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Mohamed, A. W., and H. Z. Sabry, "Constrained optimization based on modified differential evolution algorithm", Information Sciences, vol. 194: Elsevier, pp. 171–208, 2012. Abstract
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Mohamed, A. W., Solving stochastic programming problems using new approach to Differential Evolution algorithm, , vol. 18, issue 2, pp. 75 - 86, 2017. AbstractWebsite

This paper presents a new approach to Differential Evolution algorithm for solving stochastic programming problems, named DESP. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triangle and the difference vector between the best and the worst individuals among the three randomly selected vectors. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with conventional DE. DESP uses Deb’s constraint handling technique based on feasibility and the sum of constraint violations without any additional parameters. Besides, a new dynamic tolerance technique to handle equality constraints is also adopted. Two models of stochastic programming (SP) problems are considered: Linear Stochastic Fractional Programming Problems and Multi-objective Stochastic Linear Programming Problems. The comparison results between the DESP and basic DE, basic particle swarm optimization (PSO), Genetic Algorithm (GA) and the available results from where it is indicated that the proposed DESP algorithm is competitive with, and in some cases superior to, other algorithms in terms of final solution quality, efficiency and robustness of the considered problems in comparison with the quoted results in the literature.

Mohamed, A. W., A. A. Hadi, and A. K. Mohamed, Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm, , vol. 11, issue 7, pp. 1501 - 1529, 2020. AbstractWebsite

This paper proposes a novel nature-inspired algorithm called Gaining Sharing Knowledge based Algorithm (GSK) for solving optimization problems over continuous space. The GSK algorithm mimics the process of gaining and sharing knowledge during the human life span. It is based on two vital stages, junior gaining and sharing phase and senior gaining and sharing phase. The present work mathematically models these two phases to achieve the process of optimization. In order to verify and analyze the performance of GSK, numerical experiments on a set of 30 test problems from the CEC2017 benchmark for 10, 30, 50 and 100 dimensions. Besides, the GSK algorithm has been applied to solve the set of real world optimization problems proposed for the IEEE-CEC2011 evolutionary algorithm competition. A comparison with 10 state-of-the-art and recent metaheuristic algorithms are executed. Experimental results indicate that in terms of robustness, convergence and quality of the solution obtained, GSK is significantly better than, or at least comparable to state-of-the-art approaches with outstanding performance in solving optimization problems especially with high dimensions.

Mohamed, A. W., and P. N. Suganthan, Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation, , vol. 22, issue 10, pp. 3215 - 3235, 2018. AbstractWebsite

This paper presents enhanced fitness-adaptive differential evolution algorithm with novel mutation (EFADE) for solving global numerical optimization problems over continuous space. A new triangular mutation operator is introduced. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. Triangular mutation operator helps the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. Besides, two novel, effective adaptation schemes are used to update the control parameters to appropriate values without either extra parameters or prior knowledge of the characteristics of the optimization problem. In order to verify and analyze the performance of EFADE, numerical experiments on a set of 28 test problems from the CEC2013 benchmark for 10, 30 and 50 dimensions, including a comparison with 12 recent DE-based algorithms and six recent evolutionary algorithms, are executed. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, EFADE is significantly better than, or at least comparable to state-of-the-art approaches with outstanding performance.

Mohamed, A. W., A. A. Hadi, and A. K. Mohamed, "Differential Evolution Mutations: Taxonomy, Comparison and Convergence Analysis", IEEE Access, vol. 9, pp. 68629 - 68662, 2021. Abstract
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Mohamed, A. W., "An Improved Differential Evolution Algorithm with Triangular Mutation for Global Numerical Optimization", Computers & Industrial Engineering, vol. 85: Elsevier, pp. 359–375, 2015. Abstract
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Mohamed, A. K., A. W. Mohamed, E. Z. Elfeky, and M. Saleh, "Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm", Machine Learning Paradigms: Theory and Application, Cham, Springer International Publishing, pp. 327 - 349, 2019. Abstract

