A Comparison of Differential Evolution and Generalized Generation Gap Model

2005 ◽  
Vol 9 (5) ◽  
pp. 549-555 ◽  
Author(s):  
Jani Rönkkönen ◽  
◽  
Saku Kukkonen ◽  
Jouni Lampinen
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Global Optimum ◽  
Superior Performance ◽  
Generation Gap ◽  
High Dimensional ◽  
Gap Model ◽  
Know How ◽  
Different Characteristics ◽  
Multimodal Problems

We compared two floating-point-encoded evolutionary algorithms (EA) – differential evolution (DE) and the generalized generation gap (G3) – using a set of problems with different characteristics. G3 is reported to offer superior performance with unimodal functions, which are, however, often solved more efficiently using derivative-based optimization for example and it is interesting to know, how these algorithms perform in multimodal global optimization problems. Our results suggest that G3 converges fast but is prone to converge prematurely rather than finding the global optimum in high-dimensional multimodal problems. DE, in contrast, appears to handle multimodal problems better but cannot match convergence speed of G3 in unimodal problems.

scholarly journals Differential Evolution with Novel Mutation and Adaptive Crossover Strategies for Solving Large Scale Global Optimization Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Ali Wagdy Mohamed ◽  
Abdulaziz S. Almazyad
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Large Scale ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
High Dimensional ◽  
Gradual Change ◽  
Comparison Results ◽  
Mutation Strategy ◽  
Common Trade

This paper presents Differential Evolution algorithm for solving high-dimensional optimization problems over continuous space. The proposed algorithm, namely, ANDE, introduces a new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better, and the worst individuals among the three randomly selected vectors. The mutation rule is combined with the basic mutation strategy DE/rand/1/bin, where the new triangular mutation rule is applied with the probability of 2/3 since it has both exploration ability and exploitation tendency. Furthermore, we propose a novel self-adaptive scheme for gradual change of the values of the crossover rate that can excellently benefit from the past experience of the individuals in the search space during evolution process which in turn can considerably balance the common trade-off between the population diversity and convergence speed. The proposed algorithm has been evaluated on the 20 standard high-dimensional benchmark numerical optimization problems for the IEEE CEC-2010 Special Session and Competition on Large Scale Global Optimization. The comparison results between ANDE and its versions and the other seven state-of-the-art evolutionary algorithms that were all tested on this test suite indicate that the proposed algorithm and its two versions are highly competitive algorithms for solving large scale global optimization problems.

scholarly journals A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Lijin Wang ◽  
Yiwen Zhong ◽  
Yilong Yin ◽  
Wenting Zhao ◽  
Binqing Wang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Optimization Algorithm ◽  
Iteration Process ◽  
Global Optimum ◽  
Backtracking Search ◽  
De Algorithm ◽  
Search Optimization ◽  
Backtracking Search Optimization Algorithm ◽  
Mutation Strategies ◽  
Multimodal Problems

The backtracking search optimization algorithm (BSA) is a new nature-inspired method which possesses a memory to take advantage of experiences gained from previous generation to guide the population to the global optimum. BSA is capable of solving multimodal problems, but it slowly converges and poorly exploits solution. The differential evolution (DE) algorithm is a robust evolutionary algorithm and has a fast convergence speed in the case of exploitive mutation strategies that utilize the information of the best solution found so far. In this paper, we propose a hybrid backtracking search optimization algorithm with differential evolution, called HBD. In HBD, DE with exploitive strategy is used to accelerate the convergence by optimizing one worse individual according to its probability at each iteration process. A suit of 28 benchmark functions are employed to verify the performance of HBD, and the results show the improvement in effectiveness and efficiency of hybridization of BSA and DE.

scholarly journals Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yuehe Zhu ◽  
Hua Wang ◽  
Jin Zhang
Keyword(s):  
Differential Evolution ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Optimal Solution ◽  
Global Optimum ◽  
Local Optimum ◽  
Local Optima ◽  
Trial Vector ◽  
Mutation Strategies

Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

Hybrid and Adaptive Metamodel Based Global Optimization

2009 ◽  
Author(s):  
J. Gu ◽  
G. Y. Li ◽  
Z. Dong
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Global Optimum ◽  
Superior Performance ◽  
Automatic Identification ◽  
Design Problems ◽  
Sample Data ◽  
Data Points

Metamodeling techniques are increasingly used in solving computation intensive design optimization problems today. In this work, the issue of automatic identification of appropriate metamodeling techniques in global optimization is addressed. A generic, new hybrid metamodel based global optimization method, particularly suitable for design problems involving computation intensive, black-box analyses and simulations, is introduced. The method employs three representative metamodels concurrently in the search process and selects sample data points adaptively according to the values calculated using the three metamodels to improve the accuracy of modeling. The global optimum is identified when the metamodels become reasonably accurate. The new method is tested using various benchmark global optimization problems and applied to a real industrial design optimization problem involving vehicle crash simulation, to demonstrate the superior performance of the new algorithm over existing search methods. Present limitations of the proposed method are also discussed.

