Mutation Strategies Of Differential Evolution Research Articles

Finding High-Dimensional D-Optimal Designs for Logistic Models via Differential Evolution.

D-optimal designs are frequently used in controlled experiments to obtain the most accurate estimate of model parameters at minimal cost. Finding them can be a challenging task, especially when there are many factors in a nonlinear model. As the number of factors becomes large and interact with one another, there are many more variables to optimize and the D-optimal design problem becomes high-dimensional and non-separable. Consequently, premature convergence issues arise. Candidate solutions get trapped in local optima and the classical gradient-based optimization approaches to search for the D-optimal designs rarely succeed. We propose a specially designed version of differential evolution (DE) which is a representative gradient-free optimization approach to solve such high-dimensional optimization problems. The proposed specially designed DE uses a new novelty-based mutation strategy to explore the various regions in the search space. The exploration of the regions will be carried out differently from the previously explored regions and the diversity of the population can be preserved. The proposed novelty-based mutation strategy is collaborated with two common DE mutation strategies to balance exploration and exploitation at the early or medium stage of the evolution. Additionally, we adapt the control parameters of DE as the evolution proceeds. Using logistic models with several factors on various design spaces as examples, our simulation results show our algorithm can find D-optimal designs efficiently and the algorithm outperforms its competitors. As an application, we apply our algorithm and re-design a 10-factor car refueling experiment with discrete and continuous factors and selected pairwise interactions. Our proposed algorithm was able to consistently outperform the other algorithms and find a more efficient D-optimal design for the problem.

Selective Pressure Strategy in differential evolution: Exploitation improvement in solving global optimization problems

The paper proposes a modification of Differential Evolution mutation strategies with the introduction of selective pressure, which is implemented by applying proportional, rank-based and tournament selection. Based on the new mutation strategies, a new algorithm called LSHADE-SP is proposed, which is a modification of the LSHADE algorithm, with various types of selective pressure implementation. The algorithm is tested against the Congress on Evolutionary Computation (CEC) 2017 competition on real-parameter optimization benchmark functions to demonstrate the advantage of using selective pressure. The comparison shows that applying linear rank, exponential rank and tournament selection deliver faster convergence, if a proper selective pressure is applied. The experiments were conducted for both classical mutation strategies, like rand/1 and best/1, and the best state-of-the art strategies, with various parameter adaptations. The results demonstrate that the algorithm with selective pressure is superior to the best state-of-the-art non-hybrid DE algorithms. The resulting algorithm, LSHADE-SP, obtained one of the best results among the algorithms that were winners of the CEC 2017 competition on real-parameter bound-constrained optimization.

WPD and DE/BBO-RBFNN for solution of rolling bearing fault diagnosis

Abstract A new system of fault diagnosis which combines wavelet packet decomposition (WPD), radical basis function neural network (RBFNN) and a hybrid differential evolution with biogeography-based optimization (DE/BBO) algorithm is designed in this paper to improve the efficiency and accuracy of rolling bearing fault diagnosis. Biogeography-based optimization (BBO) is a new biogeography inspired algorithm, however it has the disadvantages of early-maturing and instable convergence. Combining BBO with differential evolution (DE) and making small modifications for the mutation strategy of DE, an improved DE/BBO algorithm is formed. Firstly, the fault feature vectors of original rolling bearing fault signals are effectively obtained by wavelet packet decomposition and reconstruction. Secondly, the RBF neural network is optimized by DE/BBO algorithm, the fault types of rolling bearing are trained and diagnosed next. The result of MATLAB simulation shows that in contrast to the traditional RBFNN, the fitness and precision of bearing fault diagnosis are higher and the root-mean-square error (RMSE) is lower because of the introduction of DE/BBO algorithm.

