LIBEA: A Lebesgue Indicator-Based Evolutionary Algorithm for multi-objective optimization

Zapotecas-Martínez, Saúl; López-Jaimes, Antonio; García-Nájera, Abel

doi:10.1016/j.swevo.2018.05.004

Cited by 48 publications

(22 citation statements)

References 44 publications

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“…The variation of the theory of the relationship between Lebesgue integration and absolute continuity or how to combine the two is an interesting thing in this paper (Bernal, 2018). In multi-objective optimization, the Lebesgue indicator-based evolution algorithm (LIBEA) is introduced to reduce computation costs (Zapotecas-Martínez et al, 2019). Lebesgue samplingbased fault diagnosis and prognosis (LS-FDP) were developed to reduce computational costs and minimize accumulated uncertainty rather than Riemann sampling-based FDP (RS-FDP).…”

Section: The Latest Resultsmentioning

confidence: 99%

A Bibliometric Analysis for Lebesgue Measure Integration in Optimization

Rusyaman¹,

Munandar²,

Chaerani³

et al. 2021

ijgor

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In solving mathematical problems so far, Riemann's integral theory is quite adequate for solving pure mathematics and applications problems. But not all problems can be solved using this integration, such as a discontinuous function that is not Riemann's integration. Lebesgue integral is an integration concept based on measure and can solve finite and unlimited function problems and be solved in a more general set domain. One of the bases of this integration is the Lebesgues measure includes the set of real numbers, where the length of the interval is the endpoints. The alternative use of this integral is widely used in various studies such as partial differential equations, quantum mechanics, and probabilistic analysis, requiring the integration of arbitrary set functions. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to Lebesgue measure in integration. Search results are obtained 832 papers in the google scholar database and 997 papers using Lebesgue measure integration in optimization. It can also be seen that the research have 4 clusters and 3 clusters respectively with scattered keywords for each cluster. Finally, using bibliographic data can be obtained Lebesgues measure in integration and optimization supports many of the research and provides productive citations to citing the study.

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Section: The Latest Resultsmentioning

confidence: 99%

A Bibliometric Analysis for Lebesgue Measure Integration in Optimization

Rusyaman¹,

Munandar²,

Chaerani³

et al. 2021

ijgor

View full text Add to dashboard Cite

show abstract

“…Menchaca-Méndez et al (2018) developed an adaptative control strategy to reduce the number of hypervolume contributions per iteration. Zapotecas-Martĺnez et al (2019) put forward a Lebesgue indicator-based evolutionary algorithm to solve continuous and box-constrained multiobjective optimization problems. However, the Evolutionary Computation Volume 29, Number 2 hypervolume indicator has a high computational cost.…”

Section: Related Workmentioning

confidence: 99%

A Decomposition-Based Evolutionary Algorithm with Correlative Selection Mechanism for Many-Objective Optimization

Liu

Wang

Bian

et al. 2021

Evolutionary Computation

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Decomposition-based evolutionary algorithms have been quite successful in dealing with multi-objective optimization problems. Recently, more and more researchers attempt to apply the decomposition approach to solve many-objective optimization problems. A many-objective evolutionary algorithm based on decomposition with correlative selection mechanism (MOEA/D-CSM) is also proposed to solve many-objective optimization problems in this paper. Since MOEA/D-SCM is based on a decomposition approach which adopts penalty boundary intersection (PBI), a set of reference points must be generated in advance. Thus, a new concept related to the set of reference points is introduced first, namely, the correlation between an individual and a reference point. Thereafter, a new selection mechanism based on the correlation is designed and called correlative selection mechanism. The correlative selection mechanism finds their correlative individuals for each reference point as soon as possible so that the diversity among population members is maintained. However, when a reference point has two or more correlative individuals, those worse correlative individuals may be removed from a population so that the solutions can be ensured to move towards the Pareto-optimal front. In a comprehensive experimental study, we apply MOEA/D-CSM to a number of many-objective test problems with 3 to 15 objec-tives and make a comparison with three state-of-the-art many-objective evolutionary algorithms, namely, NSGA-III, MOEA/D and RVEA. Experimental results show that the proposed MOEA/D-CSM can produce competitive results on most of the problems considered in this study.

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“…In other words, IBEAs use many more iterations (computational efforts) to approximate the real Pareto front of a problem. As a consequence, extensive investigations concerning the design of IBEAs using the Lebesgue measure as a quality indicator have been studied in the last few years [11][12][13][14][15]. To date, the development of EMOAs based on the hypervolume indicator is recognized as an actual area of investigation within the EMOO community, and this is precisely the topic of the investigation presented in this work.…”

Section: Introductionmentioning

confidence: 98%

Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

2021

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One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the most investigated indicators in the designing of indicator-based evolutionary algorithms (IBEAs). The main deficiency of IBEAs that use the Lebesgue measure is their computational cost which increases with the number of objectives of the problem. On this matter, the investigation presented in this paper introduces an evolutionary algorithm based on the Lebesgue measure to deal with box-constrained continuous multi-objective optimization problems. The proposed algorithm implicitly uses the regularity property of continuous multi-objective optimization problems that has suggested effectiveness when solving continuous problems with rough Pareto sets. On the other hand, the survival selection mechanism considers the local property of the Lebesgue measure, thus reducing the computational time in our algorithmic approach. The emerging indicator-based evolutionary algorithm is examined and compared versus three state-of-the-art multi-objective evolutionary algorithms based on the Lebesgue measure. In addition, we validate its performance on a set of artificial test problems with various characteristics, including multimodality, separability, and various Pareto front forms, incorporating concavity, convexity, and discontinuity. For a more exhaustive study, the proposed algorithm is evaluated in three real-world applications having four, five, and seven objective functions whose properties are unknown. We show the high competitiveness of our proposed approach, which, in many cases, improved the state-of-the-art indicator-based evolutionary algorithms on the multi-objective problems adopted in our investigation.

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LIBEA: A Lebesgue Indicator-Based Evolutionary Algorithm for multi-objective optimization

Cited by 48 publications

References 44 publications

A Bibliometric Analysis for Lebesgue Measure Integration in Optimization

A Bibliometric Analysis for Lebesgue Measure Integration in Optimization

A Decomposition-Based Evolutionary Algorithm with Correlative Selection Mechanism for Many-Objective Optimization

Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

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