Conventional Differential Evolution Algorithm Research Articles

A Hybrid Chaotic-Based Multiobjective Differential Evolution Technique for Economic Emission Dispatch Problem

The economic emission dispatch problem (EEDP) is a nonconvex and nonsmooth multiobjective optimization problem in the power system field. Generally, fuel cost and total emissions of harmful gases are the problem objective functions. The EEDP decision variables are output powers of thermal generating units (TGUs). To make the EEDP problem more practical, valve point loading effects (VPLEs), prohibited operation zones (POZs), and power balance constraints should be included in the problem constraints. In order to solve this complex and constrained EEDP, a new multiobjective optimization technique combining the differential evolution (DE) algorithm and chaos theory is proposed in this study. In this new multiobjective optimization technique, a nondomination sorting principle and a crowding distance calculation are employed to extract an accurate Pareto front. To avoid being trapped in local optima and enhance the conventional DE algorithm, two different chaotic maps are used in its initialization, crossover, and mutation phases instead of random numbers. To overcome difficulties caused by the equality constraint describing the power balance constraint, a slack TGU is defined to compensate for the gap between the total generation and the sum of the system load and total power losses. Then, the optimal power outputs of all thermal units except the slack unit are determined by the suggested optimization technique. To assess the effectiveness and applicability of the proposed method for solving the EEDP, the six-unit and ten-unit systems are used. Moreover, obtained results are compared with other new optimization techniques already developed and tested for the same purpose. The superior performance of the ChMODE is also evaluated by using various metrics such as inverted generational distance (IGD), hyper-volume (HV), spacing metric (SM), and the average satisfactory degree (ASD).

Particle swarm-differential evolution algorithm with multiple random mutation

Differential evolution (DE) algorithm has attracted considerable attention because of its effectiveness and simplicity. However, previous studies have validated that DE still suffers from some limitations such as premature convergence and slow convergence especially dealing with multimodal optimization problems. To address these concerning issues, we propose an innovative optimization method named particle swarm-differential evolution algorithm with multiple random mutation (MRPSODE) in this paper. The proposed MRPSODE algorithm is based on multiple random mutation framework cooperating with mean particle swarm mutation strategy, DE/current-to-rand/1 mutation strategy and disturbance strategy. Firstly, we incorporate the modified mean particle swarm mutation strategy into DE algorithm to improve the global convergence ability. Secondly, DE/current-to-rand/1 mutation strategy is adopted to increase the population diversity and produce perturbations to avoid the algorithm trapping into a local optimum. Thirdly, we propose a disturbance strategy to help the population escape from local optima, so as to enhance the exploration ability. Finally, to ensure that the proposed algorithm can get satisfactory solutions with a fast convergence speed, we design a multiple random mutation framework, in which these three mutation strategies can effectively play their advantages and make up for the shortcomings of others. To evaluate the performance of the proposed algorithm, three different experiments are constructed on twenty-nine classical benchmark functions. The simulation results demonstrate that, (1) MRPSODE significantly outperforms conventional PSO and DE algorithms, (2) MRPSODE can achieve better performance than nine well-known DE variants in terms of solution quality and robustness, (3) MRPSODE is superior to nine latest heuristic-based algorithms. Furthermore, MRPSODE is successfully applied to seven typical constrained optimization problems and performs better than almost all compared methods.

Differential evolution method integrated with a fuzzy decision-making mechanism and Virtual Mutant agent: Theory and application

The current study deals with upgrading the Differential Evolution (DE) method by equipping it with a novel fuzzy decision-making strategy and a new auxiliary agent called Virtual Mutant. The new algorithm is called Fuzzy Differential Evolution incorporated Virtual Mutant (FDEVM) The presented fuzzy strategy employs two nine-rule mapping mechanisms to adjust the internal parameters of the algorithm considering governing conditions of the current problem. Also, the Virtual Mutant providing reasonable attractive and compulsive effects on the other agents, plays important role in increasing the efficiency of the algorithm. These two new enhancements (i.e., adding the fuzzy module and Virtual Mutant) converts the conventional DE algorithm to a self-adaptive and parameter-free approach which can dynamically adjust its search behavior during the optimization process. Consequently, the search performance of the presented FDEVM is tested on a suite of unconstrained mathematical functions and constrained engineering problems. The outcomes are reported and compared with those obtained by six other well-established search techniques. The acquired results indicate that the proposed method could improve the search process in the terms of computational cost, stability and accuracy.

