Standard Differential Evolution Research Articles

An improved adaptive differential evolution algorithm for single unmanned aerial vehicle multitasking

Single unmanned aerial vehicle (UAV) multitasking plays an important role in multiple UAVs cooperative control, which is as well as the most complicated and hardest part. This paper establishes a three-dimensional topographical map, and an improved adaptive differential evolution (IADE) algorithm is proposed for single UAV multitasking. As an optimized problem, the efficiency of using standard differential evolution to obtain the global optimal solution is very low to avoid this problem. Therefore, the algorithm adopts the mutation factor and crossover factor into dynamic adaptive functions, which makes the crossover factor and variation factor can be adjusted with the number of population iteration and individual fitness value, letting the algorithm exploration and development more reasonable. The experimental results implicate that the IADE algorithm has better performance, higher convergence and efficiency to solve the multitasking problem compared with other algorithms.

Cost Minimizations and Performance Enhancements of Power Systems Using Spherical Prune Differential Evolution Algorithm Including Modal Analysis

A novel application of the spherical prune differential evolution algorithm (SpDEA) to solve optimal power flow (OPF) problems in electric power systems is presented. The SpDEA has several merits, such as its high convergence speed, low number of parameters to be designed, and low computational procedures. Four objectives, complete with their relevant operating constraints, are adopted to be optimized simultaneously. Various case studies of multiple objective scenarios are demonstrated under MATLAB environment. Static voltage stability index of lowest/weak bus using modal analysis is incorporated. The results generated by the SpDEA are investigated and compared to standard multi-objective differential evolution (MODE) to prove their viability. The best answer is chosen carefully among trade-off Pareto points by using the technique of fuzzy Pareto solution. Two power system networks such as IEEE 30-bus and 118-bus systems as large-scale optimization problems with 129 design control variables are utilized to point out the effectiveness of the SpDEA. The realized results among many independent runs indicate the robustness of the SpDEA-based approach on OPF methodology in optimizing the defined objectives simultaneously.

Comparison of a novel dominance-based differential evolution method with the state-of-the-art methods for solving multi-objective real-valued optimization problems

Differential Evolution algorithm (DE) is a well-known nature-inspired method in evolutionary computations scope. This paper adds some new features to DE algorithm and proposes a novel method focusing on ranking technique. The proposed method is named as Dominance-Based Differential Evolution, called DBDE from this point on, which is the improved version of the standard DE algorithm. The suggested DBDE applies some changes on the selection operator of the Differential Evolution (DE) algorithm and modifies the crossover and initialization phases to improve the performance of DE. The dominance ranks are used in the selection phase of DBDE to be capable of selecting higher quality solutions. A dominance-rank for solution X is the number of solutions dominating X. Moreover, some vectors called target vectors are used through the selection process. Effectiveness and performance of the proposed DBDE method is experimentally evaluated using six well-known benchmarks, provided by CEC2009, plus two additional test problems namely Kursawe and Fonseca & Fleming. The evaluation process emphasizes on specific bi-objective real-valued optimization problems reported in literature.
 Likewise, the Inverted Generational Distance (IGD) metric is calculated for the obtained results to measure the performance of algorithms. To follow up the evaluation rules obeyed by all state-of-the-art methods, the fitness evaluation function is called 300.000 times and 30 independent runs of DBDE is carried out. Analysis of the obtained results indicates that the performance of the proposed algorithm (DBDE) in terms of convergence and robustness outperforms the majority of state-of-the-art methods reported in the literature

A novel wrapper-based feature subset selection method using modified binary differential evolution algorithm

In classification problems, normally there exists a large number of features, but not all of them contributing to the improvement of classification performance. These redundant features make the classification problem time consuming and often result in poor performance. Feature selection methods have been proposed to reduce the number of features, minimize computational cost, and maximize classification accuracy. As a wrapper-based approach, evolutionary algorithms have been widely applied in feature subset selection tasks. However, some of them trap into local minima, especially when the number of features increases, while others are not efficient in computational time. This paper proposes a Modified Differential Evolution (DE) approach to Feature Selection (MDEFS) by utilizing two new mutation strategies to create a feasible balance between exploration and exploitation and maintain the classification performance in an acceptable range concerning both the number of features and accuracy. Some modifications are made to the standard DE crossover and its key control parameters to enhance the proposed algorithm’s capabilities further. The proposed method has been compared to several state-of-the-art methods utilizing standard datasets from the UCI repository and results of the experiments demonstrate the superiority of the proposed approach.

