scholarly journals A NEW PROBABILISTIC ALGORITHM FOR SOLVING A CLASS OF SINGLE OR MULTI-OBJECTIVE OPTIMAL PROBLEMS

2009 ◽  
Vol 12 (11) ◽  
pp. 11-26
Author(s):  
Hao Van Tran ◽  
Thong Huu Nguyen
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Fixed Number ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Probabilistic Algorithm ◽  
Multi Objective ◽  
Single Objective

We consider a class of single-objective optimization problems which haves the character: there is a fixed number k (1≤k<n) that is independent of the size n of the problem such that if we only need to change values of k variables then it has the ability to find a better solution than the current one, let us call it Ok. In this paper, we propose a new numerical optimization technique, Search Via Probability (SVP) algorithm, for solving single objective optimization problems of the class Ok. The SVP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each of iterations, and on the performance of SVP algorithm we create good conditions for its appearance. We tested this approach by implementing the SVP algorithm on some test single-objective and multi objective optimization problems, and we found good and very stable results.

Multi-Objective Optimal Control Design With the Simple Cell Mapping Method

2013 ◽  
Author(s):  
Yousef Sardahi ◽  
Yousef Naranjani ◽  
Wei Liang ◽  
Jian-Qiao Sun ◽  
Carlos Hernandez ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Control Design ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Cell Mapping ◽  
Multi Objective ◽  
Simple Cell Mapping ◽  
Pareto Sets ◽  
Single Objective

Controls are often designed to meet different and conflicting goals. Consider the well-known LQR optimal control. The performance index contains a response measure and a control penalty, which are conflicting requirements. Proper linear or nonlinear combinations of the conflicting objective functions have led to single objective optimization problems. However, such a single objective optimization is dependent on the combination algorithm, and only provides a narrow window of all possible optimal solutions that a system may have. Multi-objective optimization provides a set of optimal solutions, known as Pareto set. There have been many studies of search algorithms for Pareto sets of multi-objective optimization problems for complex dynamical systems. Recently, the simple cell mapping (SCM) method due to C.S. Hsu has been found to be a highly effective tool to compute Pareto sets. This paper applies the SCM method to several control design problems of linear and nonlinear dynamical systems. The results of the work are very exciting to report.

scholarly journals Modelling Diversity of Solutions

2020 ◽  
Vol 34 (02) ◽  
pp. 1528-1535
Author(s):  
Linnea Ingmar ◽  
Maria Garcia de la Banda ◽  
Peter J. Stuckey ◽  
Guido Tack
Keyword(s):  
General Framework ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Solution ◽  
Single Objective

For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimization problems, as they have no single “best solution” and, thus, it is useful to find a representation of the non-dominated solutions (the Pareto frontier). However, it also applies to single objective optimization problems, where one may be interested in finding several (close to) optimal solutions that illustrate some form of diversity. The same applies to satisfaction problems. This is because models usually idealize the problem in some way, and a diverse pool of solutions may provide a better choice with respect to considerations that are omitted or simplified in the model. This paper describes a general framework for finding k diverse solutions to a combinatorial problem (be it satisfaction, single-objective or multi-objective), various approaches to solve problems in the framework, their implementations, and an experimental evaluation of their practicality.

Enhancement of Labyrinth Seals Efficiency by Means of a Multi-Objective Optimization Technique

2018 ◽  
Author(s):  
Mikhail Gritckevich ◽  
Kunyuan Zhou ◽  
Vincent Peltier ◽  
Markus Raben ◽  
Olga Galchenko
Keyword(s):  
Optimization Technique ◽  
Leakage Flow ◽  
Multi Objective Optimization ◽  
Labyrinth Seals ◽  
Engine Operation ◽  
Turbine Engine ◽  
Multi Objective ◽  
Single Objective ◽  
Ansys Workbench ◽  
Comprehensive Study

A comprehensive study of several labyrinth seals has been performed in the framework of both single-objective and multi-objective optimizations with the main focus on the effect of stator grooves formed due to the rubbing during gas turbine engine operation. For that purpose, the developed optimization workflow based on the DLR-AutoOpti optimizer and ANSYS-Workbench CAE environment has been employed to reduce the leakage flow and windage heating for several seals. The obtained results indicate that the seal designs obtained from optimizations without stator grooves have worse performance during the lifecycle than those with the stator grooves, justifying the importance of considering this effect for real engineering applications.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

scholarly journals A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 465 ◽  
Author(s):  
Peng Ni ◽  
Jiale Gao ◽  
Yafei Song ◽  
Wen Quan ◽  
Qinghua Xing
Keyword(s):  
Optimization Problems ◽  
Pareto Set ◽  
Benchmark Problems ◽  
Small Range ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective ◽  
The Law ◽  
Cloud Theory

In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.

scholarly journals An Overview of Few Nature Inspired Optimization Techniques and Its Reliability Applications

2020 ◽  
Vol 5 (4) ◽  
pp. 732-743
Author(s):  
Nitin Uniyal ◽  
Sangeeta Pant ◽  
Anuj Kumar
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Research Fields ◽  
Research Problems ◽  
Nature Inspired Algorithms ◽  
New Algorithms ◽  
Single Objective

Optimization has been a hot topic due to its inevitably in the development of new algorithms in almost every applied branch of Mathematics. Despite the broadness of optimization techniques in research fields, there is always an open scope of further refinement. We present here an overview of nature-inspired optimization with a subtle background of fundamentals and classification and their reliability applications. An attempt has been made to exhibit the contrast nature of multi objective optimization as compared to single objective optimization. Though there are various techniques to achieve the optimality in optimization problems but nature inspired algorithms have proved to be very efficient and gained special attention in modern research problems. The purpose of this article is to furnish the foundation of few nature inspired optimization techniques and their reliability applications to an interested researcher.

Robustness Against Large Variations in Multi-Objective Optimization Problems

2013 ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis
Keyword(s):  
Optimization Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Design Environment ◽  
Multi Objective ◽  
Uncertainty Sources ◽  
Design Variables ◽  
Robustness Index ◽  
Environment Parameters

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.

scholarly journals Sen's Multi Objective Optimization (MOO) Technique-An Extension

2020 ◽  
Vol 06 (09) ◽  
pp. 77-79
Author(s):  
Chandra Sen
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

Linear programming has been very popular for achieving (maximizing or minimizing) a single objective with certain constraints. However, when objectives are more than one, linear programming becomes inefficient. Sen's multi-objective optimization (MOO) technique [1] is efficient in achieving multiple objectives simultaneously. Few modifications in Sen's MOO technique are proposed for improving its applicability for solving multi-objective optimization problems.

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