Optimum sizing of members of truss structures using direct design and a self-adaptive mutationdifferential evolution

Direct design using nonlinear inelastic analysis has been recently enabled for structural design as this approach can directly predict the behaviour of a structure as a whole, which eliminates capacity checks for individual structural members. However, the use of direct design is often accompanied by excessive computational efforts, especially for complicated structural design problems such as optimization or reliability analysis. In this study, we introduce an efficient method for the sizing optimization of truss structures employing nonlinear inelastic analysis for the direct design of structures. The objective function is the total weight of the structure while the strength and serviceability constraints are evaluated with nonlinear inelastic analysis. To save computational cost, an improved differential evolution (DE) algorithm is employed. Compared to the conventional DE algorithm, the proposed method has two major improvements: (1) a self-adaptive mutation strategy based on the p-best method to enhance the balance between global and local searches and (2) use of the multi-comparison technique (MCT) to reduce redundant structural analyses. The numerical results of a 72-bar truss case study demonstrate that the performance of the proposed method has significant advantages over the traditional DE method.

Energy-efficient train trajectory optimization based on improved differential evolution algorithm and multi-particle model

Urban rail transit is an efficient public transport, and reducing their energy consumption is beneficial to climate change and sustainable development. Current researches in metro train trajectory optimization are mainly based on the single-particle train operation model, and the selection of energy-saving operation strategy under time-varying passenger flow is not taken into consideration. Therefore, considering the practical line environment and uncertain trainload simultaneously, this paper establishes a multi-particle operation model and develops a new optimization method based on mutated dichotomy and differential evolutionary algorithm to solve the model. Then, the influence of various passenger flow and line information on the train trajectory optimization is analyzed from the perspective of trainload capacity based on the proposed method, and the selection basis of the optimal energy-saving train operation strategy was determined. Finally, a case study was conducted in the Nanning Rail Transit Line 1 and Line 5, respectively. The results show that the proposed method has strong efficiency for energy conservation and better optimization performance than the conventional differential evolution algorithm in solving train trajectory optimization problem. And the simulation results of the Line 5, which is a fully automatic operation line, also verified the reliability of the selection basis.

A Self-Adaptive Differential Evolution Algorithm for Scheduling a Single Batch-Processing Machine With Arbitrary Job Sizes and Release Times.

Batch-processing machines (BPMs) can process a number of jobs at a time, which can be found in many industrial systems. This article considers a single BPM scheduling problem with unequal release times and job sizes. The goal is to assign jobs into batches without breaking the machine capacity constraint and then sort the batches to minimize the makespan. A self-adaptive differential evolution algorithm is developed for addressing the problem. In our proposed algorithm, mutation operators are adaptively chosen based on their historical performances. Also, control parameter values are adaptively determined based on their historical performances. Our proposed algorithm is compared to CPLEX, existing metaheuristics for this problem and conventional differential evolution algorithms through comprehensive experiments. The experimental results demonstrate that our proposed self-adaptive algorithm is more effective than other algorithms for this scheduling problem.

Novel binary differential evolution algorithm for knapsack problems

The capability of the conventional differential evolution algorithm to solve optimization problems in continuous spaces has been well demonstrated and documented in the literature. However, differential evolution has been commonly considered inapplicable for several binary/permutation-based real-world problems because of its arithmetic reproduction operator. Moreover, many limitations of the standard differential evolution algorithm, such as slow convergence and becoming trapped in local optima, have been defined. In this paper, a novel technique which makes a simple differential evolution algorithm suitable and very effective for solving binary-based problems, such as binary knapsack ones, is proposed. It incorporates new components, such as representations of solutions, a mapping method and a diversity technique. Also, a new efficient fitness evaluation approach for calculating and, at the same time, repairing knapsack candidate solutions, is introduced. To assess the performance of this new algorithm, four datasets with a total of 44 instances of binary knapsack problems are considered. Its performance and those of 22 state-of-the-art algorithms are compared, with the experimental results demonstrating its superiority in terms of both the quality of solutions and computational times. It is also capable of finding new solutions which are better than the current best ones for five large knapsack problems.

