◽  
Large Scale Systems ◽  
Interaction Prediction ◽  
Design Variables ◽  
Subsystem Level

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.

Multiple Target Exploration Approach for Design Exploration Using a Swarm Intelligence and Clustering

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Hyeongmin Han ◽  
Sehyun Chang ◽  
Harrison Kim
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Complete Solution ◽  
Solution Space ◽  
Analytical Models ◽  
Target Point ◽  
Design Exploration ◽  
Exploration Process ◽  
Engineering Design Problems

In engineering design problems, performance functions evaluate the quality of designs. Among the designs, some of them are classified as good designs if responses from performance functions satisfy a target point or range. An infinite set of good designs in the design space is defined as a solution space of the design problem. In practice, since the performance functions are analytical models or black-box simulations which are computationally expensive, it is difficult to obtain a complete solution space. In this paper, a method that finds a finite set of good designs, which is included in a solution space, is proposed. The method formulates the problem as optimization problems and utilizes gray wolf optimizer (GWO) in the way of design exploration. Target points of the exploration process are defined by clustering intermediate solutions for every iteration. The method is tested with a simple two-dimensional problem and an automotive vehicle design problem to validate and check the quality of solution points.

Multi-Objective Collaborative Optimization of Spring

2014 ◽  
Vol 599-601 ◽  
pp. 362-367
Author(s):  
Yun Peng ◽  
Ai Min Gong ◽  
Hai Yan Huang
Keyword(s):  
Natural Vibration ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Natural Vibration Frequency ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Relative Value ◽  
Structural Mass

A framework for solving the multi-objective optimization problems of spring in multidisciplinary design environment is advised in this paper. Based on the collaborative optimization (CO) algorithm, a new system level objective function is advised to minimize relative value among the structural mass, the height and the natural vibration frequency. The proposed models were demonstrated with a multi-objective optimization problem of a spring. The optimal design of the spring obtained indicates the great potential of decreasing structural mass and vibration level and increasing natural frequency reserve under the constraints. The analysis progress and results show that the model is feasible and well-suited for using in actual optimization problems of spring design.

Collaborative Optimization Algorithm Based on the Penalty Function

2014 ◽  
Vol 538 ◽  
pp. 447-450
Author(s):  
Zhi Xia Jiang ◽  
Pin Chao Meng ◽  
Yan Zhong Li ◽  
Wei Shi Yin
Keyword(s):  
Penalty Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Feasible Region ◽  
Relaxation Factor ◽  
Algorithm Stability ◽  
Calculation Process ◽  
Relaxation Factors

The paper discusses the collaborative optimization problems with bounded. Based the penalty function the system-level optimization convert to a unconstraint programming. To the discipline-level optimization, the normalized weighted coefficients are used and combine relaxation factors to solve. It uses the relaxation factor to expand the feasible region, and possibly makes the iteration in the calculation process run inside feasible region. The data have shown that the algorithm has expanded the choice range of the initial points with high calculation accuracy and better algorithm stability.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4613
Author(s):  
Shah Fahad ◽  
Shiyou Yang ◽  
Rehan Ali Khan ◽  
Shafiullah Khan ◽  
Shoaib Ahmed Khan
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Quantum Particle ◽  
Particle Swarm ◽  
Continuous Variables ◽  
Design Problems ◽  
Swarm Optimization ◽  
Electromagnetic Design ◽  
Quantum Particle Swarm Optimization ◽  
Engineering Design Problems

Electromagnetic design problems are generally formulated as nonlinear programming problems with multimodal objective functions and continuous variables. These can be solved by either a deterministic or a stochastic optimization algorithm. Recently, many intelligent optimization algorithms, such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC), have been proposed and applied to electromagnetic design problems with promising results. However, there is no universal algorithm which can be used to solve engineering design problems. In this paper, a stochastic smart quantum particle swarm optimization (SQPSO) algorithm is introduced. In the proposed SQPSO, to tackle the premature convergence problem in order to improve the global search ability, a smart particle and a memory archive are adopted instead of mutation operations. Moreover, to enhance the exploration searching ability, a new set of random numbers and control parameters are introduced. Experimental results validate that the adopted control policy in this work can achieve a good balance between exploration and exploitation. Finally, the SQPSO has been tested on well-known optimization benchmark functions and implemented on the electromagnetic TEAM workshop problem 22. The simulation result shows an outstanding capability of the proposed algorithm in speeding convergence compared to other algorithms.

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.

Hider: A Methodology for Early-Stage Exploration of Design Space

1996 ◽  
Author(s):  
Sudhakar Y. Reddy
Keyword(s):  
Design Space ◽  
Optimization Problems ◽  
Early Stage ◽  
Simulation Models ◽  
Design Tool ◽  
System Level ◽  
Complex Simulation ◽  
Machine Learning Approach ◽  
Detailed Simulation ◽  
And Performance

Abstract This paper describes HIDER, a methodology that enables detailed simulation models to be used during the early stages of system design. HIDER uses a machine learning approach to form abstract models from the detailed models. The abstract models are used for multiple-objective optimization to obtain sets of non-dominated designs. The tradeoffs between design and performance attributes in the non-dominated sets are used to interactively refine the design space. A prototype design tool has been developed to assist the designer in easily forming abstract models, flexibly defining optimization problems, and interactively exploring and refining the design space. To demonstrate the practical applicability of this approach, the paper presents results from the application of HIDER to the system-level design of a wheel loader. In this demonstration, complex simulation models for cycle time evaluation and stability analysis are used together for early-stage exploration of design space.

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