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 Multiobjective Memetic Estimation of Distribution Algorithm Based on an Incremental Tournament Local Searcher

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Kaifeng Yang ◽  
Li Mu ◽  
Dongdong Yang ◽  
Feng Zou ◽  
Lei Wang ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Distribution Model ◽  
Test Problems ◽  
Multiobjective Problems ◽  
Estimation Of Distribution ◽  
Distributed Solutions ◽  
Accelerate Convergence ◽  
Low Dimensional

A novel hybrid multiobjective algorithm is presented in this paper, which combines a new multiobjective estimation of distribution algorithm, an efficient local searcher andε-dominance. Besides, two multiobjective problems with variable linkages strictly based on manifold distribution are proposed. The Pareto set to the continuous multiobjective optimization problems, in the decision space, is a piecewise low-dimensional continuous manifold. The regularity by the manifold features just build probability distribution model by globally statistical information from the population, yet, the efficiency of promising individuals is not well exploited, which is not beneficial to search and optimization process. Hereby, an incremental tournament local searcher is designed to exploit local information efficiently and accelerate convergence to the true Pareto-optimal front. Besides, sinceε-dominance is a strategy that can make multiobjective algorithm gain well distributed solutions and has low computational complexity,ε-dominance and the incremental tournament local searcher are combined here. The novel memetic multiobjective estimation of distribution algorithm, MMEDA, was proposed accordingly. The algorithm is validated by experiment on twenty-two test problems with and without variable linkages of diverse complexities. Compared with three state-of-the-art multiobjective optimization algorithms, our algorithm achieves comparable results in terms of convergence and diversity metrics.

scholarly journals Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

2020 ◽  
Vol 10 (6) ◽  
pp. 2075 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Inequality Constraints ◽  
Optimization Methods ◽  
Ordinal Optimization ◽  
Np Hard ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Hard Problems ◽  
Np Hard Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

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.

Engineering Design Optimization Using an Advanced Hybrid Algorithm

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Novel Mutation ◽  
Solution Space ◽  
Selection Strategy ◽  
Engineering Design Optimization ◽  
Global And Local ◽  
Search Capability

An advanced hybrid algorithm (haDEPSO) proposed in this paper for engineering design optimization problems. It integrated with suggested advanced differential evolution (aDE) and particle swarm optimization (aPSO). In aDE introduced a novel mutation, crossover and selection strategy, to avoiding premature convergence. And aPSO consists of novel gradually varying parameters, to escape stagnation. So, convergence characteristic of aDE and aPSO provides different approximation to the solution space. Thus, haDEPSO achieve better solutions due to integrating merits of aDE and aPSO. Also, in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. Proposed hybrid haDEPSO as well as its integrating component aDE and aPSO has been applied to five engineering design optimization problems. Numerical, statistical and graphical experiments (best, worst, mean and standard deviation plus convergence analysis) confirm the superiority of the proposed algorithms over many state-of-the-art algorithms.

Multi-Objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment

2013 ◽  
Vol 21 (1) ◽  
pp. 149-177 ◽  
Author(s):  
Vui Ann Shim ◽  
Kay Chen Tan ◽  
Jun Yong Chia ◽  
Abdullah Al Mamun
Keyword(s):  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Computational Time ◽  
Decision Variable ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Noisy Environment ◽  
Multi Objective ◽  
Noisy Information ◽  
Estimation Of Distribution

Many real-world optimization problems are subjected to uncertainties that may be characterized by the presence of noise in the objective functions. The estimation of distribution algorithm (EDA), which models the global distribution of the population for searching tasks, is one of the evolutionary computation techniques that deals with noisy information. This paper studies the potential of EDAs; particularly an EDA based on restricted Boltzmann machines that handles multi-objective optimization problems in a noisy environment. Noise is introduced to the objective functions in the form of a Gaussian distribution. In order to reduce the detrimental effect of noise, a likelihood correction feature is proposed to tune the marginal probability distribution of each decision variable. The EDA is subsequently hybridized with a particle swarm optimization algorithm in a discrete domain to improve its search ability. The effectiveness of the proposed algorithm is examined via eight benchmark instances with different characteristics and shapes of the Pareto optimal front. The scalability, hybridization, and computational time are rigorously studied. Comparative studies show that the proposed approach outperforms other state of the art algorithms.

scholarly journals An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Pooja Verma ◽  
Raghav Prasad Parouha
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Structural Engineering ◽  
Large Scale ◽  
Optimization Problems ◽  
Novel Mutation ◽  
Solution Space ◽  
Selection Strategy ◽  
Engineering Design Optimization ◽  
Global And Local

