Ranking Vectors by Means of the Dominance Degree Matrix

Zhou, Yuejiao; Chen, Zefeng; Zhang, Mengjie

doi:10.1109/tevc.2016.2567648

Cited by 40 publications

(19 citation statements)

References 57 publications

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“…The slowest algorithm is DDA-NS. Our results are quite contradictory to the results reported in [31] where DDA-NS is the fastest algorithm in most cases. Please note, however, that in [31] the algorithms were implemented in MATLAB which, as the authors note, is very efficient in matrix operations.…”

Section: Nd-tree-based Non-dominated Sortingcontrasting

confidence: 99%

“…Our results are quite contradictory to the results reported in [31] where DDA-NS is the fastest algorithm in most cases. Please note, however, that in [31] the algorithms were implemented in MATLAB which, as the authors note, is very efficient in matrix operations. On the other hand, the CPU times reported in [31] are of orders of magnitude higher compared to our experiment which suggests rather that the MATLAB implementation of M-Front and ENS-BS/SS is quite inefficient.…”

Section: Nd-tree-based Non-dominated Sortingcontrasting

confidence: 99%

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ND-Tree-Based Update: A Fast Algorithm for the Dynamic Nondominance Problem

Jaszkiewicz

Lust

2018

IEEE Trans. Evol. Computat.

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In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic nondominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new ND-Tree data structure in which each node represents a subset of points contained in a hyperrectangle defined by its local approximate ideal and nadir points. By building subsets containing points located close in the objective space and using basic properties of the local ideal and nadir points we can efficiently avoid searching many branches in the tree. ND-Tree may be used in multiobjective evolutionary algorithms and other multiobjective metaheuristics to update an archive of potentially non-dominated points. We prove that the proposed algorithm has sub-linear time complexity under mild assumptions. We experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front methods using artificial and realistic benchmarks with up to 10 objectives and show that with this new method substantial reduction of the number of point comparisons and computational time can be obtained. Furthermore, we apply the method to the non-dominated sorting problem showing that it is highly competitive to some recently proposed algorithms dedicated to this problem.

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Section: Nd-tree-based Non-dominated Sortingcontrasting

confidence: 99%

Section: Nd-tree-based Non-dominated Sortingcontrasting

confidence: 99%

ND-Tree-Based Update: A Fast Algorithm for the Dynamic Nondominance Problem

Jaszkiewicz

Lust

2018

IEEE Trans. Evol. Computat.

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“…Being simple, flexible, free from derivatives and being able to approximate the true PF with multiple solutions in a single run [16], [17], multiobjective evolutionary algorithms (MOEAs) have achieved great successes when optimizing MOPs with mostly two or three objectives [18]- [22]. Since the output of MOEAs for an MOP is a set of Pareto nondominated solutions, Pareto dominance naturally becomes a feasible criterion for selecting individuals during the evolutionary process [23].…”

Section: Introductionmentioning

confidence: 99%

A Scalar Projection and Angle-Based Evolutionary Algorithm for Many-Objective Optimization Problems

Zhou

Chen

et al. 2019

IEEE Trans. Cybern.

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In decomposition-based multiobjective evolutionary algorithms, the setting of search directions (or weight vectors), and the choice of reference points (i.e., the ideal point or the nadir point) in scalarizing functions, are of great importance to the performance of the algorithms. This paper proposes a new decomposition-based many-objective optimizer by simultaneously using adaptive search directions and two reference points. For each parent, binary search directions are constructed by using its objective vector and the two reference points. Each individual is simultaneously evaluated on two fitness functions-which are motivated by scalar projections-that are deduced to be the differences between two penalty-based boundary intersection (PBI) functions, and two inverted PBI functions, respectively. Solutions with the best value on each fitness function are emphasized. Moreover, an angle-based elimination procedure is adopted to select diversified solutions for the next generation. The use of adaptive search directions aims at effectively handling problems with irregular Pareto-optimal fronts, and the philosophy of using the ideal and nadir points simultaneously is to take advantages of the complementary effects of the two points when handling problems with either concave or convex fronts. The performance of the proposed algorithm is compared with seven state-of-the-art multi-/many-objective evolutionary algorithms on 32 test problems with up to 15 objectives. It is shown by the experimental results that the proposed algorithm is flexible when handling problems with different types of Pareto-optimal fronts, obtaining promising results regarding both the quality of the returned solution set and the efficiency of the new algorithm.

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“…• Dominance Degree Approach for Non-dominated Sorting (DDA-NS) [16] is based on the concept of dominance matrix to build their dominance degree matrix to be applied to compute the ranking of each solution.…”

Section: Algorithm Complexity Best Casementioning

confidence: 99%

Merge Nondominated Sorting Algorithm for Many-Objective Optimization

Moreno

Rodríguez

Nebro

et al. 2021

IEEE Trans. Cybern.

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Many Pareto-based multi-objective evolutionary algorithms require to rank the solutions of the population in each iteration according to the dominance principle, what can become a costly operation particularly in the case of dealing with manyobjective optimization problems. In this paper, we present a new efficient algorithm for computing the non-dominated sorting procedure, called Merge Non-Dominated Sorting (MNDS), which has a best computational complexity of Θ(N logN ) and a worst computational complexity of Θ(M N 2 ). Our approach is based on the computation of the dominance set of each solution by taking advantage of the characteristics of the merge sort algorithm. We compare the MNDS against four well-known techniques that can be considered as the state-of-the-art. The results indicate that the MNDS algorithm outperforms the other techniques in terms of number of comparisons as well as the total running time.

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Ranking Vectors by Means of the Dominance Degree Matrix

Cited by 40 publications

References 57 publications

ND-Tree-Based Update: A Fast Algorithm for the Dynamic Nondominance Problem

ND-Tree-Based Update: A Fast Algorithm for the Dynamic Nondominance Problem

A Scalar Projection and Angle-Based Evolutionary Algorithm for Many-Objective Optimization Problems

Merge Nondominated Sorting Algorithm for Many-Objective Optimization

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