Hybrid differential evolution algorithm and genetic operator for multi-trip vehicle routing problem with backhauls and heterogeneous fleet in the beverage logistics industry

Logistics is increasingly challenging because of increased competition and the uncertainty introduced by globalization. The drinks distribution system considered here uses glass bottles for soft drinks to deliver to all customers who need soft drinks in glass bottles, before making any pickups of empty glass bottles from clients to return to the company. This study aims at both an integer linear programming formulation and a novel hybrid differential evolution algorithm involving a genetic operator with fuzzy logic controller, for solving the multi-trip vehicle routing problem with backhauls and a heterogeneous fleet. The objective function is to minimize total cost, which is related to distance travelled. For validation, we designed numerical experiments to compare the proposed approaches with LINGO computational software, using the conventional differential evolution algorithm and differential evolution with selected genetic operator and fuzzy logic controller in real settings. The experimental results demonstrate the practical viability of the proposed approaches.

Optimization of nonlinear inelastic steel frames considering panel zones

In this article, an efficient methodology is developed to optimize nonlinear steel frames under several load combinations. For that purpose, inelastic advanced analyses of steel frames are performed using plastic hinge beam–column elements to reduce computational efforts. An improved differential evolution (DE) algorithm is utilized as a global optimizer to refine the solution accuracy and enhance the convergence speed. Compared to the conventional DE algorithm, this newly developed method provides four major improvements such as: (1) a new mutation strategy based on the p-best method; (2) the multi-comparison technique (MCT) to decrease the number of unnecessary objective function evaluations; (3) a promising individual method (PIM) to choose trial individuals; and (4) a trial matrix containing all evaluated individuals to avoid objective function evaluations of duplicate individuals. Furthermore, panel zones are taken account of optimum design for the first time. Doubler plates are designed to prevent panel-zone shear deformations. Three mid- to large-size steel frames considering several load combinations required by AISC-LRFD are considered. Five new and efficient meta-heuristic algorithms are employed for comparison.

Improved Differential Evolution Algorithm for Multi-Target Response Inversion Detected by a Portable Transient Electromagnetic Sensor

The superimposed response of multi-target causes difficulty in locating and characterizing each target when detecting unexploded ordnance with a portable transient electromagnetic sensor, constructed with a single-layer transmitting coil and five three-component receiving coils. Differential evolution (DE) algorithm is improved here with Gram–Schmidt orthogonalization and position rearrangement for superimposed response inversion based on the multisource model, which represents the multi-target response with a set of magnetic dipoles distributed over the interrogated area. The Gram–Schmidt orthogonalization turns the coefficient matrix of each target into an orthonormal basis. Accordingly, the best magnetic polarization tensor can be directly extracted from the superimposed response without inverting large and potentially ill-conditioned matrices. The position rearrangement groups the positions of individuals in the contemporary population to maximize the likelihood that the positions in the same group belong to the same target. The convergence speed of multi-target inversion is accelerated with the crossover operation of DE algorithm performed within the groups. Simulated experiment results show that the error in estimated position and characteristic response for improved DE algorithm is only 10% of that of the conventional DE algorithm. Field experiment is also conducted, and its results show that the error in estimated position for improved DE algorithm is only 20% of that of the conventional DE algorithm. The improved DE algorithm can accurately estimate the position and characteristic response of each target from superimposed response.

An improved differential evolution algorithm for learning high-fidelity quantum controls

Precisely and efficiently designing control pulses for the preparation of quantum states and quantum gates are the fundamental tasks for quantum computation. Gradient-based optimal control methods are the routine to design such pulses. However, the gradient information is often difficult to calculate or measure, especially when the system is not well calibrated or in the presence of various uncertainties. Gradient-free evolutionary algorithm is an alternative choice to accomplish this task but usually with low-efficiency. Here, we design an efficient mutation rule by using the information of the current and the former individuals together. This leads to our improved differential evolution algorithm, called daDE. To demonstrate its performance, we numerically benchmark the pulse optimization for quantum states and quantum gates preparations on small-scale NMR system. Further numerical comparisons with conventional differential evolution algorithms show that daDE has great advantages on the convergence speed and robustness to several uncertainties including pulse imperfections and measurement errors.

