Fast Implementation of the Steady-State NSGA-II Algorithm for Two Dimensions Based on Incremental Non-Dominated Sorting

Buzdalov, Maxim; Yakupov, Ilya; Stankevich, A. S.

doi:10.1145/2739480.2754728

Cited by 16 publications

(26 citation statements)

References 17 publications

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“…To our best knowledge, most, if not all, studies on the NDS are discussed in the context of a generational evolution model, whereas few have considered the situation for a steady-state evolution model yet. Buzdalov et al [19] presented an incremental NDS for the steady-state EMO. But unfortunately, this method can only work for the 2-D case.…”

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confidence: 99%

Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Deb

Zhang

et al. 2017

IEEE Trans. Cybern.

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Abstract-Nondominated sorting (NDS), which divides a population into several nondomination levels (NDLs), is a basic step in many evolutionary multiobjective optimization (EMO) algorithms. It has been widely studied in a generational evolution model, where the environmental selection is performed after generating a whole population of offspring. However, in a steady-state evolution model, where a population is updated right after the generation of a new candidate, the NDS can be extremely time consuming. This is especially severe when the number of objectives and population size become large. In this paper, we propose an efficient NDL update method to reduce the cost for maintaining the NDL structure in steady-state EMO. Instead of performing the NDS from scratch, our method only updates the NDLs of a limited number of solutions by extracting the knowledge from the current NDL structure. Notice that our NDL update method is performed twice at each iteration. One is after the reproduction, the other is after the environmental selection. Extensive experiments fully demonstrate that, comparing to the other five state-of-the-art NDS methods, our proposed method avoids a significant amount of unnecessary comparisons, not only in the synthetic data sets, but also in some real optimization scenarios. Last but not least, we find that our proposed method is also useful for the generational evolution model. Index Terms-Computational complexity, nondominated sorting (NDS), nondomination level (NDL), Pareto dominance, steady-state evolutionary multiobjective optimization (EMO).

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confidence: 99%

Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Deb

Zhang

et al. 2017

IEEE Trans. Cybern.

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“…There were 1000 runs of each version on each problem. Median values of the hypervolume indicator (evaluated as in papers [2,5]) are presented in Table 1.…”

Section: Methodsmentioning

confidence: 99%

“…The algorithm and the data structure are presented in [7], and an INDS-based steady-state version of NSGA-II is presented and analysed in [2]. The insertion and removal complexities are at most O(N ) and are provably lower under several conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we experimentally show that this trend spreads over many different ways of introducing steadiness to this algorithm: the "more steady" the algorithm is, the better results it yields. As we use the approach from [2], computational running times are almost the same regardless steadiness, so we concentrate on result quality only.…”

Section: Introductionmentioning

confidence: 99%

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Various Degrees of Steadiness in NSGA-II and Their Influence on the Quality of Results

Buzdalov

Parfenov

2015

Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Steady-state evolutionary algorithms are often favoured over generational ones due to better scalability in parallel and distributed environments. However, in certain conditions they are able to produce results of better quality as well.We consider several ways to introduce various "degrees of steadiness" in the NSGA-II algorithm, some of which have not been known in literature, and show experimentally (on a corpus of 21 test problems) the presence of a general trend: algorithms with more steadiness yield better results.

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“…Numerous MOEAs have been proposed to MOPs (see e.g. [3,4,14,28,30,31]). There are three main classes of approaches to develop MOEAs, which are known as Pareto-dominance based (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Reduction of the Pareto Set in Bicriteria Asymmetric Traveling Salesman Problem

Zakharov

Kovalenko

2018

Communications in Computer and Information Science

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0000−0003−2469−023X] and Yulia V. Kovalenko 2,3[0000−0003−4791−7011]Abstract. We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of "quanta of information" that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper shows the degree of reduction of the Pareto set approximation for various "quanta of information" and various structures of the bi-ATSP instances generated randomly.Keywords: Reduction of the Pareto set · Multi-objective genetic algorithm · Computational experiment 2 Problem Statement An instance of the traveling salesman problem [2] (TSP) is given by a complete graph G = (V, E), where V = {v 1 , . . . , v n } is the set of vertices and set E

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Fast Implementation of the Steady-State NSGA-II Algorithm for Two Dimensions Based on Incremental Non-Dominated Sorting

Cited by 16 publications

References 17 publications

Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Various Degrees of Steadiness in NSGA-II and Their Influence on the Quality of Results

Reduction of the Pareto Set in Bicriteria Asymmetric Traveling Salesman Problem

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