Grey Optimization Problems Using Prey-Predator Algorithm

2018 ◽  
pp. 31-46
Author(s):  
Nawaf N. Hamadneh
Keyword(s):  
Optimization Problems ◽  
System Modeling ◽  
Optimization Methods ◽  
Metaheuristic Algorithms ◽  
Grey System ◽  
Solution Methods ◽  
Grey Systems Theory ◽  
Deterministic Solution ◽  
Best Parameter ◽  
Grey Number

The optimization problems are the problem of finding the best parameter values which optimize the objective functions. The optimization methods are divided into two types: deterministic and non-deterministic methods. Metaheuristic algorithms fall in the non-deterministic solution methods. Prey-predator algorithm is one of the well-known metaheuristic algorithms developed for optimization problems. It has gained popularity within a short time and is used in different applications, and it is an easy algorithm to understand and also to implement. The grey systems theory was initialized as uncertain systems. Each grey system is described with grey numbers, grey equations, and grey matrices. A grey number has uncertain value, but there is an interval or a general set of numbers, within that the value lies is known. In this chapter, the author will review and show that grey system modeling is very useful to use with prey-predator algorithm. The benchmark functions, grey linear programming, and grey model GM (1,1) are used as examples of grey system.

scholarly journals THE EFFICIENCY ANALYSIS OF MULTI-AGENT OPTIMIZATION METHODS OF AIRCRAFT DESIGNS ELEMENTS

2019 ◽  
Vol 22 (2) ◽  
pp. 96-108
Author(s):  
A. V. Panteleev ◽  
M.M. S. Karane
Keyword(s):  
Optimization Problems ◽  
Optimization Methods ◽  
Metaheuristic Algorithms ◽  
Great Success ◽  
Structural Elements ◽  
Development Environment ◽  
Fish School ◽  
Krill Herd ◽  
Multi Agent ◽  
The Given

The article considers the use of three multi-agent methods for optimizing structural elements of aircraft. The research describes strategies for finding solutions to multi-agent metaheuristic algorithms, such as: fish school search, krill herd, and imperialist competition algorithm. The work of these methods is based on the processes occurring in an environment that features many agents. Agents have the opportunity to exchange information in order to find a solution to the problem. These methods allow you to find an approximate solution, but, nevertheless, with great success are used in practice. In this regard, the described metaheuristic algorithms were applied to the optimization problems of structural elements of aircraft such as: welded beam, high pressure vessel, gearbox and tension spring. The article adduces the formulation of these problems: the objective function, a set of constraints and a set of admissible solutions are indicated, recommendations on the choice of parameters of the methods used are given. To solve the problems of optimizing the elements of aircraft construction, a set of software elements was formed in the development environment of Microsoft Visual Studio in C #. This complex of programs allows you to solve the given problems by each of the described multi-agent methods. The software allows you to select a method, a task and select the method parameters and the penalty function coefficients in the best possible way. The results of the solution were compared with each other and with the well- known solution. According to the numerical results of solving these tasks, we can conclude that the algorithmic and software created allow us to find a solution close to the exact one in a reasonable time.

Explanations about grey information and framework of grey system modeling

2017 ◽  
Vol 7 (2) ◽  
pp. 179-193 ◽  
Author(s):  
Naiming Xie
Keyword(s):  
System Modeling ◽  
Evolutionary Process ◽  
Grey System Theory ◽  
Limited Data ◽  
Grey System ◽  
Content Type ◽  
System Models ◽  
Different Types ◽  
Grey Number ◽  
Uncertainty Models

Purpose The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST). Design/methodology/approach GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper. Findings The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling. Practical implications Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect. Originality/value Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

scholarly journals Bio-Inspired Algorithms and Its Applications for Optimization in Fuzzy Clustering

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 122
Author(s):  
Fevrier Valdez ◽  
Oscar Castillo ◽  
Patricia Melin
Keyword(s):  
Fuzzy Clustering ◽  
Real World ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Metaheuristic Algorithms ◽  
Natural Phenomena ◽  
Algorithm Development ◽  
Real World Applications ◽  
Nature Inspired Algorithms ◽  
Relationship Of

In recent years, new metaheuristic algorithms have been developed taking as reference the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm development has been widely used by many researchers in solving optimization problems. These algorithms have been compared with the traditional ones and have demonstrated to be superior in many complex problems. This paper attempts to describe the algorithms based on nature, which are used in optimizing fuzzy clustering in real-world applications. We briefly describe the optimization methods, the most cited ones, nature-inspired algorithms that have been published in recent years, authors, networks and relationship of the works, etc. We believe the paper can serve as a basis for analysis of the new area of nature and bio-inspired optimization of fuzzy clustering.