Implementation of self adaptive mutation factor and cross-over probability based differential evolution algorithm for node localization in wireless sensor networks

Node localization or positioning is essential for many position aware protocols in a wireless sensor network. The classical global poisoning system used for node localization is limited because of its high cost and its unavailability in the indoor environments. So, several localization algorithms have been proposed in the recent past to improve localization accuracy and to reduce implementation cost. One of the popular approaches of localization is to define localization as a least square localization (LSL) problem. During optimization of LSL problem, the performance of the classical Gauss–Newton method is limited because it can be trapped by local minima. By contrast, differential evolution (DE) algorithm has high localization accuracy because it has an ability to determine global optimal solution to the LSL problem. However, the convergence speed of the conventional DE algorithm is low as it uses fixed values of mutation factor and cross-over probability. Thus, in this paper, a self-adaptive mutation factor cross-over probability based differential evolution (SA-MCDE) algorithm is proposed for LSL problem to improve convergence speed. The SA-MCDE algorithm adaptively adjusts the mutation factor and cross-over probability in each generation to better explore and exploit the global optimal solution. Thus, improved localization accuracy with high convergence speed is expected from the SA-MCDE algorithm. The rigorous simulation results conducted for several localization algorithms declare that the propose SA-MCDE based localization has about (40–90) % more localization accuracy over the classical techniques.

Automatic generation control of a multi-area power system with renewable energy source under deregulated environment: adaptive fuzzy logic-based differential evolution (DE) algorithm

In this paper, an adaptive fuzzy logic-based differential evolution (DE) algorithm is proposed to optimize the gain of proportional–integral–derivative (PID) controllers. Using the proposed controller, the speed regulation parameters are tuned. Here, fuzzy logic is used to generate the controlled range of population set to DE algorithm. So that most favourable offspring population is created and the drawback of conventional DE algorithm is reduced. Using the proposed controller, the approximation errors and the external disturbance effects are minimized. The proposed method is implemented in MATLAB/Simulink working platform and the effectiveness is verified by multi-source two-area power generation system with renewable energy source. Three test cases are used to evaluate the simulation behaviour of proposed method. Simulation results of the tested power systems prove the effectiveness of the proposed load frequency control and proved its superiority over traditional PID controller, DE-tuned PID controller and fuzzy logic—DE algorithm-based PID controller. Comparison results show that proposed method has less overshoot, undershoot and fast settling time.

A State Evaluation Adaptive Differential Evolution Algorithm for FIR Filter Design

Due to conventional differential evolution algorithm is often trapped in local optima and premature convergence in high dimensional optimization problems, a State Evaluation Adaptive Differential Evolution algorithm (SEADE) is proposed in this paper. By using independent scale factor on each dimension of optimization problem, and evaluating the distribution of population on each dimension, the SEADE correct the control parameters adaptively. External archive and a moving window evaluation mechanism on evolution state are introduced in SEADE to detect whether the evolution is stagnation or not, and with the help of opposition-based population, the algorithm can jump out of local optima basins. The results of experiments on several benchmarks show that the proposed algorithm is capable of improving the search performance of high dimensional optimization problems. And it is more efficient in design FIR digital filter using SEADE than conventional method like Parks-McClellan algorithm.

Supply allocation: bi-level programming and differential evolution algorithm for Natural Disaster Relief

Delivering relief supplies to victims of natural disasters is a very complicated process faced with many challenges: damaged road network, high demand for various materials, scarcity of resources, multi-supply and multi-demand sites, limited transport capacity, etc. Traditionally, outreach maximization is the focus of emergency relief. In this research, we propose a bi-level programming model which takes the aforementioned challenges into full account. We consider two objectives: minimizing the distribution time, and maximizing the allocation fairness. Because the problem is NP-hard, we design an improved differential evolution (IDE) algorithm and numerically compare it with several conventional differential evolution algorithms, including CoDE, SaDE, JADE and JDE. We found that the proposed IDE outperforms the existing algorithms. The feasibility and validity of the proposed model and the IDE algorithm are verified by applying them to the 2008 Wenchuan earthquake in western China.

An Improved Differential Evolution Algorithm and Its Application to Large-Scale Artificial Neural Networks

A new differential evolution (DE) algorithm is presented in this paper. The proposed algorithm monitors the evolutionary progress of each individual and assigns appropriate control parameters depends on whether the individual is successfully evolved or not. We conducted the performance evaluation on CEC 2014 benchmark problems and confirmed that the proposed algorithm outperformed than the conventional DE algorithm. In addition, we apply the proposed DE algorithm as an optimization technique of training large scale multilayer perceptron. We conducted the performance evaluation on an artificial neural network that has approximately 1,000 weights and confirmed again that the proposed algorithm performed better than the conventional DE algorithm. As a result, we proposed a new DE algorithm that has better optimization performance for solving large-scale global optimization problems.

