Ali Wagdy Mohamed

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.

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.

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.

During the last decade, large-scale global optimization has been one of the active research fields. Optimization algorithms are affected by the curse of dimensionality associated with this kind of complex problems. To solve this problem, a new memetic framework for solving large-scale global optimization problems is proposed in this paper. In the proposed framework, success history-based differential evolution with linear population size reduction and semi-parameter adaptation (LSHADE-SPA) is used for global exploration, while a modified version of multiple trajectory search is used for local exploitation. The framework introduced in this paper is further enhanced by the concept of divide and conquer, where the dimensions are randomly divided into groups, and each group is solved separately. The proposed framework is evaluated using IEEE CEC2010 and the IEEE CEC2013 benchmarks designed for large-scale global optimization. The comparison results between our framework and other state-of-the-art algorithms indicate that our proposed framework is competitive in solving large-scale global optimization problems.

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.

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.

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.

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.

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.

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.

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.