An evolutionary based framework for many-objective optimization problems

2018 ◽  
Vol 35 (4) ◽  
pp. 1805-1828 ◽  
Author(s):  
Kimia Bazargan Lari ◽  
Ali Hamzeh
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Fitness Function ◽  
Population Diversity ◽  
Numerical Results ◽  
Superior Performance ◽  
High Dimensional ◽  
Test Problems ◽  
Content Type ◽  
Objective Space

Purpose Recently, many-objective optimization evolutionary algorithms have been the main issue for researchers in the multi-objective optimization community. To deal with many-objective problems (typically for four or more objectives) some modern frameworks are proposed which have the potential of achieving the finest non-dominated solutions in many-objective spaces. The effectiveness of these algorithms deteriorates greatly as the problem’s dimension increases. Diversity reduction in the objective space is the main reason of this phenomenon. Design/methodology/approach To properly deal with this undesirable situation, this work introduces an indicator-based evolutionary framework that can preserve the population diversity by producing a set of discriminated solutions in high-dimensional objective space. This work attempts to diversify the objective space by proposing a fitness function capable of discriminating the chromosomes in high-dimensional space. The numerical results prove the potential of the proposed method, which had superior performance in most of test problems in comparison with state-of-the-art algorithms. Findings The achieved numerical results empirically prove the superiority of the proposed method to state-of-the-art counterparts in the most test problems of a known artificial benchmark. Originality/value This paper provides a new interpretation and important insights into the many-objective optimization realm by emphasizing on preserving the population diversity.

A Three Particles Algorithm for Solving Some Very High Dimensional Benchmark Unconstrained Optimization Problems Using a Fuzzy Fitness Criterium

2018 ◽  
Vol 26 (Suppl. 1) ◽  
pp. 93-119
Author(s):  
Sergio G. De-Los-Cobos-Silva ◽  
Roman A. Mora-Gutiérrez ◽  
Eric A. Rincón-García ◽  
Pedro Lara-Velázquez ◽  
Miguel A. Gutiérrez-Andrade ◽  
...  
Keyword(s):  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Global Optimum ◽  
Numerical Results ◽  
High Dimensional ◽  
Benchmark Problems ◽  
Benchmark Problem ◽  
Original Algorithm ◽  
Unconstrained Optimization Problems ◽  
Very High

This work focuses predominantly on unconstrained optimization problems and presents an original algorithm (the code can be downloaded from Ref. 1), which is used for solving a variety of benchmark problems whose dimensions range from 2 to 2.5 millions, using only 3 particles. The algorithm was tested in 36 benchmark continuous unconstrained optimization problems, on a total of 312 instances. The results are presented comparing two fitness criteria: crisp and a fuzzy. The numerical results show that the proposed algorithm is able to reach the global optimum in every benchmark problem.

Heterogeneous Differential Evolution with Memory Enhanced Brownian and Quantum Individuals for Dynamic Optimization Problems

2017 ◽  
Vol 32 (02) ◽  
pp. 1859003 ◽  
Author(s):  
Weizu Wu ◽  
Dongqing Xie ◽  
Liqun Liu
Keyword(s):  
Differential Evolution ◽  
Dynamic Optimization ◽  
Environmental Changes ◽  
Optimization Problems ◽  
Continuous Process ◽  
Evolutionary Information ◽  
Optimization Framework ◽  
Optimum Solution ◽  
Different Characteristics ◽  
With Memory

In order to solve the dynamic optimization problem (DOP), this paper proposes to use a heterogeneous differential evolution (HDE) algorithm framework with memory enhanced Brownian and quantum (MEBQ) individual scheme. The proposed HDE/MEBQ algorithm has the following two advantages when solving DOP. First and foremost, the HDE optimization framework can satisfy the problem requirement of different characteristics. DOP is actually a continuous process to solve different kinds of optimization problems to meet new requirements when the search environmental change occurs. Therefore, HDE/MEBQ is able to fastly respond to the environmental changes of DOP as the HDE framework uses multiple populations with heterogeneous parameters and operators to meet different search requirements in various search environments. Secondly, according to the phenomenon that most of the environmental changes may not be too drastic in real-world applications, historical information in the past may be useful for finding the optimum solution in the new environment. Thus, the MEBQ scheme used in HDE/MEBQ provides helpful historical evolutionary information from the elite ancestors for guiding individuals to evolve in a new environment strongly and to obtain faster convergence and a more precise solution. We evaluated HDE/MEBQ on several DOPs from CEC 2009 and compared with several state-of-the-art dynamic evolutionary algorithms. The results show that HDE/MEBQ performs superior in statistics and gets very competitive results in most of the test conditions, especially in complex DOPs.

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