A Fast Method of Constructing the Non-dominated Set: Arena's Principle

Tang, Suqin; Cai, Zixing; Zheng, Jinhua

doi:10.1109/icnc.2008.823

Cited by 26 publications

(15 citation statements)

References 2 publications

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“…It's worth noting that, in 2004, Yukish [47] also used this divide-and-conquer strategy to develop the non-dominated sorting algorithm similar to Jensen's algorithm. In 2008, Tang et al [48] utilized arena's principle to construct the non-dominated set. Experiments have shown that the performance of this method outperforms the fast non-dominated sorting of NSGA-II, especially when there is a small proportion of non-dominated solutions in the evolving population.…”

Section: Introductionmentioning

confidence: 99%

Ranking Vectors by Means of the Dominance Degree Matrix

Zhou

Chen

Zhang

2017

IEEE Trans. Evol. Computat.

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In MOEAs, there are varieties of vector ranking schemes, including non-dominated sorting, dominance counting and so on. Usually, these vector ranking schemes in the classical MOEAs are of high computational complexity. Thus, in recent years, many researchers put emphasis on the further improvement of the computational complexity of the vector ranking schemes. In this paper, we propose the dominance degree matrix for a set of vectors and design a fast method to construct this new data structure, which requires O(mN log N ) comparisons on average. The dominance degree matrix is constructed based on the properties of Pareto domination, and it can convert the dominance comparison into counting the number of special element pairs. Based on the dominance degree matrix, we develop a new and efficient implementation of non-dominated sorting called DDA-NS, which has an average time complexity of O(mN 2 ) but only requires O(mN log N ) objective function value comparisons on average. Empirical results demonstrate that DDA-NS clearly outperforms six other representative approaches for non-dominated sorting in most cases and DDA-NS performs well when dealing with large-size and many-objective populations. In addition, we also use the dominance degree matrix to form a new method for calculating the dominance strength for SPEA2, which greatly improves the efficiency of the naive calculation method in SPEA2. Experiments on benchmark problems show that the NSGA-II and NSGA-III framework embedding DDA-NS and the SPEA2 framework embedding the new method of calculating the dominance strength indeed achieve the improvement of the runtime.

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Section: Introductionmentioning

confidence: 99%

Ranking Vectors by Means of the Dominance Degree Matrix

Zhou

Chen

Zhang

2017

IEEE Trans. Evol. Computat.

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“…Tang et al [11] used arena's principle to assign solutions to a front, which has been shown to have a better computational efficiency than the fast non-dominated sort and Jensen's sort in empirical evaluations. This approach randomly selects one solution from the population, regarded as an "arena host", and all the remaining solutions in the population are compared with the "arena host".…”

Section: A Non-dominated Sorting Methodsmentioning

confidence: 99%

“…Jensen [10] adopted a divide-and-conquer strategy for non-dominated sorting, the time complexity of which is O(N log M −1 N ). Tang et al [11] proposed a novel non-dominated sorting approach based on arena's principle, i.e., each winner will be the next "arena host" to be challenged. This approach has been proved to have the same time complexity as the fast non-dominated sort, while empirical results show that it outperforms the fast non-dominated sort in terms of computational efficiency, since it can achieve a time complexity O(M N √ N ) in some best cases.…”

mentioning

confidence: 99%

An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization

Zhang

Tian

Cheng

et al. 2015

IEEE Trans. Evol. Computat.

426

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Abstract-Evolutionary algorithms have been shown to be powerful for solving multi-objective optimization problems, where non-dominated sorting is a widely adopted technique in selection. This technique, however, can be computationally expensive, especially when the number of individuals in the population becomes large. This is mainly due to the fact that in most existing non-dominated sorting algorithms, a solution needs to be compared with all other solutions before it can be assigned to a front. In this work, we propose a novel, computationally efficient approach to non-dominated sorting, termed efficient non-dominated sort (ENS). In ENS, a solution to be assigned to a front needs to be compared only with those that have already been assigned to a front, thereby avoiding many unnecessary dominance comparisons. Based on this new approach, two non-dominated sorting algorithms have been suggested. Both theoretical analysis and empirical results show that the ENS-based sorting algorithms are computationally more efficient than the state-of-the-art nondominated sorting methods.

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“…There are various off-line algorithm proposed for nondominating sorting e.g. Fast Non-dominated Sort [9], Climbing Sort [15], Deductive Sort [15], Arena's Sort [24], ENS-SS [16], ENS-BS [16]. In the worst case, the time complexity of each algorithm is O(M N 2 ).…”

Section: S O R T I N Gmentioning

confidence: 99%