scholarly journals A Comparative Study of EAG and PBIL on Large-Scale Global Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Imtiaz Hussain Khan
Keyword(s):  
Global Optimization ◽  
Comparative Study ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Cost ◽  
Population Based ◽  
Statistical Information ◽  
Location Information ◽  
Solution Quality ◽  
Estimation Of Distribution

Estimation of Distribution Algorithms (EDAs) use global statistical information effectively to sample offspring disregarding the location information of the locally optimal solutions found so far. Evolutionary Algorithm with Guided Mutation (EAG) combines global statistical information and location information to sample offspring, aiming that this hybridization improves the search and optimization process. This paper discusses a comparative study of Population-Based Incremental Learning (PBIL), a representative of EDAs, and EAG on large-scale global optimization problems. We implemented PBIL and EAG to build an experimental setup upon which simulations were run. The performance of these algorithms was analyzed in terms of solution quality and computational cost. We found that EAG performed better than PBIL in attaining a good quality solution, but the latter performed better in terms of computational cost. We also compared the performance of EAG and PBIL with MA-SW-Chains, the winner of CEC’2010, and found that the overall performance of EAG is comparable to MA-SW-Chains.

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: 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.

Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization

2018 ◽  
Vol 26 (4) ◽  
pp. 569-596 ◽  
Author(s):  
Yuping Wang ◽  
Haiyan Liu ◽  
Fei Wei ◽  
Tingting Zong ◽  
Xiaodong Li
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Real World ◽  
Large Scale ◽  
Divide And Conquer ◽  
Group Method ◽  
Objective Functions ◽  
Elementary Functions ◽  
Cooperative Coevolution ◽  
Solution Quality

For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]”, “[Formula: see text]” and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.

scholarly journals Restricted Boltzmann Machine-Assisted Estimation of Distribution Algorithm for Complex Problems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Lin Bao ◽  
Xiaoyan Sun ◽  
Yang Chen ◽  
Guangyi Man ◽  
Hui Shao
Keyword(s):  
Optimization Problems ◽  
Probability Model ◽  
Computational Cost ◽  
Evolutionary Process ◽  
Estimation Of Distribution Algorithm ◽  
Restricted Boltzmann Machine ◽  
Model Management ◽  
Boltzmann Machine ◽  
Complex Problems ◽  
Estimation Of Distribution

A novel algorithm, called restricted Boltzmann machine-assisted estimation of distribution algorithm, is proposed for solving computationally expensive optimization problems with discrete variables. First, the individuals are evaluated using expensive fitness functions of the complex problems, and some dominant solutions are selected to construct the surrogate model. The restricted Boltzmann machine (RBM) is built and trained with the dominant solutions to implicitly extract the distributed representative information of the decision variables in the promising subset. The visible layer’s probability of the RBM is designed as the sampling probability model of the estimation of distribution algorithm (EDA) and is updated dynamically along with the update of the dominant subsets. Second, according to the energy function of the RBM, a fitness surrogate is developed to approximate the expensive individual fitness evaluations and participates in the evolutionary process to reduce the computational cost. Finally, model management is developed to train and update the RBM model with newly dominant solutions. A comparison of the proposed algorithm with several state-of-the-art surrogate-assisted evolutionary algorithms demonstrates that the proposed algorithm effectively and efficiently solves complex optimization problems with smaller computational cost.

scholarly journals A GPU-Enabled Compact Genetic Algorithm for Very Large-Scale Optimization Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 758
Author(s):  
Andrea Ferigo ◽  
Giovanni Iacca
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Search Space ◽  
Large Scale Problems ◽  
Processing Power ◽  
Compact Genetic Algorithm ◽  
Estimation Of Distribution ◽  
Feasible Solutions ◽  
Compact Optimization

The ever-increasing complexity of industrial and engineering problems poses nowadays a number of optimization problems characterized by thousands, if not millions, of variables. For instance, very large-scale problems can be found in chemical and material engineering, networked systems, logistics and scheduling. Recently, Deb and Myburgh proposed an evolutionary algorithm capable of handling a scheduling optimization problem with a staggering number of variables: one billion. However, one important limitation of this algorithm is its memory consumption, which is in the order of 120 GB. Here, we follow up on this research by applying to the same problem a GPU-enabled “compact” Genetic Algorithm, i.e., an Estimation of Distribution Algorithm that instead of using an actual population of candidate solutions only requires and adapts a probabilistic model of their distribution in the search space. We also introduce a smart initialization technique and custom operators to guide the search towards feasible solutions. Leveraging the compact optimization concept, we show how such an algorithm can optimize efficiently very large-scale problems with millions of variables, with limited memory and processing power. To complete our analysis, we report the results of the algorithm on very large-scale instances of the OneMax problem.

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.

Hybrid Harmony Search Algorithm for Global Optimization Problems

2014 ◽  
Vol 1065-1069 ◽  
pp. 3438-3441
Author(s):  
Guo Jun Li
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Population Based ◽  
Harmony Search Algorithm ◽  
Search Method ◽  
Local Optima ◽  
Population Based Algorithm ◽  
Better Than

Harmony search (HS) algorithm is a new population based algorithm, which imitates the phenomenon of musical improvisation process. Its own potential and shortage, one shortage is that it easily trapped into local optima. In this paper, a hybrid harmony search algorithm (HHS) is proposed based on the conception of swarm intelligence. HHS employed a local search method to replace the pitch adjusting operation, and designed an elitist preservation strategy to modify the selection operation. Experiment results demonstrated that the proposed method performs much better than the HS and its improved algorithms (IHS, GHS and NGHS).

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