Musrrat Ali

An efficient Differential Evolution based algorithm for solving multi-objective optimization problems

In the present study, a modified variant of Differential Evolution (DE) algorithm for solving multi-objective optimization problems is presented. The proposed algorithm, named Multi-Objective Differential Evolution Algorithm (MODEA) utilizes the advantages of Opposition-Based Learning for generating an initial population of potential candidates and the concept of random localization in mutation step. Finally, it introduces a new selection mechanism for generating a well distributed Pareto optimal front. The performance of proposed algorithm is investigated on a set of nine bi-objective and five tri-objective benchmark test functions and the results are compared with some recently modified versions of DE for MOPs and some other Multi Objective Evolutionary Algorithms (MOEAs). The empirical analysis of the numerical results shows the efficiency of the proposed algorithm.

An optimized watermarking technique based on self-adaptive DE in DWT-SVD transform domain

The performance of differential evolution (DE) algorithm is significantly affected by its parameters setting that are highly problem dependent. In this paper, an optimal discrete wavelet transform-singular value decomposition (DWT-SVD) based image watermarking scheme using self-adaptive differential evolution (SDE) algorithm is presented. SDE adjusts the mutation factor F and the crossover rate Cr dynamically in order to balance an individuals exploration and exploitation capability for different evolving phases. Two-level DWT is applied to the cover image to transform it into sub-bands of different frequencies and then apply the SVD to each sub-band at level second. After applying one-level DWT to the watermark and subsequent application of SVD, the principal components of each sub-band are properly scaled down by multiplying with different scaling factors to make the watermark invisible. These scaled principal components are inserted into the singular value matrix of the corresponding blocks of the host image. The scaling factors are optimized using the self-adaptive DE algorithm to obtain the highest possible robustness with better imperceptibility. Experimental results show that the proposed scheme maintains a satisfactory image quality and watermark can still be identified after various attacks even though the watermarked image is seriously distorted.

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.

An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony

Digital image watermarking is the process of authenticating a digital image by embedding a watermark into it and thereby protecting the image from copyright infringement. This paper proposes a novel robust image watermarking scheme developed in the wavelet domain based on the singular value decomposition (SVD) and artificial bee colony (ABC) algorithm. The host image is transformed into an invariant wavelet domain by applying redistributed invariant wavelet transform, subsequently the low frequency sub-band of wavelet transformed image is segmented into non-overlapping blocks. The most suitable embedding blocks are selected using the human visual system for the watermark embedding. The watermark bits are embedded into the target blocks by modifying the first column coefficients of the left singular vector matrix of SVD decomposition with the help of a threshold and the visible distortion caused by the embedding is compensated by modifying the coefficients of the right singular vector matrix employing compensation parameters. Furthermore, ABC is employed to obtain the optimized threshold and compensation parameters. Experimental results, compared with the related existing schemes, demonstrated that the proposed scheme not only possesses the strong robustness against image manipulation attacks, but also, is comparable to other schemes in term of visual quality.

Multi-level image thresholding by synergetic differential evolution

The multi-level image thresholding is often treated as a problem of optimization. Typically, finding the parameters of these problems leads to a nonlinear optimization problem, for which obtaining the solution is computationally expensive and time-consuming. In this paper a new multi-level image thresholding technique using synergetic differential evolution (SDE), an advanced version of differential evolution (DE), is proposed. SDE is a fusion of three algorithmic concepts proposed in modified versions of DE. It utilizes two criteria (1) entropy and (2) approximation of normalized histogram of an image by a mixture of Gaussian distribution to find the optimal thresholds. The experimental results show that SDE can make optimal thresholding applicable in case of multi-level thresholding and the performance is better than some other multi-level thresholding methods.

Differential evolution algorithm for the selection of optimal scaling factors in image watermarking

Abstract In this paper, an innovative watermarking scheme based on differential evolution (DE) in the transform domain is proposed. The insertion and extraction of the watermark are performed in discrete wavelet transform-singular value decomposition (DWT–SVD) transform domain. In the embedding process, the host image is transformed into sub-bands of different frequencies by third-level DWT and then subsequent application of SVD on low pass (LL) and high pass (HH) sub-bands at level third. The watermark image is properly scaled down by multiplying with different scaling factors (SFs) and embedded in the Singular value matrix of LL and HH sub-bands of the host image to make the watermark invisible and robust. We applied an optimization technique, differential evolution, to search optimal scaling factors to improve the quality of watermarked image and robustness of the watermark. In order to overcome the false positive problem, a binary watermark is also embedded in the host image in a lossless manner. According to the numerical results, the quality of watermarked image is satisfactory and embedded watermark is extracted successfully even if the watermarked image is exposed to various image processing and geometric attacks.

Unconventional initialization methods for differential evolution

The crucial role played by the initial population in a population-based heuristic optimization cannot be neglected. It not only affects the search for several iterations but often also has an influence on the final solution. If the initial population itself has some knowledge about the potential regions of the search domain then it is quite likely to accelerate the rate of convergence of the optimization algorithm. In the present study we propose two schemes for generating the initial population of differential evolution (DE) algorithm. These schemes are based on quadratic interpolation (QI) and nonlinear simplex method (NSM) in conjugation with computer generated random numbers. The idea is to construct a population that is biased towards the optimum solution right from the very beginning of the algorithm. The corresponding algorithms named as QIDE (using quadratic interpolation) and NSDE (using non linear simplex method), are tested on a set of 20 traditional benchmark problems with box constraints and 7 shifted (non-traditional) functions taken from literature. Comparison of numerical results with traditional DE and opposition based DE (ODE) show that the proposed schemes considered by us for generating the random numbers significantly improves the performance of DE in terms of convergence rate and average CPU time.

Mixed Mutation Strategy Embedded Differential Evolution

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimizing real valued optimization problems. Traditional investigations with differential evolution have used a single mutation operator. Using a variety of mutation operators that can be integrated during evolution could hold the potential to generate a better solution with less computational effort. In view of this, in this paper a mixed mutation strategy which uses the concept of evolutionary game theory is proposed to integrate basic differential evolution mutation and quadratic interpolation to generate a new solution. Throughout of this paper we refer this new algorithm as, differential evolution with mixed mutation strategy (MSDE). The performance of proposed algorithm is investigated and compared with basic differential evolution. The experiments conducted shows that proposed algorithm outperform the basic DE algorithm in all the benchmark problems.

Differential Evolution with Parent Centric Crossover

Differential evolution (DE) has emerged as a powerful tool for solving optimization problems in the last few years. However, the convergence rate of DE still does not meet all the requirements, and attempts to speed up differential evolution are considered necessary. In order to improve the performance of DE, we propose a modified DE algorithm called DEPCX which uses parent centric approach to manipulate the solution vectors. The performance of DEPCX is evaluated on a test bed of five functions. Numerical results are compared with original differential evolution (DE) and with TDE, another recently modified version of DE. Empirical results indicate that this modification enables the algorithm to get a better transaction between the convergence rate and robustness.

A Modified Differential Evolution Algorithm and Its Application to Engineering Problems

In the present study a Modified Differential Evolution (MDE) algorithm is proposed. This algorithm is different in three ways from basic DE. For initialization it utilizes opposition-based learning while in basic DE uniform random numbers serve this task. Secondly, in basic DE mutant individual is random while in MDE it is tournament best and finally MDE utilizes only one set of population as against two sets as used in basic DE. The performance of proposed algorithm is investigated and compared with basic differential evolution. The experiments conducted shows that proposed algorithm outperform the basic DE algorithm in all the benchmark problems and real life applications