Multiobjective Differential Evolution Based on Fuzzy Performance Feedback

2014 ◽  
Vol 5 (4) ◽  
pp. 45-64 ◽  
Author(s):  
Chatkaew Jariyatantiwait ◽  
Gary G. Yen
Keyword(s):  
Evolutionary Algorithms ◽  
Differential Evolution ◽  
Performance Feedback ◽  
Performance Metrics ◽  
Fuzzy Inference ◽  
Optimization Problems ◽  
Evolution Process ◽  
Exploration And Exploitation ◽  
Multiobjective Optimization Problems ◽  
Mutation Strategy

Differential evolution is often regarded as one of the most efficient evolutionary algorithms to tackle multiobjective optimization problems. The key to success of any multiobjective evolutionary algorithms (MOEAs) is maintaining a delicate balance between exploration and exploitation throughout the evolution process. In this paper, the authors propose a Fuzzy-based Multiobjective Differential Evolution (FMDE) that uses performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. The authors apply the fuzzy inference rules to these metrics in order to dynamically adjust the associated control parameters of a chosen mutation strategy used in this algorithm. One parameter controls the degree of greedy or exploitation, while another regulates the degree of diversity or exploration of the reproduction phase. Therefore, the authors can appropriately adjust the degree of exploration and exploitation through performance feedback. The performance of FMDE is evaluated on well-known ZDT and DTLZ test suites. The results validate that the proposed algorithm is competitive with respect to chosen state-of-the-art MOEAs.

5 by 5 Microstrip Antenna Array Design by Multiobjective Differential Evolution based on Fuzzy Performance Feedback

2016 ◽  
Vol 7 (4) ◽  
pp. 1-22 ◽  
Author(s):  
Chatkaew Jariyatantiwait ◽  
Gary G. Yen
Keyword(s):  
Evolutionary Algorithms ◽  
Differential Evolution ◽  
Antenna Array ◽  
Performance Feedback ◽  
Microstrip Antenna ◽  
Side Lobe Level ◽  
Pareto Optimal ◽  
Exploration And Exploitation ◽  
Array Design ◽  
Microstrip Antenna Array

Differential evolution is often regarded as one of the most efficient evolutionary algorithms to tackle multiobjective optimization problems. The key to success of any multiobjective evolutionary algorithms (MOEAs) is maintaining a delicate balance between exploration and exploitation throughout the evolution process. In this paper, the authors develop an Improved version of the Fuzzy-based Multiobjective Differential Evolution (IFMDE) that exploits performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution progress. They apply the fuzzy inference rules, derived from domain knowledge, to these metrics in order to dynamically adjust the associated control parameters of a chosen mutation and crossover strategy used in this algorithm. One mutation parameter controls the degree of greedy or exploitation, while another regulates the degree of diversity or exploration of the reproduction phase. On the other hand, crossover rate controls the fraction of trial vector elements inherited from the mutant vectors. In doing so collectively, the authors can appropriately adjust the degree of exploration and exploitation through performance feedback. A 5 by 5 microstrip antenna array design problem is formulated as a three-objective optimization problem. The proposed IFMDE is applied to tackle this problem under real-world complications. Since the objective evaluations of a 5 by 5 microstrip antenna array are computationally very expensive, a radial basis function neural network is trained as a surrogate model for the fitness function approximations. The experimental results demonstrate the ability of IFMDE that it can find not only one, but a set of Pareto optimal solutions, specifically in terms of side lobe level and reflection coefficient. These multiple Pareto-optimal configurations can then be chosen from by a decision maker given dynamic operating environments, constraints and uncertainties.

scholarly journals A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2163
Author(s):  
Xingping Sun ◽  
Da Wang ◽  
Hongwei Kang ◽  
Yong Shen ◽  
Qingyi Chen
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Solution Space ◽  
Population Diversity ◽  
Exploration And Exploitation ◽  
Two Stage ◽  
Mutation Strategy ◽  
Strategy Combination ◽  
Evolution Algorithm

For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, DE/current/1, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including DE/current/1 and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal 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 Multiscale Cooperative Differential Evolution Algorithm

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Yongzhao Du ◽  
Yuling Fan ◽  
Xiaofang Liu ◽  
Yanmin Luo ◽  
Jianeng Tang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Early Stage ◽  
Differential Evolution Algorithm ◽  
Search Range ◽  
Adaptive Parameter ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Evolution Algorithms ◽  
The Individual

A multiscale cooperative differential evolution algorithm is proposed to solve the problems of narrow search range at the early stage and slow convergence at the later stage in the performance of the traditional differential evolution algorithms. Firstly, the population structure of multipopulation mechanism is adopted so that each subpopulation is combined with a corresponding mutation strategy to ensure the individual diversity during evolution. Then, the covariance learning among populations is developed to establish a suitable rotating coordinate system for cross operation. Meanwhile, an adaptive parameter adjustment strategy is introduced to balance the population survey and convergence. Finally, the proposed algorithm is tested on the CEC 2005 benchmark function and compared with other state-of-the-art evolutionary algorithms. The experiment results showed that the proposed algorithm has better performance in solving global optimization problems than other compared algorithms.

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