A path planning method for UAVs based on multi-objective pigeon-inspired optimisation and differential evolution

Inspired by the behaviour of pigeon flocks, an improved method of path planning and autonomous formation for unmanned aerial vehicles based on the pigeon-inspired optimisation and differential evolution is proposed in this paper. Firstly, the mathematical model for UAV path planning is devised as a multi-objective optimisation with three indices, i.e., the length of a path, the sinuosity of a path, and the risk of a path. Then, the method integrated by pigeon-inspired optimisation and mutation strategies of differential evolution is developed to optimise feasible paths. Besides, Pareto dominance is applied to select the global best position of a pigeon. Finally, a series of simulation results compared with standard particle swarm optimisation algorithm and standard differential evolution algorithm show the effectiveness of our method.

How close simple EAs’ optimal solutions can approach global optima: experience from water distribution system design problems

Abstract An issue regarding near-optimal solutions identified by evolutionary algorithms (EAs) is that their absolute deviations from the global optima are often unknown, and hence an EA's performance in handling real-world problems remains unclear. To this end, this paper investigates how close optimal solutions from simple EAs can approach the global optimal for water distribution system (WDS) design problems through an experiment with the number of decision variables ranging from 21 to 3,400. Three simple EAs are considered: the standard differential evolution, the standard genetic algorithm and the creeping genetic algorithm (CGA). The CGA consistently identifies optimal solutions with deviations lower than 50% to the global optimal, even for the WDS with 3,400 decision variables, but the performance of the other two EAs is heavily case study dependent. Results obtained build knowledge regarding these simple EAs’ ability in handling WDS design problems with different sizes. We must acknowledge that these results are conditioned on the WDSs and the parameterization strategies used, and future studies should focus on generalizing the findings obtained in this paper.

Differential Evolution in Robust Optimization Over Time Using a Survival Time Approach

This study presents an empirical comparison of the standard differential evolution (DE) against three random sampling methods to solve robust optimization over time problems with a survival time approach to analyze its viability and performance capacity of solving problems in dynamic environments. A set of instances with four different dynamics, generated by two different configurations of two well-known benchmarks, are solved. This work also introduces a comparison criterion that allows the algorithm to discriminate among solutions with similar survival times to benefit the selection process. The results show that the standard DE holds a good performance to find ROOT solutions, improving the results reported by state-of-the-art approaches in the studied environments. Finally, it was found that the chaotic dynamic, disregarding the type of peak movement in the search space, is a source of difficulty for the proposed DE algorithm.

Adaptive weighted dynamic differential evolution algorithm for emergency material allocation and scheduling

AbstractEmergency material allocation and scheduling is a combination optimization problem, which is essentially a Non‐deterministic Polynomial (NP) problem. Aiming at the problems such as slow convergence, easy prematurely falling into local optimum, and parameter constraints to solve high‐dimensional and multi‐modal combination optimization problems, this article proposes an adaptive weighted dynamic differential evolution (AWDDE) algorithm. The algorithm uses a chaotic mapping strategy to initialize the population. By weighting the standard differential evolution (DE) mutation strategy, a new weighted mutation operator is proposed. The scaling factor and cross probability can be adaptively adjusted. A disturbance operator is introduced to randomly generate the perturbation mutation and to accelerate the premature individuals to jump out of the local optimum. The algorithm is applied to the problem of emergency material allocation and scheduling, and a two‐stage emergency material allocation and scheduling model is established. Compared with the standard DE algorithm and the chaos adaptive particle swarm algorithm, the results show that the AWDDE algorithm has the characteristics of stronger global optimization ability and faster convergence speed compared with other optimization algorithms, which provide assistance for smart cities research, including smart city services, applications, case studies, and policymaking considerations for emergency management.

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.

An improved gravitational search algorithm to the hybrid flowshop with unrelated parallel machines scheduling problem

ABSTRACT The hybrid flowshop scheduling problem with unrelated parallel machines exists in many industrial manufacturers, which is an NP-hard combinatorial optimisation problem. To solve this problem more effectively, an improved gravitational search (IGS) algorithm is proposed which combines three strategies: generate new individuals using the mutation strategy of the standard differential evolution (DE) algorithm and preserve the optimal solution via a greedy strategy; substitute the exponential gravitational constant of the standard gravitational search (GS) algorithm with a linear function; improve the velocity update formula of the standard GS algorithm by mixing an adaptive weight and the global search strategy of the standard particle swarm optimisation (PSO) algorithm. Benchmark examples are solved to demonstrate the proposed IGS algorithm is superior to the standard genetic algorithm, DE, GS, DE with local search, estimation of distribution algorithm and artificial bee colony algorithms. Two more examples from a real-world water-meter manufacturing enterprise are effectively solved.

