Self-Organizing Map-Based Weight Design for Decomposition-Based Many-Objective Evolutionary Algorithm

Gu, Fangqing; Cheung, Yiu-ming

doi:10.1109/tevc.2017.2695579

Cited by 122 publications

(31 citation statements)

References 51 publications

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“…Gu et al [37] used the equidistant interpolation to periodically update the weight vectors on the estimated Pareto front. Later, they proposed a weight adaptation method by training an self-organising map according to the current solutions [38]. Jain and Deb [39] introduced an adaptive version of NSGA-III [25] (A-NSGA-III) for irregular Pareto fronts.…”

Section: Related Workmentioning

confidence: 99%

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

Yao

2020

Evolutionary Computation

125

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The quality of solution sets generated by decomposition-based evolutionary multiobjective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often lead to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this paper, we propose an approach to adapt the weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating five parts in the weight adaptation -weight generation, weight addition, weight deletion, archive maintenance, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerated, 6) the badly-scaled, and 7) the high-dimensional.

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Section: Related Workmentioning

confidence: 99%

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

Yao

2020

Evolutionary Computation

125

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“…However, since the piecewise linear interpolation may fail to estimate highly nonlinear PFs and can easily cause overfitting, the estimation will be largely impaired by some outliers, which is not uncommon at the early stage of the optimization. Recently, Gu and Cheung [18] have developed a reference point generation method based on self-organizing map (SOM) [19]. It uses the objective vectors of recent solutions to train a SOM network periodically.…”

Section: Introductionmentioning

confidence: 99%

Learning to Decompose: A Paradigm for Decomposition-Based Multiobjective Optimization

Kwong

et al. 2019

IEEE Trans. Evol. Computat.

105

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Decomposition-based evolutionary multi-objective optimization algorithms decompose a multi-objective optimization problem into subproblems using a set of predefined reference points. The convergence is guaranteed by optimizing the single-objective or simplified multi-objective subproblems while the diversity is handled by the evenly distributed reference points. Nevertheless, studies have shown that the performance of decomposition-based algorithms is strongly dependent on the Pareto front shapes due to unadaptable reference points and subproblem formulation. In this paper, we investigate the causes from three aspects and propose a learning-to-decompose paradigm consisting of a learning module and an optimization module to address these issues. Specifically, given the current non-dominated solutions from the optimization module, which can be any decomposition-based multi-objective optimizer, the learning module learns an analytical model that characterizes the estimated PF. Thereafter, useful information are extracted from the learned model to guide the decomposition in the optimization module. In particular, we utilize the learned model to sample reference points compliant to the PF and formulate subproblems with appropriate contours and search directions according to the current status. We integrate the learning-todecompose paradigm with two most popular decompositionbased evolutionary optimizers, i.e., MOEA/D and NSGA-III, and compare them with several state-of-the-art adaptive methods. The comprehensive experiments validate the effectiveness and robustness of the proposed paradigm on 14 test problems with various Pareto front shapes.

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“…For example, MOEA/D-AWA [15] produces new weight vectors by non-dominated solutions found by now to adjust the weight vectors periodically for finding the appropriate convergence direction. Self-organizing map (SOM) is applied in MOEA/D-SOM [16] to adjusting the weight vectors for MOEA/D. The problem is that training a SOM network costs a lot of calculation and the performance of SOM depends on the distribution of initial random individuals which probably not reflecting the true distribution of the Pareto front.…”

Section: Introductionmentioning

confidence: 99%

Generating multiple reference vectors for a class of many-objective optimization problems with degenerate Pareto fronts

Hua

Jin

Hao

et al. 2020

Complex Intell. Syst.

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Many-objective optimization problems with degenerate Pareto fronts are hard to solve for most existing many-objective evolutionary algorithms. This is particularly true when the shape of the degenerate Pareto front is very narrow, and there are many dominated solutions near the Pareto front. To solve this particular class of many-objective optimization problems, a new evolutionary algorithm is proposed in this paper. In this algorithm, a set of reference vectors is generated to locate the potential Pareto front and then generate a set of location vectors. With the help of the location vectors, the solutions near the Pareto front are mapped to the hyperplane and clustered to generate more reference vectors pointing to Pareto front. This way, the location vectors are able to efficiently guide the population to converge towards the Pareto front. The effectiveness of the proposed algorithm is examined on two typical test problems with degenerate Pareto fronts, namely DTLZ5 and DTLZ6 with 5-40 objectives. Our experimental results show that the proposed algorithm has a clear advantage in dealing with this class of many-objective optimization problems. In addition, the proposed algorithm has also been successfully applied to optimization of process parameters of polyester fiber filament melt-transportation.

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Self-Organizing Map-Based Weight Design for Decomposition-Based Many-Objective Evolutionary Algorithm

Cited by 122 publications

References 51 publications

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

Learning to Decompose: A Paradigm for Decomposition-Based Multiobjective Optimization

Generating multiple reference vectors for a class of many-objective optimization problems with degenerate Pareto fronts

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