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This paper presents the differential evolution algorithm with adaptive mutation and crossover strategies (DEAMC) for solving nonlinear regression problems. The DEAMC algorithm adaptively uses two mutation strategies and two ranges of crossover rate. We evaluate its performance on the National Institute of Standards and Technology (NIST) nonlinear-regression benchmark containing many models of varying levels of difficulty and compare it with classic differential evolution (DE), enhanced differential evolution algorithm with an adaptation of switching crossover strategy (DEASC), and controlled random search methods (CRS4HC, CRS4HCe). We also apply the proposed method to solve parameter identification applications and compare it with enhanced chaotic grasshopper optimization algorithms (ECGOA), self-adaptive differential evolution with dynamic mutation and pheromone strategy (SDE-FMP), and JAYA and its variant methods. The experimental results show that DEAMC is more reliable and gives more accurate results than the compared methods. [ABSTRACT FROM AUTHOR]

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Differential evolution (DE) is a population-based optimization algorithm widely used to solve a variety of continuous optimization problems. The self-adaptive DE algorithm improves the DE by encoding individual parameters to produce and propagate better solutions. This paper proposes a self-adaptive differential evolution algorithm with dynamic fitness-ranking mutation and pheromone strategy (SDE-FMP). The algorithm introduces the dynamical mutation operation using the fitness rank of the individuals to divide the population into three groups and then select groups and their vectors with adaptive probabilities to create a mutant vector. Mutation and crossover operations use the encoded scaling factor and the crossover rate values in a target vector to generate the corresponding trial vector. The values are changed according to the pheromone when the trial vector is inferior in the selection, whereas the pheromone is increased when the trial vector is superior. In addition, the algorithm also employs the resetting operation to unlearn and relearn the dominant pheromone values in the progressing search. The proposed SDE-FMP algorithm using the suitable resetting periods is compared with the well-known adaptive DE algorithms on several test problems. The results show that SDE-FMP can give high-precision solutions and outperforms the compared methods. [ABSTRACT FROM AUTHOR]

In this paper we investigate the parameter estimation of solar photovoltaic (PV) models using the self-adaptive differential evolution algorithm with dynamic fitness-ranking mutation and pheromone strategy (SDE-FMP). The dynamic mutation divides the population into three groups according to fitness values and selects groups and their vectors with adaptive probabilities to create a mutant vector. The algorithm also encodes scaling factor and crossover rate values into target vectors to use in mutation and crossover operations and adjusts them with pheromones in the selection process. Experimental results show that the SDE-FMP algorithm can give the solutions with the lowest errors and is overall competitive with the compared methods regarding the mean errors. [ABSTRACT FROM AUTHOR]

Differential evolution algorithm (DE) is a well-known population-based method for solving continuous optimization problems. It has a simple structure and is easy to adapt to a wide range of applications. However, with suitable population sizes, its performance depends on the two main control parameters: scaling factor (F) and crossover rate (CR). The classical DE method can achieve high performance by a time-consuming tunning process or a sophisticated adaptive control implementation. We propose in this paper an adaptive differential evolution algorithm with a pheromone-based learning strategy (ADE-PS) inspired by ant colony optimization (ACO). The ADE-PS embeds a pheromone-based mechanism that manages the probabilities associated with the partition values of F and CR. It also introduces a resetting strategy to reset the pheromone at a specific time to unlearn and relearn the progressing search. The preliminary experiments find a suitable number of subintervals (ns) for partitioning the control parameter ranges and the reset period (rs) for resetting the pheromone. Then the comparison experiments evaluate ADE-PS using the suitable ns and rs against some adaptive DE methods in the literature. The results show that ADE-PS is more reliable and outperforms several well-known methods in the literature. [ABSTRACT FROM AUTHOR]

Designing an efficient optimization method which also has a simple structure is generally required by users for its applications to a wide range of practical problems. In this research, an enhanced differential evolution algorithm with adaptation of switching crossover strategy (DEASC) is proposed as a general-purpose population-based optimization method for continuous optimization problems. DEASC extends the solving ability of a basic differential evolution algorithm (DE) whose performance significantly depends on user selection of the control parameters: scaling factor, crossover rate and population size. Like the original DE, the proposed method is aimed at e ciency, simplicity and robustness. The appropriate population size is selected to work in accordance with good choices of the scaling factors. Then, the switching crossover strategy of using low or high crossover rates are incorporated and adapted to suit the problem being solved. In this manner, the adaptation strategy is just a convenient add-on mechanism. To verify the performance of DEASC, it is tested on several benchmark problems of various types and di culties, and compared with some well-known methods in the literature. It is also applied to solve some practical systems of nonlinear equations. Despite its much simpler algorithmic structure, the experimental results show that DEASC greatly enhances the basic DE. It is able to solve all the test problems with fast convergence speed and overall outperforms the compared methods which have more complicated structures. In addition, DEASC also shows promising results on high dimensional test functions. [ABSTRACT FROM AUTHOR]

In this research, an improved differential evolution algorithm with a restart technique (DE-R) is designed for solutions of systems of nonlinear equations which often occurs in solving complex computational problems involving variables of nonlinear models. DE-R adds a new strategy for mutation operation and a restart technique to prevent premature convergence and stagnation during the evolutionary search to the basic DE algorithm. The proposed method is evaluated on various real world and synthetic problems and compared with the recently developed methods in the literature. Experiment results show that DE-R can successfully solve all the test problems with fast convergence speed and give high quality solutions. It also outperforms the compared methods. [ABSTRACT FROM AUTHOR]