scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

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 Cooperative Coevolution with Two-Stage Decomposition for Large-Scale Global Optimization Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
H. D. Yue ◽  
Y. Sun
Keyword(s):  
Global Optimization ◽  
Decomposition Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Decomposition Methods ◽  
Unit Vector ◽  
Cooperative Coevolution ◽  
Two Stage ◽  
Computational Resources ◽  
Dynamic Decomposition

Cooperative coevolution (CC) is an effective framework for solving large-scale global optimization (LSGO) problems. However, CC with static decomposition method is ineffective for fully nonseparable problems, and CC with dynamic decomposition method to decompose problems is computationally costly. Therefore, a two-stage decomposition (TSD) method is proposed in this paper to decompose LSGO problems using as few computational resources as possible. In the first stage, to decompose problems using low computational resources, a hybrid-pool differential grouping (HPDG) method is proposed, which contains a hybrid-pool-based detection structure (HPDS) and a unit vector-based perturbation (UVP) strategy. In the second stage, to decompose the fully nonseparable problems, a known information-based dynamic decomposition (KIDD) method is proposed. Analytical methods are used to demonstrate that HPDG has lower decomposition complexity compared to state-of-the-art static decomposition methods. Experiments show that CC with TSD is a competitive algorithm for solving LSGO problems.

scholarly journals A Modified Bat Algorithm for Solving Large-Scale Bound Constrained Global Optimization Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Wali Khan Mashwani ◽  
Ihsan Mehmood ◽  
Maharani Abu Bakar ◽  
Ismail Koçcak
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Large Scale ◽  
Impact Analysis ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Stochastic Algorithm ◽  
Optimum Solution ◽  
The Impact ◽  
Modified Bat Algorithm

In the last two decades, the field of global optimization has become very active, and, in this regard, many deterministic and stochastic algorithms were developed for solving various optimization problems. Among them, swarm intelligence (SI) is a stochastic algorithm that is more flexible and robust and has had the ability to find an optimum solution for high-dimensional optimization and search problems. SI-based algorithms are mainly inspired by the social behavior of fish schooling or bird flocking. Among the SI-based algorithms, Bat algorithm (BA) is one of the recently developed evolutionary algorithms. It employs an echolocation behavior of microbats by varying pulse rates of emission and loudness to perform their search process. In this paper, a modified Bat algorithm (MBA) is developed. The main focus of the MBA is to further enhance the exploration and exploitation search abilities of the original Bat algorithm. The performance of the modified Bat algorithm (MBA) is examined over the benchmark functions designed for evolutionary algorithms competition in the special session of 2005 IEEE Congress on Evolutionary Computation. The used benchmark functions include the unimodal, multimodal, and hybrid benchmark functions with high dimensionality. Furthermore, the impact analysis with respect to different values of temperatures is conducted by executing the proposed algorithm twenty-five times independently by using each benchmark function with different random seeds.

scholarly journals Enhancing Cooperative Coevolution with Selective Multiple Populations for Large-Scale Global Optimization

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xingguang Peng ◽  
Yapei Wu
Keyword(s):  
Global Optimization ◽  
Large Scale ◽  
State Of The Art ◽  
Divide And Conquer ◽  
Cooperative Coevolution ◽  
Local Optima ◽  
Comparison Results ◽  
Dynamic Landscape ◽  
Problem Solving Process ◽  
Significant Superiority

The cooperative coevolution (CC) algorithm features a “divide-and-conquer” problem-solving process. This feature has great potential for large-scale global optimization (LSGO) while inducing some inherent problems of CC if a problem is improperly decomposed. In this work, a novel CC named selective multiple population- (SMP-) based CC (CC-SMP) is proposed to enhance the cooperation of subproblems by addressing two challenges: finding informative collaborators whose fitness and diversity are qualified and adapting to the dynamic landscape. In particular, a CMA-ES-based multipopulation procedure is employed to identify local optima which are then shared as potential informative collaborators. A restart-after-stagnation procedure is incorporated to help the child populations adapt to the dynamic landscape. A biobjective selection is also incorporated to select qualified child populations according to the criteria of informative individuals (fitness and diversity). Only selected child populations are active in the next evolutionary cycle while the others are frozen to save computing resource. In the experimental study, the proposed CC-SMP is compared to 7 state-of-the-art CC algorithms on 20 benchmark functions with 1000 dimensionality. Statistical comparison results figure out significant superiority of the CC-SMP. In addition, behavior of the SMP scheme and sensitivity to the cooperation frequency are also analyzed.

scholarly journals Improving Scalable K-Means++

Algorithms ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 6
Author(s):  
Joonas Hämäläinen ◽  
Tommi Kärkkäinen ◽  
Tuomo Rossi
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Random Projection ◽  
Divide And Conquer ◽  
High Dimensional ◽  
Data Generation ◽  
Large Scale Problems ◽  
Clustering Data ◽  
Very High ◽  
High Dimensional Clustering

Two new initialization methods for K-means clustering are proposed. Both proposals are based on applying a divide-and-conquer approach for the K-means‖ type of an initialization strategy. The second proposal also uses multiple lower-dimensional subspaces produced by the random projection method for the initialization. The proposed methods are scalable and can be run in parallel, which make them suitable for initializing large-scale problems. In the experiments, comparison of the proposed methods to the K-means++ and K-means‖ methods is conducted using an extensive set of reference and synthetic large-scale datasets. Concerning the latter, a novel high-dimensional clustering data generation algorithm is given. The experiments show that the proposed methods compare favorably to the state-of-the-art by improving clustering accuracy and the speed of convergence. We also observe that the currently most popular K-means++ initialization behaves like the random one in the very high-dimensional cases.

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