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 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 Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

scholarly journals Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit

2020 ◽  
Vol 28 (3) ◽  
pp. 339-378 ◽  
Author(s):  
Zhun Fan ◽  
Wenji Li ◽  
Xinye Cai ◽  
Hui Li ◽  
Caimin Wei ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Real World ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Dominance Principle ◽  
Constrained Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multiobjective optimization problems. In fact, many real-world multiobjective problems contain a number of constraints. To promote research on constrained multiobjective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multiobjective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness, and diversity-hardness. We then develop a general toolkit to construct difficulty adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. In fact, the combination of the three primary constraint functions with different parameters allows the construction of a large variety of CMOPs, with difficulty that can be defined by a triplet, with each of its parameters specifying the level of one of the types of primary difficulty. Furthermore, the number of objectives in this toolkit can be scaled beyond three. Based on this toolkit, we suggest nine difficulty adjustable and scalable CMOPs and nine CMaOPs, to be called DAS-CMOP1-9 and DAS-CMaOP1-9, respectively. To evaluate the proposed test problems, two popular CMOEAs—MOEA/D-CDP (MOEA/D with constraint dominance principle) and NSGA-II-CDP (NSGA-II with constraint dominance principle) and two popular constrained many-objective evolutionary algorithms (CMaOEAs)—C-MOEA/DD and C-NSGA-III—are used to compare performance on DAS-CMOP1-9 and DAS-CMaOP1-9 with a variety of difficulty triplets, respectively. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility-, and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

scholarly journals Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

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.

Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection

2008 ◽  
Vol 16 (2) ◽  
pp. 225-255 ◽  
Author(s):  
Maoguo Gong ◽  
Licheng Jiao ◽  
Haifeng Du ◽  
Liefeng Bo
Keyword(s):  
Multiobjective Optimization ◽  
Heuristic Search ◽  
Performance Metrics ◽  
Optimization Problems ◽  
Selection Method ◽  
Immune Algorithm ◽  
Nsga Ii ◽  
Selection Technique ◽  
Multiobjective Optimization Problems ◽  
Low Dimensional

Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. We compare NNIA with NSGA-II, SPEA2, PESA-II, and MISA in solving five DTLZ problems, five ZDT problems, and three low-dimensional problems. The statistical analysis based on three performance metrics including the coverage of two sets, the convergence metric, and the spacing, show that the unique selection method is effective, and NNIA is an effective algorithm for solving multiobjective optimization problems. The empirical study on NNIA's scalability with respect to the number of objectives shows that the new algorithm scales well along the number of objectives.

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 Dynamic Multiobjective Optimization Algorithm Based on Average Distance Linear Prediction Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhiyong Li ◽  
Hengyong Chen ◽  
Zhaoxin Xie ◽  
Chao Chen ◽  
Ahmed Sallam
Keyword(s):  
Multiobjective Optimization ◽  
Prediction Model ◽  
Linear Prediction ◽  
Prediction Models ◽  
Optimization Problems ◽  
Average Distance ◽  
Test Problems ◽  
Multiobjective Optimization Problems ◽  
Dynamic Multiobjective Optimization ◽  
Linear Prediction Model

Many real-world optimization problems involve objectives, constraints, and parameters which constantly change with time. Optimization in a changing environment is a challenging task, especially when multiple objectives are required to be optimized simultaneously. Nowadays the common way to solve dynamic multiobjective optimization problems (DMOPs) is to utilize history information to guide future search, but there is no common successful method to solve different DMOPs. In this paper, we define a kind of dynamic multiobjectives problem with translational Paretooptimal set (DMOP-TPS) and propose a new prediction model named ADLM for solving DMOP-TPS. We have tested and compared the proposed prediction model (ADLM) with three traditional prediction models on several classic DMOP-TPS test problems. The simulation results show that our proposed prediction model outperforms other prediction models for DMOP-TPS.

Sign in / Sign up

Export Citation Format

Share Document