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Abstract Optimal active–reactive power dispatch problems (OARPD) are non-convex and highly nonlinear complex optimization problems. Typically, such problems are expensive in terms of computational time and cost due to the load variations over the scheduling period. The conventional constraint-based solvers that are generally used to tackle such problems require a considerable high budget and may not provide high quality solutions. In the last decade, complexity of OARPD has further increased due to the incorporation of renewable energy sources such as: wind, solar and small-hydro generators. More specifically, the incorporation of renewable sources introduces uncertainty in generation on top of the load variations in conventional OARPD, making the problem more complicated. Recently, Differential Evolution (DE) is viewed as an excellent algorithm to solve OARPD problems, due to its effectiveness to optimize the objective function which is subject to many operational constraints. A new efficient Differential Evolution algorithm, denoted as DE a -AR, is propounded to solve the contemporary stochastic optimal power flow OARPD problems considering the renewable generators. DE a -AR uses arithmetic recombination crossover and adapts the scaling factor based on Laplace distribution. In addition, an efficient archive strategy that acts as a corresponding image of the population and stores the inferior individuals for later use, is also incorporated. The target behind using this strategy is to consider the information of inferior individuals as a direction toward finding new good solutions. The IEEE 57-bus system is used to evaluate the OARPD problems with different stochastic scenarios based on different probability distributions employed to model parameters of renewable energy sources. The performance of the proposed work is compared with other state-of-the-art algorithms. Simulation results indicate that the proposed technique can solve the OARPD problems with renewable sources effectively and can provide high quality solutions. The proposed algorithm is ranked the first with a Friedman rank equals to 1.8333 with a clear statistical significant difference compared with the most recent studies on the used problems. Highlights • A new efficient differential evolution algorithm is propounded to solve OPF problems. • The contemporary stochastic OPF with renewable generators is considered. • The performance is compared with the best performing algorithms. • The simulation results indicate that the new technique can provide competitive performance. [ABSTRACT FROM AUTHOR]

Many parameter adaptation methods were proposed for Differential Evolution (DE) algorithm. Although these methods succeed in enhancing the performance of DE when solving a diverse set of optimization problems, locating the optimal solution is still a challenging task in most of these methods for complex optimization problems. To improve the performance of DE, this study presents a new enhanced algorithm based on our published work namely LSHADE with ensemble parameter sinusoidal adaptation, LSHADE-EpSin, which ranked the joint winner in IEEE CEC2016 competition on real-parameter single objective optimization. The method proposes a mixture of two sinusoidal formulas and a Cauchy distribution to balance the exploration and the exploitation of already found best solutions. A restart method is used at later generations to enhance the quality of the found solutions. The proposed algorithm also introduces a novel approach to adapt the population size by using a niching-based reduction scheme. In this mechanism, two separate niches are used before performing the population reduction, to reduce the population size in an effective manner. The proposed algorithm namely ensemble sinusoidal differential evolution with niching reduction, E s DE r -NR, is tested on the IEEE CEC2014 problems used in the special session and competitions on real-parameter single objective optimization of the IEEE CEC2016. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to the other state-of-the-art algorithms from the literature including CMA-ES variants. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a simple, yet very effective, population-based search technique. However, it is challenging to maintain a balance between exploration and exploitation behaviors of the DE algorithm. In this paper, we boost the population diversity while preserving simplicity by introducing a multi-population DE to solve large-scale global optimization problems. In the proposed algorithm, called m DE- b ES, the population is divided into independent subgroups, each with different mutation and update strategies. A novel mutation strategy that uses information from either the best individual or a randomly selected one is used to produce quality solutions to balance exploration and exploitation. Selection of individuals for some of the tested mutation strategies utilizes fitness-based ranks of these individuals. Function evaluations are divided into epochs. At the end of each epoch, individuals between the subgroups are exchanged to facilitate information exchange at a slow pace. The performance of the algorithm is evaluated on a set of 19 large-scale continuous optimization problems. A comparative study is carried out with other state-of-the-art optimization techniques. The results show that m DE- b ES has a competitive performance and scalability behavior compared to the contestant algorithms. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) has been a simple yet effective algorithm for global optimization problems. The performance of DE highly depends on its operators and parameter settings. In the last couple of decades, many advanced variants of DE have been proposed by modifying the operators and introducing new parameter tuning methods. However, the majority of the works on advanced DE have been concentrated upon the mutation and crossover operators. The initialization and selection operators are less explored in the literature. In this work, we implement the orthogonal array-based initialization of the population and propose a neighborhood search strategy to construct the initial population for the DE-based algorithms. We also introduce a conservative selection scheme to improve the performance of the algorithm. We analyze the influence of the proposed initialization and selection schemes on several variants of DE. Results suggest that the proposed methods highly improve the performance of DE algorithm and its variants. Furthermore, we introduce an ensemble strategy for parameter adaptation techniques in DE. Incorporating all the proposed initialization, selection, and parameter adaptation strategies, we develop a new variant of DE, named OLSHADE-CS. The performance of OLSHADE-CS is found to be highly competitive and significantly better in many cases when compared with the performance of the state-of-the-art algorithms on CEC benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, a neighborhood mutation strategy is proposed and integrated with various niching differential evolution (DE) algorithms to solve multimodal optimization problems. Although variants of DE are highly effective in locating a single global optimum, no DE variant performs competitively when solving multi-optima problems. In the proposed neighborhood based differential evolution, the mutation is performed within each Euclidean neighborhood. The neighborhood mutation is able to maintain the multiple optima found during the evolution and evolve toward the respective global/local optimum. To test the performance of the proposed neighborhood mutation DE, a total of 29 problem instances are used. The proposed algorithms are compared with a number of state-of-the-art multimodal optimization approaches and the experimental results suggest that although the idea of neighborhood mutation is simple, it is able to provide better and more consistent performance over the state-of-the-art multimodal algorithms. In addition, a comparative survey on niching algorithms and their applications are also presented. [ABSTRACT FROM AUTHOR]