MOEA/HD: A Multiobjective Evolutionary Algorithm Based on Hierarchical Decomposition

Xu, Hang; Zeng, Wenhua; Zhang, Defu; Zeng, Xiangxiang

doi:10.1109/tcyb.2017.2779450

Cited by 120 publications

(51 citation statements)

References 62 publications

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“…To further confirm the value of our approach, we also used the mean percentile ranking (MPR), an evaluation index based on recall, to evaluate the performance of the algorithm. This evaluation index has been applied in recommendation algorithm and analyses of the performance for predicting drug-targets (Hu et al, 2008;Johnson, 2014;Li et al, 2015;Ding et al, 2017;Hao et al, 2019;Liu et al, 2019b;Liu et al, 2019c; and disease biomarkers (Chen et al, 2016;Zeng et al, 2016;Hong et al, 2019;Xu et al, 2019). For each disease, the genes were ranked in descending order according to the calculated gene-disease predictive value.…”

Section: Evaluation Indexes and Methodsmentioning

confidence: 99%

Pathogenic Gene Prediction Algorithm Based on Heterogeneous Information Fusion

et al. 2020

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Complex diseases seriously affect people's physical and mental health. The discovery of disease-causing genes has become a target of research. With the emergence of bioinformatics and the rapid development of biotechnology, to overcome the inherent difficulties of the long experimental period and high cost of traditional biomedical methods, researchers have proposed many gene prioritization algorithms that use a large amount of biological data to mine pathogenic genes. However, because the currently known genedisease association matrix is still very sparse and lacks evidence that genes and diseases are unrelated, there are limits to the predictive performance of gene prioritization algorithms. Based on the hypothesis that functionally related gene mutations may lead to similar disease phenotypes, this paper proposes a PU induction matrix completion algorithm based on heterogeneous information fusion (PUIMCHIF) to predict candidate genes involved in the pathogenicity of human diseases. On the one hand, PUIMCHIF uses different compact feature learning methods to extract features of genes and diseases from multiple data sources, making up for the lack of sparse data. On the other hand, based on the prior knowledge that most of the unknown gene-disease associations are unrelated, we use the PU-Learning strategy to treat the unknown unlabeled data as negative examples for biased learning. The experimental results of the PUIMCHIF algorithm regarding the three indexes of precision, recall, and mean percentile ranking (MPR) were significantly better than those of other algorithms. In the top 100 global prediction analysis of multiple genes and multiple diseases, the probability of recovering true gene associations using PUIMCHIF reached 50% and the MPR value was 10.94%. The PUIMCHIF algorithm has higher priority than those from other methods, such as IMC and CATAPULT.

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Section: Evaluation Indexes and Methodsmentioning

confidence: 99%

Pathogenic Gene Prediction Algorithm Based on Heterogeneous Information Fusion

et al. 2020

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“…Note that is set to be a very small number, say 10 −6 , in case = 0. Actually, in most existing MOEA/Ds [19][20][21][22][23][24][25], the ideal reference point is usually used as the initial point of all weight vectors, which is estimated by using the best value of each objective found so far during evolution. Note that all the solutions should be dominated by the ideal reference point in the objective space.…”

Section: Preliminariesmentioning

confidence: 99%

“…In IMOEA/DU [22], a crossover operator based on uniform design and selection strategy based on decomposition are used to help MOEAs to improve the search efficiency. Recently, in MOEA/HD [23], subproblems are layered into different hierarchies, aiming to better balance convergence and diversity during evolution. In MOEA/D-CPDE [24], the best individual in each generation will be regarded as a seed, which will evolve two individuals by cloud generator.…”

Section: Introductionmentioning

confidence: 99%

“…The use of the ideal reference point can speed up convergence, but it will also cause the loss of diversity. The representative MOEA/Ds, such as MOEA/D [17] and its variants MOEA/D-DE [19], MOEA/D-STM [20], MOEA/D-ATO [21], IMOEA/DU [22], MOEA/HD [23], MOEA/D-CPDE [24], and DAA [25], all adopt the ideal point as the reference point for all the search directions. However, it can be observed from Figure 2(b) that the current population is pushed away from the nadir reference point as far as possible.…”

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confidence: 99%

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Evolutionary Search with Multiple Utopian Reference Points in Decomposition‐Based Multiobjective Optimization

Lin

Zhu

et al. 2019

Complexity

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Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted.

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“…The second idea for solving LMOPs is problem transformation, which aims to convert the original LMOP into a small-scale problem, so that it can be handled by general optimizers. Different from traditional decomposition based MOEAs (e.g., those based on hierarchical decomposition [9] or Minkowski distance [10]) using a set of weights to transfer multi-objective optimization into single-objective optimization, WOF [11] uses a set 0000-0000/00$00.00 c ⃝ 0000 IEEE of weights to alter the decision variables, where each weight is related to multiple decision variables and the number of weights is much smaller than the number of decision variables. As a result, a small-scale problem can be established by considering the weights as variables to be optimized.…”

Section: Introductionmentioning

confidence: 99%

Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks

Tian

Lü

Zhang

et al. 2021

IEEE Trans. Cybern.

188

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Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this paper proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10,000 decision variables by only 100,000 evaluations.

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MOEA/HD: A Multiobjective Evolutionary Algorithm Based on Hierarchical Decomposition

Cited by 120 publications

References 62 publications

Pathogenic Gene Prediction Algorithm Based on Heterogeneous Information Fusion

Pathogenic Gene Prediction Algorithm Based on Heterogeneous Information Fusion

Evolutionary Search with Multiple Utopian Reference Points in Decomposition‐Based Multiobjective Optimization

Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks

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