scholarly journals Evaluation and application of Fuzzy Differential Evolution approach for benchmark optimization and reservoir operation problems

2013 ◽  
Vol 15 (4) ◽  
pp. 1456-1473 ◽  
Author(s):  
Dejan Vucetic ◽  
Slobodan P. Simonovic
Keyword(s):  
Differential Evolution ◽  
Reservoir Operation ◽  
Optimization Problems ◽  
Search Space ◽  
Search Technique ◽  
Continuous Space ◽  
De Algorithm ◽  
Alternative Approach ◽  
Fuzzy Interval

The differential evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm is handled stochastically and therefore does not adequately capture vague preliminary knowledge. This paper proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information on the search space can be represented and used to deliver a more focused search. The proposed FDE algorithm utilizes (a) fuzzy numbers to represent vague knowledge and (b) random alpha-cut levels for the search initialization. The alpha-cut intervals created during the initialization are used for fuzzy interval based mutation in successive search iterations. Four benchmark functions are used to demonstrate performance of the new FDE and its practical value. Additionally, the application of the FDE algorithm is illustrated through a reservoir operation case study problem. The new algorithm shows faster convergence in most of these functions.

scholarly journals Differential Evolution with Population and Strategy Parameter Adaptation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
V. Gonuguntla ◽  
R. Mallipeddi ◽  
Kalyana C. Veluvolu
Keyword(s):  
Differential Evolution ◽  
Population Size ◽  
Optimization Problems ◽  
Search Space ◽  
Benchmark Problems ◽  
Parameter Adaptation ◽  
De Algorithm ◽  
Probabilistic Technique ◽  
Number Of Individuals ◽  
Strategy Parameters

Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality.

scholarly journals SWARM DIRECTIONS EMBEDDED DIFFERENTIAL EVOLUTION FOR FASTER CONVERGENCE OF GLOBAL OPTIMIZATION PROBLEMS

2012 ◽  
Vol 21 (03) ◽  
pp. 1240013 ◽  
Author(s):  
MUSRRAT ALI ◽  
MILLIE PANT ◽  
AJITH ABRAHAM ◽  
CHANG WOOK AHN
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Empirical Studies ◽  
Real Life ◽  
Search Space ◽  
Benchmark Problems ◽  
De Algorithm ◽  
Information Sharing Mechanism

In the present study we propose a new hybrid version of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms called Hybrid DE or HDE for solving continuous global optimization problems. In the proposed HDE algorithm, information sharing mechanism of PSO is embedded in the contracted search space obtained by the basic DE algorithm. This is done to maintain a balance between the two antagonist factors; exploration and exploitation thereby obtaining a faster convergence. The embedding of swarm directions to the basic DE algorithm is done with the help of a "switchover constant" called α which keeps a record of the contraction of search space. The proposed HDE algorithm is tested on a set of 10 unconstrained benchmark problems and four constrained real life, mechanical design problems. Empirical studies show that the proposed scheme helps in improving the convergence rate of the basic DE algorithm without compromising with the quality of solution.

A New Differential Evolution Based Metaheuristic for Discrete Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Ricardo Sérgio Prado ◽  
Rodrigo César Pedrosa Silva ◽  
Frederico Gadelha Guimarães ◽  
Oriane Magela Neto
Keyword(s):  
Combinatorial Optimization ◽  
Differential Evolution ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Search Space ◽  
Combinatorial Problems ◽  
Combinatorial Optimization Problems ◽  
De Algorithm ◽  
The Difference

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

Optimization of Antenna Design Problems Using Binary Differential Evolution

2018 ◽  
pp. 614-636
Author(s):  
Sotirios K. Goudos
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Phase Shifters ◽  
Antenna Design ◽  
Design Problems ◽  
Array Design ◽  
Search Spaces ◽  
De Algorithm ◽  
Discrete Phase ◽  
Binary Differential Evolution

Differential Evolution (DE) is a popular evolutionary algorithm that has been applied to several antenna design problems. However, DE is best suited for continuous search spaces. Therefore, in order to apply it to combinatorial optimization problems for antenna design a binary version of the DE algorithm has to be used. In this chapter, the author presents a design technique based on Novel Binary DE (NBDE). The main benefit of NBDE is reserving the DE updating strategy to binary space. This chapter presents results from design cases that include array thinning, phased array design with discrete phase shifters, and conformal array design with discrete excitations based on NBDE.

