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Xiong, G., L. Li, A. W. Mohamed, X. Yuan, and J. Zhang, A new method for parameter extraction of solar photovoltaic models using gaining–sharing knowledge based algorithm, , vol. 7, pp. 3286 - 3301, 2021. AbstractWebsite

For the solar photovoltaic (PV) system to operate efficiently, it is necessary to effectively establish an equivalent model of PV cell and extract the relevant unknown model parameters accurately. This paper introduces a new metaheuristic algorithm, i.e., gaining-sharing knowledge based algorithm (GSK) to solve the solar PV model parameter extraction problem. This algorithm simulates the process of knowledge acquisition and sharing in the human life cycle and is with strong competitiveness in solving optimization problems. It includes two significant phases. The first phase is the beginner–intermediate or junior acquisition and sharing stage, and the second phase is the intermediate–expert or senior acquisition and sharing stage. In order to verify the effectiveness of GSK, it is applied to five PV models including the single diode model, double diode model, and three PV modules. The influence of population size on the algorithm performance is empirically investigated. Besides, it is further compared with some other excellent metaheuristic algorithms including basic algorithms and advanced algorithms. Among the five PV models, the root mean square error values between the measured data and the calculated data of GSK are 9.8602E−04 ± 2.18E−17, 9.8280E−04 ± 8.72E−07, 2.4251E−03 ± 1.04E−09, 1.7298E−03 ± 6.25E−18, and 1.6601E−02 ± 1.44E−16, respectively. The results show that GSK has overall better robustness, convergence, and accuracy.

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Wu, W., H. Ouyang, A. W. Mohamed, C. Zhang, and S. Li, Enhanced harmony search algorithm with circular region perturbation for global optimization problems, , vol. 50, issue 3, pp. 951 - 975, 2020. AbstractWebsite

To improve the searching effectiveness of the harmony search (HS) algorithm, an enhanced harmony search algorithm with circular region perturbation (EHS_CRP) is proposed in this paper. In the EHS_CRP algorithm, a global and local dimension selection strategy is designed to accelerate the search speed of the algorithm. A selection learning operator based on the global and local mean level is proposed to improve the balance between exploration and exploitation. Circular region perturbation is employed to avoid the algorithm stagnation and get a better exploration region. To assess performance, the proposed algorithm is compared with 10 state-of-the-art swarm intelligent approaches in a large set of global optimization problems. The simulation results confirm that EHS_CRP has a significant advantage in terms of accuracy, convergence speed, stability and robustness. Moreover, EHS_CRP performs better than other tested methods in engineering design optimization problems. Thus, the EHS_CRP algorithm is a viable and reliable alternative for some difficult and multidimensional real-world problems.

Wagdy Mohamed, A., H. Z. Sabry, and A. Farhat, "Advanced Differential Evolution algorithm for global numerical optimization", IEEE International Conference on Computer Applications and Industrial Electronics (ICCAIE), pp. 156–161, 2011. Abstract
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Said Ali Hassan, Khalid Alnowibet, P. A. A. W. M., "Optimum Location of Field Hospitals for COVID-19: A Nonlinear Binary Metaheuristic Algorithm", Computers, Materials & Continua, vol. 68, no. 1, pp. 1183–1202, 2021. AbstractWebsite

Determining the optimum location of facilities is critical in many fields, particularly in healthcare. This study proposes the application of a suitable location model for field hospitals during the novel coronavirus 2019 (COVID-19) pandemic. The used model is the most appropriate among the three most common location models utilized to solve healthcare problems (the set covering model, the maximal covering model, and the P-median model). The proposed nonlinear binary constrained model is a slight modification of the maximal covering model with a set of nonlinear constraints. The model is used to determine the optimum location of field hospitals for COVID-19 risk reduction. The designed mathematical model and the solution method are used to deploy field hospitals in eight governorates in Upper Egypt. In this case study, a discrete binary gaining–sharing knowledge-based optimization (DBGSK) algorithm is proposed. The DBGSK algorithm is based on how humans acquire and share knowledge throughout their life. The DBGSK algorithm mainly depends on two junior and senior binary stages. These two stages enable DBGSK to explore and exploit the search space efficiently and effectively, and thus it can solve problems in binary space.

