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.

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.

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.

A novel collaborative optimization algorithm in solving complex optimization problems

2016 ◽  
Vol 21 (15) ◽  
pp. 4387-4398 ◽  
Author(s):  
Wu Deng ◽  
Huimin Zhao ◽  
Li Zou ◽  
Guangyu Li ◽  
Xinhua Yang ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
Complex Optimization

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.

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.

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

scholarly journals Chunking and cooperation in particle swarm optimization for feature selection

2021 ◽  
Author(s):  
Malek Sarhani ◽  
Stefan Voß
Keyword(s):  
Feature Selection ◽  
Particle Swarm Optimization ◽  
Cooperative Learning ◽  
Optimization Problems ◽  
Practical Importance ◽  
Particle Swarm ◽  
Large Datasets ◽  
Social Phenomena ◽  
Swarm Optimization ◽  
Complex Optimization

AbstractBio-inspired optimization aims at adapting observed natural behavioral patterns and social phenomena towards efficiently solving complex optimization problems, and is nowadays gaining much attention. However, researchers recently highlighted an inconsistency between the need in the field and the actual trend. Indeed, while nowadays it is important to design innovative contributions, an actual trend in bio-inspired optimization is to re-iterate the existing knowledge in a different form. The aim of this paper is to fill this gap. More precisely, we start first by highlighting new examples for this problem by considering and describing the concepts of chunking and cooperative learning. Second, by considering particle swarm optimization (PSO), we present a novel bridge between these two notions adapted to the problem of feature selection. In the experiments, we investigate the practical importance of our approach while exploring both its strength and limitations. The results indicate that the approach is mainly suitable for large datasets, and that further research is needed to improve the computational efficiency of the approach and to ensure the independence of the sub-problems defined using chunking.

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