Centroid Opposition-Based Differential Evolution

2014 ◽  
Vol 5 (4) ◽  
pp. 1-25 ◽  
Author(s):  
Shahryar Rahnamayan ◽  
Jude Jesuthasan ◽  
Farid Bourennani ◽  
Greg F. Naterer ◽  
Hojjat Salehinejad
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Extreme Points ◽  
Search Space ◽  
Population Based ◽  
Effective Population ◽  
Centroid Point ◽  
Opposite Point ◽  
Novel Concept ◽  
Multiple Variants

The capabilities of evolutionary algorithms (EAs) in solving nonlinear and non-convex optimization problems are significant. Differential evolution (DE) is an effective population-based EA, which has emerged as very competitive. Since its inception in 1995, multiple variants of DE have been proposed with higher performance. Among these DE variants, opposition-based differential evolution (ODE) established a novel concept in which individuals must compete with theirs opposites in order to make an entry in the next generation. The generation of opposite points is based on the current extreme points (i.e., maximum and minimum) in the search space. This paper develops a new scheme that utilizes the centroid point of a population to calculate opposite individuals. The classical scheme of an opposite point is modified. Incorporating this new scheme into DE leads to an enhanced ODE that is identified as centroid opposition-based differential evolution (CODE). The accuracy of the CODE algorithm is comprehensively evaluated on well-known complex benchmark functions and compared with the performance of conventional DE, ODE, and other state-of-the-art algorithms. The results for CODE are found to be promising.

Enhanced Directed Differential Evolution Algorithm for Solving Constrained Engineering Optimization Problems

2019 ◽  
Vol 10 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Ali Wagdy Mohamed ◽  
Ali Khater Mohamed ◽  
Ehab Z. Elfeky ◽  
Mohamed Saleh
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Test Problems ◽  
New Mutation ◽  
De Algorithm ◽  
Engineering Problems ◽  
Evolution Algorithm ◽  
Mutation Scheme ◽  
Exploration Exploitation

The performance of Differential Evolution is significantly affected by the mutation scheme, which attracts many researchers to develop and enhance the mutation scheme in DE. In this article, the authors introduce an enhanced DE algorithm (EDDE) that utilizes the information given by good individuals and bad individuals in the population. The new mutation scheme maintains effectively the exploration/exploitation balance. Numerical experiments are conducted on 24 test problems presented in CEC'2006, and five constrained engineering problems from the literature for verifying and analyzing the performance of EDDE. The presented algorithm showed competitiveness in some cases and superiority in other cases in terms of robustness, efficiency and quality the of the results.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

2013 ◽  
Vol 415 ◽  
pp. 349-352
Author(s):  
Hong Wei Zhao ◽  
Hong Gang Xia
Keyword(s):  
Differential Evolution ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Local Optimum ◽  
Local Optima ◽  
De Algorithm ◽  
Evolution Algorithm ◽  
Improved Differential Evolution Algorithm

Differential evolution (DE) is a population-based stochastic function minimizer (or maximizer), whose simple yet powerful and straightforward features make it very attractive for numerical optimization. However, DE is easy to trapped into local optima. In this paper, an improved differential evolution algorithm (IDE) proposed to speed the convergence rate of DE and enhance the global search of DE. The IDE employed a new mutation operation and modified crossover operation. The former can rapidly enhance the convergence of the MDE, and the latter can prevent the MDE from being trapped into the local optimum effectively. Besides, we dynamic adjust the scaling factor (F) and the crossover rate (CR), which is aimed at further improving algorithm performance. Based on several benchmark experiment simulations, the IDE has demonstrated stronger convergence and stability than original differential (DE) algorithm and other algorithms (PSO and JADE) that reported in recent literature.

