Relation Between Weight Vectors and Solutions in MOEA/D

Ishibuchi, Hisao; Doi, Ken; Masuda, Hiroyuki; Nojima, Yusuke

doi:10.1109/ssci.2015.127

Cited by 14 publications

(10 citation statements)

References 21 publications

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“…Most MOEA/D variants adopt the ideal point as its reference point. The use of the ideal point would be effective when the population's diversity is easy to maintain as argued in [15]. In contrast, a utopian point is helpful for approximating the PF boundary.…”

Section: Introductionmentioning

confidence: 99%

On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Wang

Zhang

et al. 2017

Swarm and Evolutionary Computation

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Decomposition based multiobjective evolutionary algorithms approximate the Pareto front of a multiobjective optimization problem by optimizing a set of subproblems in a collaborative manner. Often, each subproblem is associated with a direction vector and a reference point. The settings of these parameters have a very critical impact on convergence and diversity of the algorithm. Some work has been done to study how to set and adjust direction vectors to enhance algorithm performance for particular problems. In contrast, little effort has been made to study how to use reference points for controlling diversity in decomposition based algorithms. In this paper, we first study the impact of the reference point setting on selection in decomposition based algorithms. To balance the diversity and convergence, a new variant of the multiobjective evolutionary algorithm based on decomposition with both the ideal point and the nadir point is then proposed. This new variant also employs an improved global replacement strategy for performance enhancement. Comparison of our proposed algorithm with some other state-of-theart algorithms is conducted on a set of multiobjective test problems. Experimental results show that our proposed algorithm is promising.

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Section: Introductionmentioning

confidence: 99%

On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Wang

Zhang

et al. 2017

Swarm and Evolutionary Computation

Self Cite

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“…Different Types of Reference Points. There have been numerous studies of decomposition approaches [35][36][37][38][39][40][41][42][43][44][45] to use different types of reference points for providing evolutionary search directions. According to the position of reference point relative to the true PF in the objective space, there have three main kinds of reference points in existing MOEA/Ds.…”

Section: Proposition 1 Letmentioning

confidence: 99%

“…However, it is found in [33][34][35][36][37][38][39][40][41][42][43][44][45] that most of MOEA/Ds adopt one single reference point for all the evolutionary search directions, which is harmful for searching the entire PF when tackling MOPs that are characterized with difficultto-approximate PF boundaries [46]. To solve this kind of MOPs, in this paper, an evolutionary search method with multiple utopian reference points is proposed for MOEA/Ds.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Search with Multiple Utopian Reference Points in Decomposition‐Based Multiobjective Optimization

Lin

Zhu

et al. 2019

Complexity

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Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted.

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“…The PBI function can produce uniformly distributed solutions in objective space by setting appropriate values for θ. There are several studies [31]- [33] that provide a sensitivity analysis of PBI, varying θ ∈ [0.1, 100]. Figure 2 illustrates some boxplots that represent the effect of the parameter sensitivity in the AASF and PBI functions.…”

Section: Multi-objective Optimization a Mop Can Be Represented Asmentioning

confidence: 99%

Studying the Effect of Robustness Measures in Offline Parameter Tuning for Estimating the Performance of MOEA/D

Pescador-Rojas

Pallez

Castellanos

et al. 2018

2018 IEEE Symposium Series on Computational Intelligence (SSCI)

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Offline parameter tuning (OPT) of multi-objective evolutionary algorithms (MOEAs) has the goal of finding an appropriate set of parameters for solving a large number of problems. According to the no free lunch theorem (NFL), no algorithm can have the best performance in all classes of optimization problems. However, it is possible to find an appropriate set of parameters of an algorithm for solving a particular class of problems. For that sake, we need to study how to estimate the aggregation quality function for an algorithmic configuration assessed on a set of optimization problems.In this paper, we study robustness measures for dealing with the parameter settings of stochastic algorithms. We focus on decomposition-based MOEAs and we propose to tune scalarizing functions for solving some classes of problems based on the Pareto front shapes using up to 7 objective functions. Based on our experimental results, we were able to derive interesting guidelines to evaluate the quality of algorithmic configurations using a combination of descriptive statistics.Index Terms-Offline parameter tuning, robustness measures, multiobjective evolutionary algorithms, scalarizing functions.

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Relation Between Weight Vectors and Solutions in MOEA/D

Cited by 14 publications

References 21 publications

On the use of two reference points in decomposition based multiobjective evolutionary algorithms

On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Evolutionary Search with Multiple Utopian Reference Points in Decomposition‐Based Multiobjective Optimization

Studying the Effect of Robustness Measures in Offline Parameter Tuning for Estimating the Performance of MOEA/D

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