An improved multi-population ensemble differential evolution

Abstract Differential evolution (DE) is a population-based stochastic optimization technique that can be applied to solve global optimization problems. The selected mutation strategies and the control parameters can affect the performance of DE. As mutation strategies have significant effects on solving optimization problems, multiple mutation strategies of DE have been developed. Multi-population ensemble DE (MPEDE) realizes an ensemble of multiple strategies, but “DE/rand/1” may be slow at exploitation of the solutions, and the control parameter by applying arithmetic mean in “DE/current-to-pbest/1” may cause premature convergence. Address these issues, an improved multi-population ensemble DE (IMPEDE) is proposed in this paper. IMPEDE proposes a new mutation strategy “DE/pbad-to-pbest/1” instead of the mutation strategy “DE/rand/1” in MPEDE, and the new strategy utilize not only the good solution information(pbest), but also the information of the bad solution (pbad) toward the good solution to balance exploration and exploitation. Furthermore, IMPEDE employs the improved parameter adaptation approach to avoid premature convergence of the “DE/current-to-pbest/1” strategy by adding the weighted Lehmer mean strategy. Experiments have been conducted with CEC2005 and CEC2017 benchmark functions, and the results have demonstrated that IMPEDE outperforms than that of MPEDE and the other four recent proposed DE methods in obtaining the global optimum and accelerating the convergence speed.

Comparison of mutation strategies in Differential Evolution – A probabilistic perspective

Abstract Differential Evolution (DE) is a state-of-the art evolutionary algorithm that solves global optimization problems in a real domain. The algorithm adapts the mutation range and direction by basing these on the differences between individuals in the current population. In this paper, we provide formulas for the expectation vectors and covariance matrices of the mutants' distribution for several operators of differential mutation. The covariance matrices are proportional to each other, which means that the main difference between the analyzed DE operators is the mutation range. This can be conveniently described using a generalized scaling factor g ( F ) , introduced in this paper. Next, we propose transformations of the scaling factors that make the expectation vectors and covariance matrices of the expected mutants' distributions equal to the respective statistics of DE/best/1 or DE/rand/1. These transformations establish a framework for a synthetic investigation of various differential mutation operators and for generalizing the results of parameter tuning. A simulation study based on the CEC′13 benchmark in 10, 30 and 50 dimensions confirms that the transformations do not influence the performance much, especially in the case of DE operators with two difference vectors.

Path Planning of Mobile Robot Based on Hybrid Multi-Objective Bare Bones Particle Swarm Optimization With Differential Evolution

An improved path planning for mobile robots is proposed based on the hybrid multi-objective bare-bones particle swarm optimization with differential evolution. The mathematical model for robot path planning is firstly devised as a tri-objective optimization with three indices, i.e., the path length, the smoothness degree of a path, and the safety degree of a path. Then, a hybrid multi-objective bare bones particle swarm optimization is developed to generate feasible paths by combining infeasible paths blocked by obstacles with feasible paths via improved mutation strategies of differential evolution. In addition, a new Pareto domination with collision constraints is developed to select the personal best position of a particle according to the definition of the collision degree of a path. Simulation results confirm the effectiveness of our algorithm.

Ensemble of differential evolution variants

Differential evolution (DE) is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications. Recently, ensemble methods receive an increasing attention in designing high-quality DE algorithms. However, previous efforts are mainly devoted to the low-level ensemble of mutation strategies of DE. This study investigates the high-level ensemble of multiple existing efficient DE variants. A multi-population based framework (MPF) is proposed to realize the ensemble of multiple DE variants to derive a new algorithm named EDEV for short. EDEV consists of three highly popular and efficient DE variants, namely JADE (adaptive differential evolution with optional external archive), CoDE (differential evolution with composite trial vector generation strategies and control parameters) and EPSDE (differential evolution algorithm with ensemble of parameters and mutation strategies). The whole population of EDEV is partitioned into four subpopulations, including three indicator subpopulations with smaller size and one reward subpopulation with much larger size. Each constituent DE variant in EDEV owns an indicator subpopulation. After every predefined generations, the most efficient constituent DE variant is determined and the reward subpopulation is assigned to that best performed DE variant as an extra reward. Through this manner, the most efficient DE variant is expected to obtain the most computational resources during the optimization process. In addition, the population partition operator is triggered at every generation, which results in timely information sharing and tight cooperation among the component DE variants. Extensive experiments and comparisons have been done based on the CEC2005 and CEC2014 benchmark suit, which shows that the overall performance of EDEV is superior to several state-of-the-art peer DE variants. The success of EDEV reveals that, through an appropriate ensemble framework, different DE variants of different merits can support one another to cooperatively solve optimization problems.

