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 Fast Image Segmentation Using Two-Dimensional Otsu Based on Estimation of Distribution Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Wuli Wang ◽  
Liming Duan ◽  
Yong Wang
Keyword(s):  
Image Segmentation ◽  
Fitness Function ◽  
Probability Model ◽  
Computational Cost ◽  
Estimation Of Distribution Algorithm ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Guided Filtering ◽  
Estimation Of Distribution ◽  
Mean Filtering

Traditional two-dimensional Otsu algorithm has several drawbacks; that is, the sum of probabilities of target and background is approximate to 1 inaccurately, the details of neighborhood image are not obvious, and the computational cost is high. In order to address these problems, a method of fast image segmentation using two-dimensional Otsu based on estimation of distribution algorithm is proposed. Firstly, in order to enhance the performance of image segmentation, the guided filtering is employed to improve neighborhood image template instead of mean filtering. Additionally, the probabilities of target and background in two-dimensional histogram are exactly calculated to get more accurate threshold. Finally, the trace of the interclass dispersion matrix is taken as the fitness function of estimation of distributed algorithm, and the optimal threshold is obtained by constructing and sampling the probability model. Extensive experimental results demonstrate that our method can effectively preserve details of the target, improve the segmentation precision, and reduce the running time of algorithms.

Restricted Boltzmann Machine-Driven Matchmaking Algorithm With Interactive Estimation of Distribution for Websites

2021 ◽  
pp. 258-276
Author(s):  
Jayashree R. ◽  
Vaithyasubramanian S.
Keyword(s):  
Probability Model ◽  
Good Choice ◽  
User Preferences ◽  
Restricted Boltzmann Machine ◽  
User Preference ◽  
Evolutionary Strategies ◽  
Boltzmann Machine ◽  
Internet Site ◽  
Group Knowledge ◽  
Estimation Of Distribution

In this chapter, restricted Boltzmann machine-driven (RBM) algorithm is presented with an enhanced interactive estimation of distribution (IED) method for websites. Indian matrimonial websites are famous intermediates for finding marriage-partners. Matchmaking is one of the most pursued objectives in matrimonial websites. The complex evaluations and full of zip user preferences are the challenges. An interactive evolutionary algorithm with powerful evolutionary strategies is a good choice for matchmaking. Initially, an IED is generated as a probability model for the estimation of a user preference and then two RBM models, one for interested and the other for not-interested, is generated to endow with a set of appropriate matches simultaneously. In the proposed matchmaking method, the RBM model is combined with social group knowledge. Some benchmarks from the matrimonial internet site are pragmatic to empirically reveal the pre-eminence of the anticipated method.

scholarly journals A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qingyang Xu ◽  
Chengjin Zhang ◽  
Li Zhang
Keyword(s):  
Probability Model ◽  
Learning Rule ◽  
Estimation Of Distribution Algorithm ◽  
Model Learning ◽  
One Dimensional ◽  
Fast Learning ◽  
Higher Dimensional ◽  
Intelligent Optimization Algorithm ◽  
Estimation Of Distribution ◽  
Gaussian Estimation

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.

scholarly journals A Hybrid Metaheuristic of Integrating Estimation of Distribution Algorithm with Tabu Search for the Max-Mean Dispersion Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Dieudonné Nijimbere ◽  
Songzheng Zhao ◽  
Haichao Liu ◽  
Bo Peng ◽  
Aijun Zhang
Keyword(s):  
Tabu Search ◽  
Probability Model ◽  
Estimation Of Distribution Algorithm ◽  
Search Procedure ◽  
Hybrid Metaheuristic ◽  
Benchmark Instances ◽  
Conditional Preference ◽  
Estimation Of Distribution ◽  
Dispersion Problem ◽  
Move Operator

This paper presents a hybrid metaheuristic that combines estimation of distribution algorithm with tabu search (EDA-TS) for solving the max-mean dispersion problem. The proposed EDA-TS algorithm essentially alternates between an EDA procedure for search diversification and a tabu search procedure for search intensification. The designed EDA procedure maintains an elite set of high quality solutions, based on which a conditional preference probability model is built for generating new diversified solutions. The tabu search procedure uses a fast 1-flip move operator for solution improvement. Experimental results on benchmark instances with variables ranging from 500 to 5000 disclose that our EDA-TS algorithm competes favorably with state-of-the-art algorithms in the literature. Additional analysis on the parameter sensitivity and the merit of the EDA procedure as well as the search balance between intensification and diversification sheds light on the effectiveness of the algorithm.

scholarly journals An Adaptive Covariance Scaling Estimation of Distribution Algorithm

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3207
Author(s):  
Qiang Yang ◽  
Yong Li ◽  
Xu-Dong Gao ◽  
Yuan-Yuan Ma ◽  
Zhen-Yu Lu ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Optimization Methods ◽  
Estimation Of Distribution Algorithm ◽  
Distribution Model ◽  
Selection Strategy ◽  
Individual Selection ◽  
Estimation Of Distribution ◽  
The Mean ◽  
Mean Vector

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

scholarly journals Ising Model Optimization Problems on a FPGA Accelerated Restricted Boltzmann Machine

2020 ◽  
Author(s):  
Saavan Patel ◽  
Lili Chen ◽  
Philip Canoza ◽  
Sayeef Salahuddin
Keyword(s):  
Optimization Problems ◽  
Restricted Boltzmann Machine ◽  
Model Optimization ◽  
Boltzmann Machine ◽  
Stochastic Sampling ◽  
Combinatorial Optimization Problems ◽  
Field Programmable ◽  
Max Cut Problem ◽  
Asymptotic Scaling ◽  
Better Than

Abstract In this work we demonstrate usage of the Restricted Boltzmann Machine (RBM) as a stochastic neural network capable of solving NP-Hard Combinatorial Optimization problems efficiently. By mapping the RBM onto a reconfigurable Field Programmable Gate Array (FPGA), we can effectively hardware accelerate the RBM's stochastic sampling algorithm. We benchmark the RBM against the DWave 2000Q Quantum Adiabatic Computer and the Optical Coherent Ising Machine on two such optimization problems: the MAX-CUT problem and the Sherrington-Kirkpatrick (SK) spin glass. The hardware accelerated RBM shows asymptotic scaling either similar or better than these other accelerators. This leads to 107x and 105x time to solution improvement compared to the DWave 2000Q on the MAX-CUT and SK problems respectively, along with a 150x and 1000x improvement compared to the Coherent Ising Machine annealer on those problems. By utilizing commodity hardware running at room temperature, the RBM shows potential for immediate and scalable use.

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