Parameters extraction of double diode photovoltaic module’s model based on hybrid evolutionary algorithm

Accurate modeling of photovoltaic (PV) modules is helpful in designing and assessing the energy production of PV systems. A new version of the differential evolution (DE) algorithm, called differential evolution with integrated mutation per iteration (DEIM), is proposed in this study to extract the seven parameters of a double-diode PV module model. This algorithm applies the attraction–repulsion concept of an electromagnetism-like algorithm to boost the mutation operation of the conventional DE algorithm. Moreover, a new adaptive strategy is proposed to tune mutation scaling and crossover rate for each generation. The proposed model is validated through experimental data and other models, which have been proposed in literature using various statistical errors. Results show that DEIM exhibits high accuracy and fast convergence speed compared with other methods. The average root mean square error, mean bias error, and absolute error at maximum power point of the proposed model are 1.713%, 0.149%, and 4.515%, respectively.

Adaptive Differential Evolution by Adjusting Subcomponent Crossover Rate for High-Dimensional Waveform Inversion

In this letter, a new adaptive differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional DE algorithms, individuals are treated as a whole and share the same fitness function and parameters. However, conventional DE algorithms have ignored the huge difference among the subcomponents in an individual and are not effective for high-dimensional problems. Therefore, for high-dimensional problems, we expand the unit of crossover rate from the whole individual to its subcomponents and propose a new adaption algorithm by adjusting the crossover rate of each subcomponent. In our algorithm, both kinds of crossover rate, including individual crossover rate and subcomponent crossover rate, play important roles in crossover operation. Based on local fitness function, the subcomponent crossover rate is adaptively obtained to improve the efficiency of crossover operation. On the other hand, the individual crossover rate is used to prevent the population diversity from decreasing in crossover operation. We embed the adaption algorithm into cooperative coevolutionary DE (CCDE) and propose a new adaptive DE by adjusting the subcomponent crossover rate named CRsADE. We have conducted experiments on waveform inversion to test the performance of the proposed algorithm. The results show that CRsADE performs better than CCDE significantly both on convergence speed and accuracy. In order to estimate the validity of CRsADE, we have also applied it to real seismic data.

Production Scheduling Oriented to Energy Consumption Optimization for Process Industry Based on Self-adaptive DE Algorithm

Considering the production scheduling problem of processes industry and the disadvantages of conventional differential evolution algorithm, a method of production scheduling oriented to energy consumption optimization for process industry is proposed in this paper, which is based on self-adaptive differential evolution algorithm. Based on the analysis of production scheduling problems for processes industry, a production scheduling model is established, whose goal is to obtain the minimum of total process energy consumption. Since the basic differential evolution algorithm has the disadvantage that the search performance is very sensitive to the parameter settings, the self-adaptive control evolution strategy are used to control the parameters scale factor(F) and crossover probability(CR) to improve the global search ability and convergence speed. A practical production scheduling problem is taken as an example here, the established model and self-adaptive differential evolution algorithm are adopted to realize scheduling simulation with the minimum total process energy consumption. The simulation results show that the production scheduling method oriented to energy consumption optimization is superior to the production scheduling method oriented to process time optimization, and it can realize the goal of reducing energy consumption.

Hybrid biogeography-based optimisation for optimal power flow incorporating FACTS devices

This paper presents hybrid biogeography–based optimisation (BBO) technique to solve optimal power flow (OPF) in power system incorporating flexible AC transmission systems (FACTS). The proposed hybrid method combines the BBO algorithm with the differential evolution (DE) to improve the performance of the conventional BBO and DE algorithms. Here, BBO is the main optimiser, while the DE is used to fine tune the solution of the BBO algorithm. Two types of FACTS devices namely, thyristor–controlled series capacitor (TCSC) and thyristor–controlled phase shifter (TCPS) are considered in this paper. The proposed method is implemented with MATLAB and tested on modified IEEE 30–bus system in five different cases. The simulation results show that the proposed HDE–BBO algorithm is effective, fast and accurate in finding the optimal parameter settings for FACTS devices to solve OPF problems. The proposed HDE–BBO method gives better solution quality compared to particle swarm optimisation with inertia weight approach (PSOIWA), real coded genetic algorithm (RGA), differential evolution (DE) and conventional BBO. The simulation study also shows that FACTS devices are capable of providing an economically attractive solution to power system problems.