This paper proposes an enhanced modified Differential Evolution algorithm (MI-EDDE) to solve global constrained optimization problems that consist of mixed/non-linear integer variables. The MI-EDDE algorithm, which is based on the constraints violation, introduces a new mutation rule that sort all individuals ascendingly due to their constraint violations (cv) value and then the population is divided into three clusters (best, better and worst) with sizes 100p%, (NP-2) * 100p% and 100p% respectively. Where p is the proportion of the partition with respect to the total number of individuals in the population (NP). MI-EDDE selects three random individuals, one of each partition to implement the mutation process. This new mutation scheme shown to enhance the global and local search capabilities and increases the convergence speed. Eighteen test problems with different features are tested to evaluate the performance of MI-EDDE, and a comparison is made with four state-of-the-art evolutionary algorithms. The results show superiority of MI-EDDE to the four algorithms in terms of the quality, efficiency and robustness of the final solutions. Moreover, MI-EDDE shows a superior performance in solving two high dimensional problems and finding better solutions than the known optimal solution.

Mohamed, A. W., H. Z. Sabry, and M. Khorshid, "An alternative differential evolution algorithm for global optimization", Journal of advanced research, vol. 3, no. 2: Elsevier, pp. 149–165, 2012. Abstract
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Mohamed, A. W., A. K. Mohamed, E. Z. Elfeky, and M. Saleh, "Enhanced Directed Differential Evolution Algorithm for Solving Constrained Engineering Optimization Problems", International Journal of Applied Metaheuristic Computing (IJAMC), vol. 10, issue 1, Hershey, PA, USA, IGI Global, pp. 1 - 28, 2019. AbstractWebsite

The performance of Differential Evolution is significantly affected by the mutation scheme, which attracts many researchers to develop and enhance the mutation scheme in DE. In this article, the authors introduce an enhanced DE algorithm (EDDE) that utilizes the information given by good individuals and bad individuals in the population. The new mutation scheme maintains effectively the exploration/exploitation balance. Numerical experiments are conducted on 24 test problems presented in CEC'2006, and five constrained engineering problems from the literature for verifying and analyzing the performance of EDDE. The presented algorithm showed competitiveness in some cases and superiority in other cases in terms of robustness, efficiency and quality the of the results.

Mohamed, A. W., Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm, , vol. 3, issue 4, pp. 205 - 231, 2017. AbstractWebsite

This paper presents enhanced adaptive differential evolution (EADE) algorithm for solving high-dimensional optimization problems over continuous space. To utilize the information of good and bad vectors in the DE population, the proposed algorithm introduces a new mutation rule. It uses two random chosen vectors of the top and bottom 100p% individuals in the current population of size NP, while the third vector is selected randomly from the middle [NP-2(100p%)] individuals. The mutation rule is combined with the basic mutation strategy DE/rand/1/bin, where the only one of the two mutation rules is applied with the probability of 0.5. This new mutation scheme helps to maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. Furthermore, we propose a novel self-adaptive scheme for gradual change of the values of the crossover rate that can excellently benefit from the past experience of the individuals in the search space during evolution process which, in turn, can considerably balance the common trade-off between the population diversity and convergence speed. The proposed algorithm has been evaluated on the 7 and 20 standard high-dimensional benchmark numerical optimization problems for both the IEEE CEC-2008 and the IEEE CEC-2010 Special Session and Competition on Large-Scale Global Optimization. The comparison results between EADE and its version and the other state-of-art algorithms that were all tested on these test suites indicate that the proposed algorithm and its version are highly competitive algorithms for solving large-scale global optimization problems.

Mohamed, A. W., and A. K. Mohamed, Adaptive guided differential evolution algorithm with novel mutation for numerical optimization, , vol. 10, issue 2, pp. 253 - 277, 2019. AbstractWebsite

This paper presents adaptive guided differential evolution algorithm (AGDE) for solving global numerical optimization problems over continuous space. In order to utilize the information of good and bad vectors in the DE population, the proposed algorithm introduces a new mutation rule. It uses two random chosen vectors of the top and the bottom 100p% individuals in the current population of size NP while the third vector is selected randomly from the middle [NP-2(100p %)] individuals. This new mutation scheme helps maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. Besides, a novel and effective adaptation scheme is used to update the values of the crossover rate to appropriate values without either extra parameters or prior knowledge of the characteristics of the optimization problem. In order to verify and analyze the performance of AGDE, Numerical experiments on a set of 28 test problems from the CEC2013 benchmark for 10, 30, and 50 dimensions, including a comparison with classical DE schemes and some recent evolutionary algorithms are executed. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, AGDE is significantly better than, or at least comparable to state-of-the-art approaches.