Said Ali Hassan, Khalid Alnowibet, P. A. A. W. M., "Managing Delivery of Safeguarding Substances as a Mitigation Against Outbreaks of Pandemics", Computers, Materials & Continua, vol. 68, no. 1, pp. 1161–1181, 2021. AbstractWebsite

The optimum delivery of safeguarding substances is a major part of supply chain management and a crucial issue in the mitigation against the outbreak of pandemics. A problem arises for a decision maker who wants to optimally choose a subset of candidate consumers to maximize the distributed quantities of the needed safeguarding substances within a specific time period. A nonlinear binary mathematical programming model for the problem is formulated. The decision variables are binary ones that represent whether to choose a specific consumer, and design constraints are formulated to keep track of the chosen route. To better illustrate the problem, objective, and problem constraints, a real application case study is presented. The case study involves the optimum delivery of safeguarding substances to several hospitals in the Al-Gharbia Governorate in Egypt. The hospitals are selected to represent the consumers of safeguarding substances, as they are the first crucial frontline for mitigation against a pandemic outbreak. A distribution truck is used to distribute the substances from the main store to the hospitals in specified required quantities during a given working shift. The objective function is formulated in order to maximize the total amount of delivered quantities during the specified time period. The case study is solved using a novel Discrete Binary Gaining Sharing Knowledge-based Optimization algorithm (DBGSK), which involves two main stages: discrete binary junior and senior gaining and sharing stages. DBGSK has the ability of finding the solutions of the introduced problem, and the obtained results demonstrate robustness and convergence toward the optimal solutions.

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Opara, K. R., A. A. Hadi, and A. W. Mohamed, "Parametrized Benchmarking: An Outline of the Idea and a Feasibility Study", Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, New York, NY, USA, Association for Computing Machinery, pp. 197–198, 2020. Abstract

Performance of real-parameter global optimization algorithms is typically evaluated using sets of test problems. We propose a new methodology of extending these benchmarks to obtain a more balanced experimental design. This can be done by selectively removing some of the transformations originally used in the definitions of the test problems such as rotation, scaling, or translation. In this way, we obtain several variants of each problem parametrized by interpretable, high-level characteristics. These binary parameters are used as predictors in a multiple regression model explaining the algorithmic performance. Linear models allow for the attribution of strength and direction of performance changes to particular characteristics of the optimization problems and thus provide insight into the underlying mechanics of the investigated algorithms. The proposed ideas are illustrated with an application example showing the feasibility of the new benchmark. Parametrized benchmarking is a step towards obtaining multi-faceted insight into algorithmic performance and the optimization problems. The overall goal is to systematize a method of matching problems to algorithms and in this way constructively address the limitations imposed by the no free lunch theorem.

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Nomer, H. A. A., K. A. Alnowibet, A. Elsayed, and A. W. Mohamed, "Neural Knapsack: A Neural Network Based Solver for the Knapsack Problem", IEEE Access, vol. 8, pp. 224200 - 224210, 2020. Abstract
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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. 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., 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., 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. K., A. W. Mohamed, E. Z. Elfeky, and M. Saleh, "Enhancing AGDE Algorithm Using Population Size Reduction for Global Numerical Optimization", The International Conference on Advanced Machine Learning Technologies and Applications (AMLTA2018), Cham, Springer International Publishing, pp. 62 - 72, 2018. Abstract

Adaptive guided differential evolution algorithm (AGDE) is a 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 * 100p% and 100p% 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.

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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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., 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. 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. 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., 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. 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. 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., 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., 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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