The Hybrid Differential Evolution with Dynamic Scaling Mutation and Wrapper Local Search for Optimization Problems

2013 ◽  
Vol 479-480 ◽  
pp. 989-995
Author(s):  
Chun Liang Lu ◽  
Shih Yuan Chiu ◽  
Chih Hsu Hsu ◽  
Shi Jim Yen
Keyword(s):  
Local Search ◽  
Differential Evolution ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimization Problems ◽  
Search Space ◽  
Dynamic Scaling ◽  
Multi Objective ◽  
Wide Range ◽  
Single Objective

In this paper, an improved hybrid Differential Evolution (DE) is proposed to enhance optimization performance by cooperating Dynamic Scaling Mutation (DSM) and Wrapper Local Search (WLS) schemes. When evolution speed is standstill, DSM can improve searching ability to achieve better balance between exploitation and exploration in the search space. Furthermore, WLS can disturb individuals to fine tune the searching range around and then properly find better solutions in the evolution progress. The effective particle encoding representation named Particle Segment Operation-Machine Assignment (PSOMA) that we previously published is also applied to always produce feasible candidate solutions for hybrid DE model to solve the Flexible Job-Shop Scheduling Problem (FJSP). To test the performance of the proposed hybrid method, the experiments contain five frequently used CEC 2005 numerical functions and three representative FJSP benchmarks for single-objective and multi-objective optimization verifications, respectively. Compare the proposed method with the other related published algorithms, the simulation results indicate that our proposed method exhibits better performance for solving most the test functions for single-objective problems. In addition, the wide range of Pareto-optimal solutions and the more Gantt chart diversities can be obtained for the multi-objective FJSP in practical decision-making considerations.

Heat Exchanger Network Optimization by Differential Evolution Method

2014 ◽  
Vol 564 ◽  
pp. 292-297 ◽  
Author(s):  
Ngo Thi Phuong Thuy ◽  
Rajashekhar Pendyala ◽  
Nejat Rahmanian ◽  
Narahari Marneni
Keyword(s):  
Heat Exchanger ◽  
Differential Evolution ◽  
Network Optimization ◽  
Energy Utilization ◽  
Heat Exchanger Network ◽  
De Algorithm ◽  
Global Cost ◽  
Pinch Technology ◽  
Recent Developments

The synthesis of heat exchanger network (HEN) is a comprehensive approach to optimize energy utilization in process industry. Recent developments in HEN synthesis (HENS) present several heuristic methods, such as Simulated Annealing (SA), Genetic Algorithm (GA), and Differential Evolution (DE). In this work, DE method for synthesis and optimization of HEN has been presented. Using DE combined with the concept of super-targeting, the optimization is determined. Then DE algorithm is employed to optimize the global cost function including the constraints, such as heat balance, the temperatures of process streams. A case study has been optimized using DE, generated structure of HEN and compared with networks obtained by other methods such as pinch technology or mathematical programming. Through the result, the proposed method has been illustrated that DE is able to apply in HEN optimization, with 16.7% increase in capital cost and 56.4%, 18.9% decrease in energy, global costs respectively.

scholarly journals Modified Grasshopper Optimization Algorithm Based Genetic Algorithm for Global Optimization Problems: The System of Nonlinear Equations Case Study

2021 ◽  
Author(s):  
Hala A. Omar ◽  
Mohammed El-Shorbagy
Keyword(s):  
Genetic Algorithm ◽  
Optimization Algorithm ◽  
Local Minimum ◽  
Optimization Problems ◽  
Search Space ◽  
System Of Nonlinear Equations ◽  
Grasshopper Optimization Algorithm ◽  
Speed Up ◽  
Grasshopper Optimization

Abstract Grasshopper optimization algorithm (GOA) is one of the promising optimization algorithms for optimization problems. But, it has the main drawback of trapping into a local minimum, which causes slow convergence or inability to detect a solution. Several modifications and combinations have been proposed to overcome this problem. In this paper, a modified grasshopper optimization algorithm (MGOA) based genetic algorithm (GA) is proposed to overcome this problem. Modifications rely on certain mathematical assumptions and varying the domain of the Cmax control parameter to escape from the local minimum and move the search process to a new improved point. Parameter C is one of the most important parameters in GOA where it balances the exploration and exploitation of the search space. These modifications aim to lead to speed up the convergence rate by reducing the repeated solutions and the number of iterations. The proposed algorithm will be tested on the 19 main test functions to verify and investigate the influence of the proposed modifications. In addition, the algorithm will be applied to solve 5 different cases of nonlinear systems with different types of dimensions and regularity to show the reliability and efficiency of the proposed algorithm. Good results were achieved compared to the original GOA.

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