Mohamed, A. W., A. A. Hadi, and K. M. Jambi, Novel mutation strategy for enhancing SHADE and LSHADE algorithms for global numerical optimization, , vol. 50, pp. 100455, 2019. AbstractWebsite

Proposing new mutation strategies to improve the optimization performance of differential evolution (DE) is an important research study. Therefore, the main contribution of this paper goes in three directions: The first direction is introducing a less greedy mutation strategy with enhanced exploration capability, named DE/current-to-ord_best/1 (ord stands for ordered) or ord_best for short. In the second direction, we introduce a more greedy mutation strategy with enhanced exploitation capability, named DE/current-to-ord_pbest/1 (ord_pbest for short). Both of the proposed mutation strategies are based on ordering three selected vectors from the current generation to perturb the target vector, where the directed differences are used to mimic the gradient decent behavior to direct the search toward better solutions. In ord_best, the three vectors are selected randomly to enhance the exploration capability of the algorithm. On the other hand, ord_pbest is designed to enhance the exploitation capability where two vectors are selected randomly and the third is selected from the global p best vectors. Based on the proposed mutation strategies, ord_best and ord_pbest, two DE variants are introduced as EDE and EBDE, respectively. The third direction of our work is a hybridization framework. The proposed mutations can be combined with DE family algorithms to enhance their search capabilities on difficult and complicated optimization problems. Thus, the proposed mutations are incorporated into SHADE and LSHADE to enhance their performance. Finally, in order to verify and analyze the performance of the proposed mutation strategies, numerical experiments were conducted using CEC2013 and CEC2017 benchmarks. The performance was also evaluated using CEC2010 designed for Large-Scale Global Optimization. Experimental results indicate that in terms of robustness, stability, and quality of the solution obtained, both mutation strategies are highly competitive, especially as the dimension increases.

Mohamed, A. W., H. F. Abutarboush, A. A. Hadi, and A. K. Mohamed, "Gaining-Sharing Knowledge Based Algorithm With Adaptive Parameters for Engineering Optimization", IEEE Access, vol. 9, pp. 65934 - 65946, 2021. Abstract
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Mohamed, A. W., "A Novel Discrete Binary Differential Evolution Algorithm", Aloy Journal of Soft Computing and Applications, vol. 2, no. 1: Aloy Publisher, 2014. Abstract
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Mohamed, A. W., A. A. Hadi, A. K. Mohamed, and N. H. Awad, "Evaluating the Performance of Adaptive GainingSharing Knowledge Based Algorithm on CEC 2020 Benchmark Problems", 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1 - 8, 19-24 July 2020, Submitted. Abstract
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Mohamed, A. W., H. Z. Sabry, and T. Abd-Elaziz, "Real parameter optimization by an effective differential evolution algorithm", Egyptian Informatics Journal, vol. 14, no. 1: Elsevier, pp. 37–53, 2013. Abstract
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Mohamed, A. K., and A. W. Mohamed, "Real-Parameter Unconstrained Optimization Based on Enhanced AGDE Algorithm", Machine Learning Paradigms: Theory and Application, Cham, Springer International Publishing, pp. 431 - 450, 2019. Abstract

Adaptive guided differential evolution algorithm (AGDE) is a differential evolution (DE) algorithm that utilizes the information of good and bad vectors in the population, it introduced a novel mutation rule in order to balance effectively the exploration and exploitation tradeoffs. It divided the population into three clusters (best, better and worst) with sizes 100p%, NP − 2 * 100% and 100% respectively. where p is the proportion of the partition with respect to the total number of individuals in the population (NP). AGDE selects three random individuals, one of each partition to implement the mutation process. Besides, a novel adaptation scheme was proposed in order to update the value of crossover rate without previous knowledge about the characteristics of the problems. This paper introduces enhanced AGDE (EAGDE) with non-linear population size reduction, which gradually decreases the population size according to a non-linear function. Moreover, a newly developed rule developed to determine the initial population size, that is related to the dimensionality of the problems. The performance of the proposed algorithm is evaluated using CEC2013 benchmarks and the results are compared with the state-of-art DE and non-DE algorithms, the results showed a great competitiveness for the proposed algorithm over the other algorithms, and the original AGDE.

