Differential Evolutionary Particle Swarm Optimization (DEEPSO): A Successful Hybrid

Abstract

This paper explores, with numerical case studies, the performance of an optimization algorithm that is a variant of EPSO, the Evolutionary Particle Swarm Optimization method. EPSO is already a hybrid approach that may be seen as a PSO with self-adaptive weights or an Evolutionary Programming approach with a self-adaptive recombination operator. The new hybrid DEEPSO retains the self-adaptive properties of EPSO but borrows the concept of rough gradient from Differential Evolution algorithms. The performance of DEEPSO is compared to a well-performing EPSO algorithm in the optimization of problems of the fixed cost type, showing consistently better results in the cases presented.

Despacho económico en microredes con penetración de energía renovable usando algoritmo de punto interior y restricciones lineales

“…Para la restricción de pérdidas y demanda se usaron diferentes coeficientes de pérdidas analizados en [6], [7], [8], [9], [10]. Especificamente en [10] se muestran los resultados de cálculo de las pérdidas cuando se usan los coeficientes de kron, los incrementales y los coeficientes obtenidos después de aplicar el algoritmo de optimización heurística DEEPSO (Differential Evolutionary Particle Swarm Optimization) que los calcula para diferentes casos de variación de demanda y de generación [11], [12], [13]. De esta manera, el presente artículo es una continuación del trabajo presentado en [10] extendiendo la formulación a su aplicación en el despacho económico y formulando unas restricciones lineales a partir de las restricciones tradicionales (sección 2).…”

Enhanced Forecasting Approach for Electricity Market Prices and Wind Power Data Series in the Short-Term

“…: (9) From Equations (5)- (9), is the new position of the particle, is the new velocity found, is a diagonal binary matrix with a value of 1 when the probability is and 0 when the probability is 1 , * are the mutated weights of inertia, memory, and cooperation of the swarm, given by a learning parameter (fixed or mutated), and 0,1 is a random Gaussian variable with 0 mean and variance 1. Also, * is the global position provided by the new weight , which is collected from a diagonal matrix, having a self-adaptive feature, and in this sense, it is a mutated element [48,49]. Components X and X guarantee that a suitable extraction really happens, considering macrogradient points in a descending direction depending on the structured comparison of and .…”

“…Also, b * g is the global position provided by the new weight w g , which is collected from a diagonal matrix, having a self-adaptive feature, and in this sense, it is a mutated element [48,49]. Components X i r1 and X i r2 guarantee that a suitable extraction really happens, considering macro-gradient points in a descending direction depending on the structured comparison of f X i r1 and f X i r2 .…”

“…DEEPSO is a successful hybrid combination of the EPSO model [44,45], which is itself a hybrid combination of its ancestor model, namely PSO, where weight factors have self-adaptive features, with evolutionary programming, which brings self-adaptive operators [48], and a differential evolution algorithm, which provides a new solution from the current particle of the swarm by adding a fraction difference between two other points found from the previously evaluated swarm [49]. The DEEPSO schema is similar to EPSO [50]; however, the movement rule Equation (6) has new notation: …”

“…The proposed HWDA approach was performed on a standard PC equipped with an Intel Core i7-3537U, 2 GHz CPU and 4 GB of RAM with Windows 10 and the MATLAB ® 2016a platform. The authors used the ANFIS and WT structure functions available in MATLAB toolboxes, while DEEPSO was programmed from scratch in MATLAB considering the information available in [49][50][51][52]. …”