AbstractAn advanced hybrid algorithm (haDEPSO) is proposed in this paper for small- and large-scale engineering design optimization problems. Suggested advanced, differential evolution (aDE) and particle swarm optimization (aPSO) integrated with proposed haDEPSO. In aDE a novel, mutation, crossover and selection strategy is introduced, to avoid premature convergence. And aPSO consists of novel gradually varying parameters, to escape stagnation. So, convergence characteristic of aDE and aPSO provides different approximation to the solution space. Thus, haDEPSO achieve better solutions due to integrating merits of aDE and aPSO. Also in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. The performance of proposed haDEPSO and its component aDE and aPSO are validated on 23 unconstrained benchmark functions, then solved five small (structural engineering) and one large (economic load dispatch)-scale engineering design optimization problems. Outcome analyses confirm superiority of proposed algorithms over many state-of-the-art algorithms.

Engineering Design Optimization Using an Advanced Hybrid Algorithm

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Novel Mutation ◽  
Solution Space ◽  
Selection Strategy ◽  
Engineering Design Optimization ◽  
Global And Local ◽  
Search Capability

An advanced hybrid algorithm (haDEPSO) proposed in this paper for engineering design optimization problems. It integrated with suggested advanced differential evolution (aDE) and particle swarm optimization (aPSO). In aDE introduced a novel mutation, crossover and selection strategy, to avoiding premature convergence. And aPSO consists of novel gradually varying parameters, to escape stagnation. So, convergence characteristic of aDE and aPSO provides different approximation to the solution space. Thus, haDEPSO achieve better solutions due to integrating merits of aDE and aPSO. Also, in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. Proposed hybrid haDEPSO as well as its integrating component aDE and aPSO has been applied to five engineering design optimization problems. Numerical, statistical and graphical experiments (best, worst, mean and standard deviation plus convergence analysis) confirm the superiority of the proposed algorithms over many state-of-the-art algorithms.

Globally Multimodal Problem Optimization Via an Estimation of Distribution Algorithm Based on Unsupervised Learning of Bayesian Networks

2005 ◽  
Vol 13 (1) ◽  
pp. 43-66 ◽  
Author(s):  
J. M. Peña ◽  
J. A. Lozano ◽  
P. Larrañaga
Keyword(s):  
Bayesian Networks ◽  
Unsupervised Learning ◽  
Genetic Drift ◽  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Estimation Of Distribution Algorithms ◽  
Estimation Of Distribution ◽  
Global Optima ◽  
Effectiveness And Efficiency ◽  
Distribution Algorithms

Many optimization problems are what can be called globally multimodal, i.e., they present several global optima. Unfortunately, this is a major source of difficulties for most estimation of distribution algorithms, making their effectiveness and efficiency degrade, due to genetic drift. With the aim of overcoming these drawbacks for discrete globally multimodal problem optimization, this paper introduces and evaluates a new estimation of distribution algorithm based on unsupervised learning of Bayesian networks. We report the satisfactory results of our experiments with symmetrical binary optimization problems.

scholarly journals A Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem

2021 ◽  
Vol 26 (3) ◽  
pp. 64
Author(s):  
Ricardo Pérez-Rodríguez
Keyword(s):  
Solution Space ◽  
Estimation Of Distribution Algorithm ◽  
Space Distribution ◽  
Scheduling Problem ◽  
Probability Models ◽  
Quay Crane Scheduling ◽  
Crane Scheduling ◽  
Hybrid Estimation ◽  
Ranking Model ◽  
Estimation Of Distribution

The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed to tackle the drawbacks of the EDAs, i.e., the lack of diversity of solutions and poor ability of exploitation. The hybridization approach, used in this investigation, uses a distance based ranking model and the moth-flame algorithm. The distance based ranking model is in charge of modelling the solution space distribution, through an exponential function, by measuring the distance between solutions; meanwhile, the heuristic moth-flame determines who would be the offspring, with a spiral function that identifies the new locations for the new solutions. Based on the results, the proposed scheme, called QCEDA, works to enhance the performance of those other EDAs that use complex probability models. The dispersion results of the QCEDA scheme are less than the other algorithms used in the comparison section. This means that the solutions found by the QCEDA are more concentrated around the best value than other algorithms, i.e., the average of the solutions of the QCEDA converges better than other approaches to the best found value. Finally, as a conclusion, the hybrid EDAs have a better performance, or equal in effectiveness, than the so called pure EDAs.

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