Mohamed, A. W., An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems, , vol. 8, issue 3, pp. 989 - 1007, 2017. AbstractWebsite

In this paper, an efficient modified Differential Evolution algorithm, named EMDE, is proposed for solving constrained non-linear integer and mixed-integer global optimization problems. In the proposed algorithm, new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best,better and the worst individuals among the three randomly selected vectors is introduced. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with basic DE. EMDE uses Deb’s constraint handling technique based on feasibility and the sum of constraints violations without any additional parameters. In order to evaluate and analyze the performance of EMDE, Numerical experiments on a set of 18 test problems with different features, including a comparison with basic DE and four state-of-the-art evolutionary algorithms are executed. Experimental results indicate that in terms of robustness, stability and efficiency, EMDE is significantly better than other five algorithms in solving these test problems. Furthermore, EMDE exhibits good performance in solving two high-dimensional problems, and it finds better solutions than the known ones. Hence, EMDE is superior to the compared algorithms.

Mohamed, A. W., A novel differential evolution algorithm for solving constrained engineering optimization problems, , vol. 29, issue 3, pp. 659 - 692, 2018. AbstractWebsite

This paper introduces a novel differential evolution (DE) algorithm for solving constrained engineering optimization problems called (NDE). The key idea of the proposed NDE is the use of new triangular mutation rule. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. The main purpose of the new approach to triangular mutation operator is the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. In order to evaluate and analyze the performance of NDE, numerical experiments on three sets of test problems with different features, including a comparison with thirty state-of-the-art evolutionary algorithms, are executed where 24 well-known benchmark test functions presented in CEC’2006, five widely used constrained engineering design problems and five constrained mechanical design problems from the literature are utilized. The results show that the proposed algorithm is competitive with, and in some cases superior to, the compared ones in terms of the quality, efficiency and robustness of the obtained final solutions.

Mohamed, A. W., A. A. Hadi, A. M. Fattouh, and K. M. Jambi, "LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems", 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 145 - 152, 5-8 June 2017, Submitted. Abstract
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Mohamed, A. K., A. W. Mohamed, E. Z. Elfeky, and M. Saleh, "Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm", Machine Learning Paradigms: Theory and Application, Cham, Springer International Publishing, pp. 327 - 349, 2019. Abstract

This paper proposes an enhanced modified Differential Evolution algorithm (MI-EDDE) to solve global constrained optimization problems that consist of mixed/non-linear integer variables. The MI-EDDE algorithm, which is based on the constraints violation, introduces a new mutation rule that sort all individuals ascendingly due to their constraint violations (cv) value and then the population is divided into three clusters (best, better and worst) with sizes 100p%, (NP-2) * 100p% and 100p% respectively. Where p is the proportion of the partition with respect to the total number of individuals in the population (NP). MI-EDDE selects three random individuals, one of each partition to implement the mutation process. This new mutation scheme shown to enhance the global and local search capabilities and increases the convergence speed. Eighteen test problems with different features are tested to evaluate the performance of MI-EDDE, and a comparison is made with four state-of-the-art evolutionary algorithms. The results show superiority of MI-EDDE to the four algorithms in terms of the quality, efficiency and robustness of the final solutions. Moreover, MI-EDDE shows a superior performance in solving two high dimensional problems and finding better solutions than the known optimal solution.

Mohamed, A. K., A. A. Hadi, and A. W. Mohamed, "Generalized Adaptive Differential Evolution algorithm for Solving CEC 2020 Benchmark Problems", 2020 2nd Novel Intelligent and Leading Emerging Sciences Conference (NILES), pp. 391 - 396, 24-26 Oct. 2020, Submitted. Abstract
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Mohamed, A. W., "RDEL: restart differential evolution algorithm with local search mutation for global numerical optimization", Egyptian Informatics Journal, vol. 15, no. 3: Elsevier, pp. 175–188, 2014. Abstract
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