How to Read Many-Objective Solution Sets in Parallel Coordinates [Educational Forum]

Li, Miqing; Zhen, Liangli; Yao, Xin

doi:10.1109/mci.2017.2742869

Cited by 96 publications

(50 citation statements)

References 54 publications

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“…For the 10-objective DTLZ2 which has a simplex-like Pareto front, all the five algorithms appear to work well ( Figure 17) despite that there exists one solution of AdaW not converging into the Pareto front. We may not be able to conclude the distribution difference of the algorithms by the parallel coordinates plots [68], but all the algorithms seem to perform similarly according to the IGD results in Table 1.…”

Section: On Many-objective Problemsmentioning

confidence: 85%

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

Yao

2020

Evolutionary Computation

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111

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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: On Many-objective Problemsmentioning

confidence: 85%

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

Yao

2020

Evolutionary Computation

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111

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“…7 plots the parallel coordinates [54] of the non-dominated solution set with (15) 1.23e+0 the median IGD value among 30 runs obtained by the algorithms based on the nine dominance relations on 5-objective DTLZ7, where each polyline in the figure denotes one solution, and each vertex on the polyline denotes one objective value. DTLZ7 has a discontinuous Pareto front challenging the MOEAs in diversity preservation.…”

Section: B Comparing Sdr With Other Dominance Relationsmentioning

confidence: 99%

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

Tian

Cheng

Zhang

et al. 2019

IEEE Trans. Evol. Computat.

274

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Abstract-Both convergence and diversity are crucial to evolutionary many-objective optimization, whereas most existing dominance relations show poor performance in balancing them, thus easily leading to a set of solutions concentrating on a small region of the Pareto fronts. In this paper, a novel dominance relation is proposed to better balance convergence and diversity for evolutionary manyobjective optimization. In the proposed dominance relation, an adaptive niching technique is developed based on the angles between the candidate solutions, where only the best converged candidate solution is identified to be nondominated in each niche. Experimental results demonstrate that the proposed dominance relation outperforms existing dominance relations in balancing convergence and diversity. A modified NSGA-II is suggested based on the proposed dominance relation, which shows competitiveness against the state-of-the-art algorithms in solving many-objective optimization problems. The effectiveness of the proposed dominance relation is also verified on several other existing multi-and many-objective evolutionary algorithms.

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“…For a visual understanding of the solutions' distribution and also of what a higher HV means, in Figure 3 we use parallel coordinates [46] to plot the final population of one typical run on the random model Model100-1. Parallel coordinates map a set of solutions in a high-dimensional space onto a 2D graph.…”

Section: Research Question 2: Comparison With Representative Multi-obmentioning

confidence: 99%

Many-Objective Test Suite Generation for Software Product Lines

Hierons

Liu

et al. 2020

ACM Trans. Softw. Eng. Methodol.

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How to Read Many-Objective Solution Sets in Parallel Coordinates [Educational Forum]

Cited by 96 publications

References 54 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

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

Many-Objective Test Suite Generation for Software Product Lines

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