Enhancing differential evolution with random neighbors based strategy

As a powerful evolutionary algorithm for solving the tough global optimization problems, differential evolution (DE) has drawn more and more attention. However, how to make a proper balance between the global and local search is a perplexing question and greatly limit the optimization performance of DE. As we all known, there are two classical mutation strategies in DE, i.e., DE/rand/1 and DE/best/1. In DE/rand/1 strategy, the base vector is chosen from the population randomly, this means its better exploration and poor exploitation. The base vector of DE/best/1 strategy is the best one of the population and the strategy has better exploitation and poor exploration. To overcome these problems, this paper proposed a random neighbor based mutation strategy (DE/neighbor/1). For each individual of the population at each generation, the neighbors are chosen from the population in a random manner. The base vector of DE/neighbor/1 mutation strategy is the best one in the neighbors. On the basis of the new strategy, an enhancing differential evolution with DE/neighbor/1 (RNDE) is proposed. The experimental studies have been tested on 27 widely used benchmark functions and the results have proved that the proposed algorithm is competitive and promising.

Segmentation of weather radar image based on hazard severity using RDE: reconstructed mutation strategy for differential evolution algorithm

Weather describes the condition of our atmosphere during a specific period of time, and climate represents a composite of day to day weather over longer period of time. Climatology attempts to analyze and explain the impact of climate so that the society can plan accordingly. Climatology analysis is often done on radar images representing various climatic conditions. These images contain varying scale of severity for any specific climatic parameter of study. The climatologists often find it convenient to analyze climatic conditions if tools are available to segment the weather images based on the severity scale which is represented by different colors. Segmentation of the weather radar image is also used for automated analysis of weather conditions. Differential evolution (DE) approach instead is used for fast selection of optimal threshold. In present paper, we have applied DE with multilevel thresholding for weather image segmentation which results in minimum computational time and excellent image quality. A new mutation strategy for DE named reconstructed differential evolution (RDE) strategy is suggested for better performance over image segmentation. Using fuzzy entropy and RDE for multilevel thresholding provides better results in comparison with last suggested methods.

New mutation strategies of differential evolution based on clearing niche mechanism

Although differential evolution (DE) algorithms have been widely proposed for tackling various of problems, the trade-off among population diversity, global and local exploration ability, and convergence rate is hard to maintain with the existing strategies. From this respective, this paper presents some new mutation strategies of DE by applying the clearing niche mechanism to the existing mutation strategies. Insteading of using random, best or target individuals as base vector, the niche individuals are utilized in these strategies. As the base vector is from a subpopulation, which is made up of the best individuals in each niche, the base vector can be guided by the global or local best ones. This mechanism is beneficial to the balance among population diversity, search capability, and convergence rate of DE, since it can both enhance the population diversity and search capability. Extensive experimental results indicate that the proposed strategies based on clearing niche mechanism can effectively enhance DE’s performance.

DPD: An intelligent parallel hybrid algorithm for economic load dispatch problems with various practical constraints

The Economic Load Dispatch (ELD) problem has attracted much attention in the field of electric power system. This paper proposes a novel parallel hybrid optimization methodology aimed at solving ELD problem with various generator constraints. The proposed approach combines the Differential Evolution (DE) and Particle Swarm Optimization (PSO). Initially the whole population (in increasing order of fitness) is divided into three groups - Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is called DPD as it uses DE-PSO-DE on a population in parallel manner. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality) have been employed in DPD cycle. Moreover, the suitable mutation strategy for both DEs used in DPD is investigated over a set of 8 popular mutation strategies. Combination of 8 mutation strategies generated 64 different variants of DPD. Top 4 DPDs are investigated through IEEE CEC 2006 functions. Based on the performance analysis, best DPD is reported and further used in solving four different typical test systems of ELD problem. Numerical and graphical results indicate the efficiency, convergence characteristic and robustness of proposed DPD.

Parameters Identification of Fluxgate Magnetic Core Adopting the Biogeography-Based Optimization Algorithm.

