DIFFERENTIAL EVOLUTION FOR SOLVING MULTIOBJECTIVE OPTIMIZATION PROBLEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 225-240 ◽  
Author(s):  
RUHUL SARKER ◽  
HUSSEIN A. ABBASS
Keyword(s):  
Differential Evolution ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Population Based ◽  
Standard Test ◽  
Evolutionary Strategies ◽  
Test Problems ◽  
Strength Pareto Evolutionary Algorithm ◽  
Multiobjective Optimization Problems

The use of evolutionary strategies (ESs) to solve problems with multiple objectives [known as vector optimization problems (VOPs)] has attracted much attention recently. Being population-based approaches, ESs offer a means to find a set of Pareto-optimal solutions in a single run. Differential evolution (DE) is an ES that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto-frontier differential evolution (PDE) algorithm to solve VOPs. The solutions provided by the proposed algorithm for two standard test problems, outperform the "strength Pareto evolutionary algorithm", one of the state-of-the-art evolutionary algorithm for solving VOPs.

THE PARETO DIFFERENTIAL EVOLUTION ALGORITHM

2002 ◽  
Vol 11 (04) ◽  
pp. 531-552 ◽  
Author(s):  
H. A. ABBASS ◽  
R. SARKER
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Standard Test ◽  
Test Problems ◽  
Pareto Optimal Solutions ◽  
Continuous Domains ◽  
Evolution Algorithm ◽  
Multiobjective Algorithms

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as Vector Optimization Problems (VOPs)) has attracted much attention recently. Being population based approaches, EAs offer a means to find a group of pareto-optimal solutions in a single run. Differential Evolution (DE) is an EA that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto Differential Evolution (PDE) algorithm to solve VOPs. The solutions provided by the proposed algorithm for five standard test problems, is competitive to nine known evolutionary multiobjective algorithms for solving VOPs.

scholarly journals Heterogeneous Differential Evolution for Numerical Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Wang ◽  
Wenjun Wang ◽  
Zhihua Cui ◽  
Hui Sun ◽  
Shahryar Rahnamayan
Keyword(s):  
Differential Evolution ◽  
Numerical Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Population Based ◽  
Stochastic Search ◽  
Test Problems ◽  
Exploration And Exploitation ◽  
Large Scale Problems

Differential evolution (DE) is a population-based stochastic search algorithm which has shown a good performance in solving many benchmarks and real-world optimization problems. Individuals in the standard DE, and most of its modifications, exhibit the same search characteristics because of the use of the same DE scheme. This paper proposes a simple and effective heterogeneous DE (HDE) to balance exploration and exploitation. In HDE, individuals are allowed to follow different search behaviors randomly selected from a DE scheme pool. Experiments are conducted on a comprehensive set of benchmark functions, including classical problems and shifted large-scale problems. The results show that heterogeneous DE achieves promising performance on a majority of the test problems.

scholarly journals Differential Evolution: A Survey and Analysis

2018 ◽  
Vol 8 (10) ◽  
pp. 1945 ◽  
Author(s):  
Tarik Eltaeib ◽  
Ausif Mahmood
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
State Of The Art ◽  
Population Based ◽  
Vital Role ◽  
Fine Tuning ◽  
Control Parameters ◽  
Hybrid Techniques ◽  
Global Optimizer

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based metaheuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. In particular, we present a state-of-the-art survey of the literature on DE and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques.

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.

scholarly journals A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Qiang Long ◽  
Changzhi Wu ◽  
Xiangyu Wang ◽  
Lin Jiang ◽  
Jueyou Li
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Selection Procedure ◽  
Population Based ◽  
Pareto Solution ◽  
Multiobjective Genetic Algorithm ◽  
Trade Offs ◽  
Multiobjective Optimization Problems ◽  
Optimum Order

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. But, normally, there are some trade-offs between the elitism and diversity. For some multiobjective problems, elitism and diversity are conflicting with each other. Therefore, solutions obtained by applying MOGAs have to be balanced with respect to elitism and diversity. In this paper, we propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust.

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