Ranking Methods in Many-Objective Evolutionary Algorithms

Jáimes, Antonio López; Quintero, Luis Vicente Santana; Coello, Carlos A. Coello

doi:10.1007/978-3-642-00267-0_15

Cited by 18 publications

(4 citation statements)

References 27 publications

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“…Corne and Knowles have demonstrated that AR can provide sufficient selection pressure towards the optimal front in a high-dimensional objective space [18]. However, due to the lack of a diversity maintenance scheme, AR may lead the evolutionary population to converge into a sub-area of the Pareto front [52]. Recently, some methods have been proposed to enhance diversity for AR.…”

Section: Comparison With the Average Ranking (Ar) Methodsmentioning

confidence: 99%

“…Many recent EMO algorithms originate from this motivation, introducing a variety of new criteria to distinguish between individuals, e.g., average ranking [52,70], fuzzy Pareto optimality [37,39], subspace partition [2,51], preference-inspired rank [88,87], grid-based rank [70,92], distance-based rank [32,71,91], and density adjustment strategies [1,66]. These methods provide ample alternatives to deal with many-objective optimization problems, despite some having the risk of leading the population to concentrate in one or several sub-areas of the whole Pareto front [50,67,81,65].…”

Section: Introductionmentioning

confidence: 99%

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Bi-goal evolution for many-objective optimization problems

Yang

Liu

2015

Artificial Intelligence

199

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This paper presents a meta-objective optimization approach, called Bi-Goal Evolution (BiGE), to deal with multi-objective optimization problems with many objectives. In multiobjective optimization, it is generally observed that 1) the conflict between the proximity and diversity requirements is aggravated with the increase of the number of objectives and 2) the Pareto dominance loses its effectiveness for a high-dimensional space but works well on a low-dimensional space. Inspired by these two observations, BiGE converts a given multi-objective optimization problem into a bi-goal (objective) optimization problem regarding proximity and diversity, and then handles it using the Pareto dominance relation in this bi-goal domain. Implemented with estimation methods of individuals' performance and the classic Pareto nondominated sorting procedure, BiGE divides individuals into different nondominated layers and attempts to put well-converged and well-distributed individuals into the first few layers. From a series of extensive experiments on four groups of well-defined continuous and combinatorial optimization problems with 5, 10 and 15 objectives, BiGE has been found to be very competitive against five state-of-the-art algorithms in balancing proximity and diversity. The proposed approach is the first step towards a new way of addressing many-objective problems as well as indicating several important issues for future development of this type of algorithms.

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Section: Comparison With the Average Ranking (Ar) Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bi-goal evolution for many-objective optimization problems

Yang

Liu

2015

Artificial Intelligence

199

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“…The smaller the order of efficiency, the better an individual is. The resulting ranking scheme is as follows [20]: 1). Identify the Pareto non-dominated solutions of P and group them into the subset (1) Q , which is given rank 1.…”

Section: Preference Order Ranking Algorithmmentioning

confidence: 99%

EDA-Based Multi-objective Optimization Using Preference Order Ranking and Multivariate Gaussian Copula

Gao

Peng

et al. 2013

Advances in Neural Networks – ISNN 2013

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Abstract. Estimation of distribution algorithms (EDAs) are a class of evolutionary optimization algorithms based on probability distribution model. This article extends the basic EDAs for tackling multi-objective optimization problems by incorporating multivariate Gaussian copulas for constructing probability distribution model, and using the concept of preference order. In the algorithm, the multivariate Gaussian copula is used to construct probability distribution model in EDAs. By estimating Kendall's τ and using the relationship of correlation matrix and Kendall's τ, correlation matrix R in Gaussian copula are firstly estimated from the current population, and then is used to generate offsprings. Preference order is used to identify the best individuals in order to guide the search process. The population with the current population and current offsprings population is sorted based on preference order, and the best individuals are selected to form the next population. The algorithm is tested to compare with NSGA-II, GDE, MOEP and MOPSO based on convergence metric and diversity metric using a set of benchmark functions. The experimental results show that the algorithm is effective on the benchmark functions.

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“…In the current literature, we can identify three main approaches to cope with many-objectives problems, namely: (i) to adopt or propose a preference relation that induces a finer grain order on the solutions than that induced by the Pareto dominance relation [3], [4], [5], [6], (ii) to reduce the number of objectives of the problem during the search process [7] or, a posteriori, during the decision making process [8], [9], and, (iii) to adopt a selection scheme that does not rely on Pareto optimality (e.g., using compromise functions [10], alternative ranking schemes [11] or a selection mechanism based on a performance measure (from which hypervolume 1 has been a popular choice, in spite of its considerably high computational cost [13], [14]). Here, we study an approach from the third class, using differential evolution as our search engine.…”

Section: Introductionmentioning

confidence: 99%

Solving multi-objective optimization problems using differential evolution and a maximin selection criterion

Menchaca-Méndez¹,

Coello²

2012

2012 IEEE Congress on Evolutionary Computation

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In this paper, we propose a new selection operator (based on a maximin scheme and a clustering technique), which is incorporated into a differential evolution algorithm to solve multi-objective optimization problems. The resulting algorithm is called Maximin-Clustering Differential Evolution (MCDE) and, is validated using standard test problems and performance measures taken from the specialized literature. Our preliminary results indicate that MCDE is able to outperform NSGA-II and that is competitive with a hypervolume-based approach (SMS-EMOA), but at a significantly lower computational cost. 1 The hypervolume (also known as the S metric or the Lebesgue Measure) of a set of solutions measures the size of the portion of objective space that is dominated by those solutions collectively [12].

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Ranking Methods in Many-Objective Evolutionary Algorithms

Cited by 18 publications

References 27 publications

Bi-goal evolution for many-objective optimization problems

Bi-goal evolution for many-objective optimization problems

EDA-Based Multi-objective Optimization Using Preference Order Ranking and Multivariate Gaussian Copula

Solving multi-objective optimization problems using differential evolution and a maximin selection criterion

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