The main part of the magnetic fluxgate sensor is the magnetic core, the hysteresis characteristic of which affects the performance of the sensor. When the fluxgate sensors are modelled for design purposes, an accurate model of hysteresis characteristic of the cores is necessary to achieve good agreement between modelled and experimental data. The Jiles-Atherton model is simple and can reflect the hysteresis properties of the magnetic material precisely, which makes it widely used in hysteresis modelling and simulation of ferromagnetic materials. However, in practice, it is difficult to determine the parameters accurately owing to the sensitivity of the parameters. In this paper, the Biogeography-Based Optimization (BBO) algorithm is applied to identify the Jiles-Atherton model parameters. To enhance the performances of the BBO algorithm such as global search capability, search accuracy and convergence rate, an improved Biogeography-Based Optimization (IBBO) algorithm is put forward by using Arnold map and mutation strategy of Differential Evolution (DE) algorithm. Simulation results show that IBBO algorithm is superior to Genetic Algorithm (GA), Particle Swarm Optimization (PSO) algorithm, Differential Evolution algorithm and BBO algorithm in identification accuracy and convergence rate. The IBBO algorithm is applied to identify Jiles-Atherton model parameters of selected permalloy. The simulation hysteresis loop is in high agreement with experimental data. Using permalloy as core of fluxgate probe, the simulation output is consistent with experimental output. The IBBO algorithm can identify the parameters of Jiles-Atherton model accurately, which provides a basis for the precise analysis and design of instruments and equipment with magnetic core.

Constrained differential evolution optimization for underwater glider path planning in sub-mesoscale eddy sampling

This paper presents an approach for tackling constrained underwater glider path planning (UGPP), where the feasible path area is defined as a corridor around the border of an ocean eddy. The objective of the glider here is to sample the oceanographic variables more efficiently while keeping a bounded trajectory. Therefore, we propose a solution based on differential evolution (DE) algorithm mechanisms, including in its configuration self-adaptation of control parameters, population size reduction, ϵ-constraint handling with adjustment, and mutation based on elitistic best vector. Different aspects of this DE configuration are studied for the constrained UGPP challenge, on a prepared benchmark set comprised of 28 different specialized scenarios. The DE configurations were tested over a benchmark set over 51 independent runs for each DE configuration aspect. Comparison and suitability for the combination of these mechanisms is reported, through the per-scenario and aggregated statistical performance differences, including different constraint handling definition strategies, different DE mutation strategies’ configurations, and population sizing parameterizations. Our proposed solution outranked all other compared algorithms, keeping a trajectory within the limits with 100% success rate in all physically feasible scenarios; on average, it improved the randomly initialized trajectories fitness by roughly 50%, even reaching perfect fitness (all-around, 360-degree eddy corridor sampling) in some scenarios.

Hybrid heuristic search method for design of digital IIR filter with conflicting objectives

The design of digital IIR filter design by using evolutionary algorithms has gained much attention in the previous years. Most of the researchers treated the design problem as a single objective optimization problem and applied the techniques for minimizing the magnitude response error. In this paper the design of filter is treated as a multi-objective problem by simultaneously minimizing the magnitude response error, linear phase response error and optimal order along with meeting the stability criterion. A hybrid heuristic search technique having differential evolution (DE) method as a global search technique and binary successive approximation based evolutionary search method as a local search technique has been proposed. Based on mean value of population, new mutation strategies have been proposed. The above proposed hybrid heuristic search technique has been applied effectively to solve the multi-parameter and multi-objective optimization problem of low-pass, high-pass, band-pass and band-stop digital IIR filter design. The obtained results reveal that the proposed technique with new proposed mutation strategies performs better than the already existing mutation strategies of DE and other algorithms applied by other researchers for the design of digital IIR filter.

