A New Decomposition-Based NSGA-II for Many-Objective Optimization

Elarbi, Maha; Bechikh, Slim; Gupta, Abhishek; Saïd, Lamjed Ben; Ong, Yew-Soon

doi:10.1109/tsmc.2017.2654301

Cited by 221 publications

(87 citation statements)

References 49 publications

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“…As shown in Fig. 1, (1-k)-dominance and L-dominance hold the same dominance areas with Pareto dominance in biobjective space, whereas the difference between (1-k)-dominance and Pareto dominance only exists when the number of objectives M ≥ 4, and the difference between L-dominance and Pareto dominance only exists when M ≥ 3, Inspired by decomposition based MOEAs, the fourth category of dominance relations is defined by a set of weight vectors, e.g., the θ-dominance relation [12] and the RP-dominance relation [13]. In θ-dominance, each candidate solution is associated with its nearest weight vector, and a candidate solution x is said to θ-dominate another one y if and only if they are associated with the same weight vector λ, and…”

Section: A Existing Dominance Relationsmentioning

confidence: 99%

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

Tian

Cheng

Zhang

et al. 2019

IEEE Trans. Evol. Computat.

272

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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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Section: A Existing Dominance Relationsmentioning

confidence: 99%

“…There exist many techniques for developing new dominance relations in the literature, such as expanding the dominance area [6], [7], gridding the objective space [8], [9], adopting the fuzzy logic [10], [11], and defining the dominance relation by weight vectors [12], [13].…”

mentioning

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.

272

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show abstract

“…One of the best methods in multiobjective optimization is the nondominated sorting genetic algorithm (NSGA-II). 32,33 This algorithm begins by the creation of a random initial population that is sorted by a nondominated sorting procedure. This initial population is the basis for obtaining subsequent offspring populations as follows:…”

Section: Multiobjective Optimization Algorithmmentioning

confidence: 99%

Passive filters' placement considering parameters' variations

Abril

2018

Int Trans Electr Energ Syst

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Summary The presence of power system harmonics due to the increasing number of nonlinear loads in modern industry has become a growing concern for the engineers. Among the harmonic mitigation methods available, the use of single tuned passive filters is 1 of the techniques most widely employed due to their simplicity and low cost. The formulation here presented considers the probabilistic nature of parameters' deviations of the filters and of the system by using the Monte Carlo statistical simulation method. The optimization determines a set of single tuned harmonic filters to obtain the maximum saving of annual cost as well as the best power quality indices of the circuit. The obtained solutions comply with the constraints of power quality and of stress of capacitors. The multiobjective optimization problem is solved by the nondominated sorting genetic algorithm. The presented methodology is tested with an example circuit of literature.

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“…The fourth idea enhances the effectiveness of the Pareto dominance by means of a set of uniformly distributed reference vectors as suggested in decomposition-based MOEAs [47,48]. θ -Dominance [48] is a dominance relation belonging to this category, where each solution is associated with its nearest reference vector, and a solution is said to dominate another one if and only if the two solutions are associated with the same reference vector and the former has better convergence and diversity than the latter.…”

Section: Rectifications Of Pareto Dominance For Many-objective Optimimentioning

confidence: 99%

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

Tian

Wang

Zhang

et al. 2017

Complex Intell. Syst.

111

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Since non-dominated sorting was first adopted in NSGA in 1995, most evolutionary algorithms have employed non-dominated sorting as one of the major criteria in their environmental selection for solving multi-and many-objective optimization problems. In this paper, we focus on analyzing the effectiveness and efficiency of nondominated sorting in multi-and many-objective evolutionary algorithms. The effectiveness of non-dominated sorting is verified by considering two popular evolutionary algorithms, NSGA-II and KnEA, which were designed for solving multiand many-objective optimization problems, respectively. The efficiency of non-dominated sorting is evaluated by comparing several state-of-the-art non-dominated sorting algorithms for multi-and many-objective optimization problems. These results provide important insights to adopt non-dominated sorting in developing novel multi-and many-objective evolutionary algorithms.

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A New Decomposition-Based NSGA-II for Many-Objective Optimization

Cited by 221 publications

References 49 publications

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

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

Passive filters' placement considering parameters' variations

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

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