Ali Wagdy Mohamed

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.

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.

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.

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.