A new ensemble algorithm of differential evolution and backtracking search optimization algorithm with adaptive control parameter for function optimization

Article history: Received July 21 2015 Received in Revised Format August 16 2015 Accepted September 8 2015 Available online September 12 2015 Differential evolution (DE) is an effective and powerful approach and it has been widely used in different environments. However, the performance of DE is sensitive to the choice of control parameters. Thus, to obtain optimal performance, time-consuming parameter tuning is necessary. Backtracking Search Optimization Algorithm (BSA) is a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. An ensemble algorithm called E-BSADE is proposed which incorporates concepts from DE and BSA. The performance of E-BSADE is evaluated on several benchmark functions and is compared with basic DE, BSA and conventional DE mutation strategy. Also the performance results are compared with state of the art PSO variant. © 2016 Growing Science Ltd. All rights reserved

A novel hybrid optimizer for solving Economic Load Dispatch problem

Abstract Economic Load Dispatch (ELD) is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a novel hybrid algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO) proposed. It is based on ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups –- Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD because it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-Redundant Search (to improve the solution quality) have been employed in DPD cycle. Many mutation strategies of DE have emerged in the last couple of years. However, its actual ability has not been well studied yet because every mutation strategy has its own pros and cons. Therefore suitable mutation strategy for both DEs used in DPD is investigated over a set of 8 popular mutation strategies. Combination of 8 mutation strategies is generated 64 different variants of DPD. Top 4 DPDs are investigated through CEC 2006 functions out of 64 different variants of DPDs. Based on the ‘performance’ analysis best DPD is reported using CEC 2006 and 5 Engineering Design Problems. Further best DPD is considered for solving ELD problem. Results reveal that the superiority of the proposed DPD.

Optimization with a novel hybrid algorithm and applications

A novel hybrid algorithm (DPD) by combination of Differential Evolution (DE) and Particle Swarm Optimization (PSO) is proposed for solving unconstrained and constrained optimization problems. It is based on ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups—Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to maintain diversity in the population) have been employed in DPD cycle. Since the performance of DE is sensitive to the choice of the mutation strategy. Therefore suitable mutation strategy for both DEs used in DPD is investigated over a set of 8 popular mutation strategies. Combination of 8 mutation strategies is generated 64 different variants of DPD. Top 4 DPDs are investigated through 20 benchmark function. Based on the ‘performance’ analysis best DPD is reported using 20 unconstrained benchmark functions, 13 constrained benchmark functions, 6 unconstrained and 3 constrained engineering design problems. To show superiority and effectiveness, best DPD is compared with various state-of-the-art approaches in terms of quality of solutions.

An Ensemble Differential Evolution for Numerical Optimization

The success of differential evolution (DE) in solving a specific problem crucially depends on appropriately choosing generation strategies and control parameter values. The mutation strategies of DE are classified into two groups: DE/rand/k without best solution and DE/best/k with best solution. The proposed algorithm utilizes two mutation strategies. The first one is from DE/rand/k and the second one is from DE/best/k. The proposed algorithm uses two control parameter settings. It randomly combines them to generate trial vectors. The novel mechanism improves the convergence rate of DE and maintains diversity of the population. The performance of the proposed algorithm is extensively evaluated on all the CEC2005 test functions and compares favorably with the several DE variants.

Efficient DE-based symbiotic cultural algorithm for neuro-fuzzy system design

This study proposes a differential-evolution-based symbiotic cultural algorithm (DESCA) for the implementation of neuro-fuzzy systems (NFS) to solve nonlinear control system problems. DESCA adopts symbiotic evolution to decompose a fuzzy system into multiple fuzzy rules as multiple subpopulations. In addition, DESCA randomly selects fuzzy rules from different subpopulations that combine into a complete solution whose performance is be evaluated. Moreover, DESCA uses various mutation strategies of differential evolution as five knowledge sources in the belief space. These knowledge sources influence the population space in the cultural algorithm and can be used as models to guide the feasible search space. Finally, the proposed algorithm is applied to various simulations. The results demonstrate the effectiveness of this approach.

An efficient hybrid technique for numerical optimization and applications

Real World Optimization Problems is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a hybrid algorithm of two popular heuristics namely Differential Evolution (DE) and Particle Swarm Optimization (PSO) engaged on a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD as it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality) have been additionally employed in DPD cycle. Moreover, the robustness of the mutation strategies of DE have been well studied and suitable mutation strategies for both DEs (for DPD) are investigated over a set of existing 8 popular mutation strategies which results 64 variants of DPD. The top DPD is further tested through the test functions of CEC2006, CEC2010 and 5 Engineering Design Problems. Also it is used to solve CEC2011 Real World Optimization problems. An excellent efficiency of the recommended DPD is confirmed over the state-of-the-art algorithms.