Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

A novel meta-heuristic optimization algorithm

We developed a hybrid method for feature selection of classification tasks.Our hybrid method combines Artificial Bee Colony with Differential Evolution.We performed experiments over fifteen datasets from the UCI Repository.Our method selects good features without reducing accuracy of classification.By selecting features with our method, we reduced time required for classification. "Dimensionality" is one of the major problems which affect the quality of learning process in most of the machine learning and data mining tasks. Having high dimensional datasets for training a classification model may lead to have "overfitting" of the learned model to the training data. Overfitting reduces generalization of the model, therefore causes poor classification accuracy for the new test instances. Another disadvantage of dimensionality of dataset is to have high CPU time requirement for learning and testing the model. Applying feature selection to the dataset before the learning process is essential to improve the performance of the classification task. In this study, a new hybrid method which combines artificial bee colony optimization technique with differential evolution algorithm is proposed for feature selection of classification tasks. The developed hybrid method is evaluated by using fifteen datasets from the UCI Repository which are commonly used in classification problems. To make a complete evaluation, the proposed hybrid feature selection method is compared with the artificial bee colony optimization, and differential evolution based feature selection methods, as well as with the three most popular feature selection techniques that are information gain, chi-square, and correlation feature selection. In addition to these, the performance of the proposed method is also compared with the studies in the literature which uses the same datasets. The experimental results of this study show that our developed hybrid method is able to select good features for classification tasks to improve run-time performance and accuracy of the classifier. The proposed hybrid method may also be applied to other search and optimization problems as its performance for feature selection is better than pure artificial bee colony optimization, and differential evolution.

A hybrid approach of differential evolution and artificial bee colony for feature selection

This paper proposes a novel global optimization algorithm called Political Optimizer (PO), inspired by the multi-phased process of politics. PO is the mathematical mapping of all the major phases of politics such as constituency allocation, party switching, election campaign, inter-party election, and parliamentary affairs. The proposed algorithm assigns each solution a dual role by logically dividing the population into political parties and constituencies, which facilitates each candidate to update its position with respect to the party leader and the constituency winner. Moreover, a novel position updating strategy called recent past-based position updating strategy (RPPUS) is introduced, which is the mathematical modeling of the learning behaviors of the politicians from the previous election. The proposed algorithm is benchmarked with 50 unimodal, multimodal, and fixed dimensional functions against 15 state of the art algorithms. We show through experiments that PO has an excellent convergence speed with good exploration capability in early iterations. Root cause of such behavior of PO is incorporation of RPPUS and logical division of the population to assign dual role to each candidate solution. Using Wilcoxon rank-sum test, PO demonstrates statistically significant performance over the other algorithms. The results show that PO outperforms all other algorithms, and consistency in performance on such a comprehensive suite of benchmark functions proves the versatility of the algorithm. Furthermore, experiments demonstrate that PO is invariant to function shifting and performs consistently in very high dimensional search spaces. Finally, the applicability on real-world applications is demonstrated by efficiently solving four engineering optimization problems.

Political Optimizer: A novel socio-inspired meta-heuristic for global optimization

To improve the optimization performance of LSHADE algorithm, an alternative adaptation approach for the selection of control parameters is proposed. The proposed algorithm, named LSHADE-SPA, uses a new semi-parameter adaptation approach to effectively adapt the values of the scaling factor of the Differential evolution algorithm. The proposed approach consists of two different settings for two control parameters F and Cr. The benefit of this approach is to prove that the semi-adaptive algorithm is better than pure random algorithm or fully adaptive or self-adaptive algorithm. To enhance the performance of our algorithm, we also introduced a hybridization framework named LSHADE-SPACMA between LSHADE-SPA and a modified version of CMA-ES. The modified version of CMA-ES undergoes the crossover operation to improve the exploration capability of the proposed framework. In LSHADE-SPACMA both algorithms will work simultaneously on the same population, but more populations will be assigned gradually to the better performance algorithm. In order to verify and analyze the performance of both LSHADE-SPA and LSHADE-SPACMA, Numerical experiments on a set of 30 test problems from the CEC2017 benchmark for 10, 30, 50 and 100 dimensions, including a comparison with LSHADE algorithm are executed. Experimental results indicate that in terms of robustness, stability, and quality of the solution obtained, of both LSHADE-SPA and LSHADE-SPACMA are better than LSHADE algorithm, especially as the dimension increases.

LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems

Constrained optimization based on modified differential evolution algorithm

An alternative differential evolution algorithm for global optimization

Real parameter optimization by an effective differential evolution algorithm

In this paper, we present an advanced differential evolution (ADE) algorithm for solving global unconstrained optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals at a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability scheme is utilized to balance the global exploration and local exploitation. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and/or premature convergence. Numerical experiments and comparisons on a set of well-known high dimensional benchmark functions indicate that the improved algorithm outperforms and is superior to other existing algorithms in terms of final solution quality, success rate, convergence rate, and robustness.

Hegazy Zaher Sabry

Papers

Constrained optimization based on modified differential evolution algorithm

An alternative differential evolution algorithm for global optimization

Real parameter optimization by an effective differential evolution algorithm

Advanced Differential Evolution algorithm for global numerical optimizatiom