Software suite for determining the tilts of tower-type structures according to terrestrial laser scanning

2020 ◽  
Vol 961 (7) ◽  
pp. 2-7
Author(s):  
A.V. Zubov ◽  
N.N. Eliseeva
Keyword(s):  
Laser Scanning ◽  
Optimization Problems ◽  
Optimization Methods ◽  
User Participation ◽  
Software Suite ◽  
Current State ◽  
Visual Basic For Applications ◽  
Operational Data ◽  
Theoretical Developments

The authors describe a software suite for determining tilt degrees of tower-type structures according to ground laser scanning indication. Defining the tilt of the pipe is carried out with a set of measured data through approximating the sections by circumferences. They are constructed using one of the simplest search engine optimization methods (evolutionary algorithm). Automatic filtering the scan of the current section from distorting data is performed by the method of assessing the quality of models constructed with that of least squares. The software was designed using Visual Basic for Applications. It contains several blocks (subprograms), with each of them performing a specific task. The developed complex enables obtaining operational data on the current state of the object with minimal user participation in the calculation process. The software suite is the result of practical implementing theoretical developments on the possibilities of using search methods at solving optimization problems in geodetic practice.

scholarly journals An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 225
Author(s):  
José García ◽  
Gino Astorga ◽  
Víctor Yepes
Keyword(s):  
Transfer Functions ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Set Covering ◽  
Covering Problem ◽  
Perturbation Operator ◽  
K Nearest Neighbors ◽  
Combinatorial Optimization Problems ◽  
Box Plots ◽  
Metaheuristic Techniques

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

An enhanced symbiotic organisms search algorithm for design optimization of trusses with frequency constraints

2021 ◽  
pp. 136943322110262
Author(s):  
Mohammad H Makiabadi ◽  
Mahmoud R Maheri
Keyword(s):  
Standard Deviation ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Metaheuristic Algorithms ◽  
Minimum Mass ◽  
Multiple Frequency ◽  
Frequency Constraints ◽  
Symbiotic Organisms Search ◽  
Symbiotic Organisms ◽  
Dynamic Frequency

An enhanced symbiotic organisms search (ESOS) algorithm is developed and presented. Modifications to the basic symbiotic organisms search algorithm are carried out in all three phases of the algorithm with the aim of balancing the exploitation and exploration capabilities of the algorithm. To verify validity and capability of the ESOS algorithm in solving general optimization problems, the CEC2014 set of 22 benchmark functions is first optimized and the results are compared with other metaheuristic algorithms. The ESOS algorithm is then used to optimize the sizing and shape of five benchmark trusses with multiple frequency constraints. The best (minimum) mass, mean mass, standard deviation of the mass, total number of function evaluations, and the values of frequency constraints are then compared with those of a number of other metaheuristic solutions available in the literature. It is shown that the proposed ESOS algorithm is generally more efficient in optimizing the shape and sizing of trusses with dynamic frequency constraints compared to other reported metaheuristic algorithms, including the basic symbiotic organisms search and its other recently proposed improved variants such as the improved symbiotic organisms search algorithm (ISOS) and modified symbiotic organisms search algorithm (MSOS).

scholarly journals Assessing the Performance of Interactive Multiobjective Optimization Methods

2021 ◽  
Vol 54 (4) ◽  
pp. 1-27
Author(s):  
Bekir Afsar ◽  
Kaisa Miettinen ◽  
Francisco Ruiz
Keyword(s):  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Interactive Methods ◽  
Value Functions ◽  
Technical Aspects ◽  
Preference Information ◽  
Multiobjective Optimization Problems ◽  
Human Decision

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

2012 ◽  
Vol 215-216 ◽  
pp. 133-137
Author(s):  
Guo Shao Su ◽  
Yan Zhang ◽  
Zhen Xing Wu ◽  
Liu Bin Yan
Keyword(s):  
Stochastic Optimization ◽  
Covariance Matrix ◽  
Optimization Problems ◽  
Fitness Function ◽  
Optimization Methods ◽  
Evolution Strategy ◽  
Covariance Matrix Adaptation ◽  
Study Results ◽  
Highly Nonlinear ◽  
Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

Nondegenerate Piecewise Linear Systems: A Finite Newton Algorithm and Applications in Machine Learning

2012 ◽  
Vol 24 (4) ◽  
pp. 1047-1084 ◽  
Author(s):  
Xiao-Tong Yuan ◽  
Shuicheng Yan
Keyword(s):  
Linear Systems ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Optimization Methods ◽  
Coefficient Matrix ◽  
Learning Problems ◽  
Support Vector ◽  
Data Sets ◽  
Piecewise Linear Systems ◽  
Vector Machines

We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008 ), and support vector machines (Cortes & Vapnik, 1995 ). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

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