Optimisation multicritère : Une approche par partage des variables

Aboulaïch, Rajae; Habbal, Abderrahmane; Moussaid, Noureddine

doi:10.46298/arima.1938

Cited by 5 publications

(3 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Aboulaich et al [16] demonstrates the equivalence between the research of the Nash equilibrium of the problem (5) and fixed point of the problem (6), for values of P binary. This equivalence is true only if P is binary.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…where ε is some parameter to be adjusted [3,16]. We say that the couple (I ⋆ C , I ⋆ S , I ⋆ Z ) is a point of Nash equilibrium [18], if and only if…”

Section: Split Of Image In Concurrent Optimizationmentioning

confidence: 99%

“…In the following we recall briefly the NBI approch [15] and the splitting algorithm proposed in [10,13,16,17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

Elmoumen¹,

Moussaid²,

Aboulaïch³

2021

Math. Model. Comput.

View full text Add to dashboard Cite

In this paper, we propose a new formulation of Nash games for solving a general multi-objectives optimization problems. The objective of this approach is to split the optimization variables, allowing us to determine numerically the strategies between two players. The first player minimizes his function cost using the variables of the first table P and the second player, using the second table Q. The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front. The second proposition of this paper is to find a Nash Equilibrium solution, which coincides with the Kalai--Smorodinsky solution. Two algorithms that calculate P, Q and their associated Nash equilibrium, by using some extension of the normal boundary intersection approach, are tried out successfully. Then, we propose a search engine to look for similar images of a given image based on multiple image representations using Color, Texture and Shape Features.

show abstract

Section: Preliminary Resultsmentioning

confidence: 99%

“…where ε is some parameter to be adjusted [3,16]. We say that the couple (I ⋆ C , I ⋆ S , I ⋆ Z ) is a point of Nash equilibrium [18], if and only if…”

Section: Split Of Image In Concurrent Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

Elmoumen¹,

Moussaid²,

Aboulaïch³

2021

Math. Model. Comput.

View full text Add to dashboard Cite

show abstract

Study of different strategies for splitting variables in multidisciplinary topology optimization

Aboulaïch¹,

Habbal²,

Moussaid³

2014

ams

View full text Add to dashboard Cite

This paper is devoted to the minimization of the thickness of an elastic structure under competitive loadings. We propose to determine an equilibrium thickness using game theory. We consider two loads exercised separately on two parts of the plate and we aim to optimize both compliances to deal with a multiloading optimization problem. Firstly, we the design variable is taken to be the thickness of the plate. In a second step, we assume that the thickness depends on two independent functions, that we consider as strategies. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. Finally, some numerical simulations are presented and discuted.

show abstract

Towards a Nash game strategy approach to blind image deconvolution: a fractional-order derivative variational framework

Salah,

Moussaid,

Abassi

et al. 2024

Math. Model. Comput.

View full text Add to dashboard Cite

Image restoration is a critical process aimed at recovering degraded images, often impacted by factors including motion blur, sensor blurring, defocused photography, optical aberrations, atmospheric distortions, and noise-induced blur. The inherent challenge lies in the typical scenario where both the original image and the blur kernel (Point Spread Function, PSF) are unknown. This restorative process finds applications in various fields, including sensing, medical imaging, astronomy, remote sensing, and criminal investigations. This paper introduces an innovative approach to blind image deconvolution based on Nash game theory. Our focus is placed on restoring linearly corrupted images without processing explicit knowledge of the original image or the blur kernel (PSF). The proposed method formulates blind deconvolution as a two-player static game, with one player dedicated to image deblurring and the other focused on estimating the PSF. The optimal solution is characterized as Nash equilibrium, resulting in effective image restoration. Moreover, we present an enhanced game formulation that incorporates fractional-order derivatives. This unique extension has the potential to improve image restoration accuracy and resilience, leading to breakthroughs in blind image deconvolution and practical applications.

show abstract

Optimisation multicritère : Une approche par partage des variables

Cited by 5 publications

References 2 publications

Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

Study of different strategies for splitting variables in multidisciplinary topology optimization

Towards a Nash game strategy approach to blind image deconvolution: a fractional-order derivative variational framework

Contact Info

Product

Resources

About