An Adaptive DE Algorithm Based Fuzzy Logic Anti-swing Controller for Overhead Crane Systems

In this paper, aiming at the under-actuated problem of the overhead crane systems, a fuzzy logic anti-swing controller is first designed according to operator experience. Moreover, for better configuring the parameters of the controller, an adaptive differential evolution with disturbance factor algorithm (ADE-D) is proposed by introducing the adaptive scaling factor, the dynamic crossover probability and disturbance factor. By implementing numeric experiment test, the results show that the adaptive differential evolution with disturbance factor algorithm outperforms the standard differential evolution algorithm and other improved differential evolution algorithms. Finally, the adaptive differential evolution with disturbance factor algorithm-based fuzzy logic anti-swing controller is simulated under different conditions and compared with other control methods; the results exhibit excellent robustness of control performance in positioning control and damping oscillation of payload.

Unsupervised Text Feature Selection Using Memetic Dichotomous Differential Evolution

Feature Selection (FS) methods have been studied extensively in the literature, and there are a crucial component in machine learning techniques. However, unsupervised text feature selection has not been well studied in document clustering problems. Feature selection could be modelled as an optimization problem due to the large number of possible solutions that might be valid. In this paper, a memetic method that combines Differential Evolution (DE) with Simulated Annealing (SA) for unsupervised FS was proposed. Due to the use of only two values indicating the existence or absence of the feature, a binary version of differential evolution is used. A dichotomous DE was used for the purpose of the binary version, and the proposed method is named Dichotomous Differential Evolution Simulated Annealing (DDESA). This method uses dichotomous mutation instead of using the standard mutation DE to be more effective for binary purposes. The Mean Absolute Distance (MAD) filter was used as the feature subset internal evaluation measure in this paper. The proposed method was compared with other state-of-the-art methods including the standard DE combined with SA, which is named DESA in this paper, using five benchmark datasets. The F-micro, F-macro (F-scores) and Average Distance of Document to Cluster (ADDC) measures were utilized as the evaluation measures. The Reduction Rate (RR) was also used as an evaluation measure. Test results showed that the proposed DDESA outperformed the other tested methods in performing the unsupervised text feature selection.

Inverse calculation of demolition robot based on gravitational search algorithm and differential evolution neural network

For the inverse calculation of laser-guided demolition robot, its global nonlinear mapping model from laser measuring point to joint cylinder stroke has been set up with an artificial neural network. Due to the contradiction between population diversity and convergence rate in the optimization of complex neural networks by using differential evolution, a gravitational search algorithm and differential evolution is proposed to accelerate the convergence rate of differential evolution population driven by gravity. Gravitational search algorithm and differential evolution is applied to optimize the inverse calculation neural network mapping model of demolition robot, and the algorithm simulation shows that gravity can effectively regulate the convergence process of differential evolution population. Compared with the standard differential evolution, the convergence speed and accuracy of gravitational search algorithm and differential evolution are significantly improved, which has better optimization stability. The calculation results show that the output accuracy of this gravitational and differential evolution neural network can meet the calculation requirements of the positioning control of demolition robot’s manipulator. The optimization using gravitational search algorithm and differential evolution is done with the connection weights of a neural network in this article, and as similar techniques can be applied to the other hyperparameter optimization problem. Moreover, such an inverse calculation method can provide a reference for the autonomous positioning of large hydraulic series manipulator, so as to improve the robotization level of construction machinery.

Adaptive Dynamic Disturbance Strategy for Differential Evolution Algorithm

To overcome the problems of slow convergence speed, premature convergence leading to local optimization and parameter constraints when solving high-dimensional multi-modal optimization problems, an adaptive dynamic disturbance strategy for differential evolution algorithm (ADDSDE) is proposed. Firstly, this entails using the chaos mapping strategy to initialize the population to increase population diversity, and secondly, a new weighted mutation operator is designed to weigh and combinemutation strategies of the standard differential evolution (DE). The scaling factor and crossover probability are adaptively adjusted to dynamically balance the global search ability and local exploration ability. Finally, a Gauss perturbation operator is introduced to generate a random disturbance variation, and to accelerate premature individuals to jump out of local optimization. The algorithm runs independently on five benchmark functions 20 times, and the results show that the ADDSDE algorithm has better global optimization search ability, faster convergence speed and higher accuracy and stability compared with other optimization algorithms, which provide assistance insolving high-dimensionaland complex problems in engineering and information science.

Maximum Power Point Tracking Technology of Photovoltaic Array under Partial Shading Based On Adaptive Improved Differential Evolution Algorithm

In the case of partial shading conditions, there will be more than one maximum power point (MPP) in photovoltaic (PV) array. The traditional maximum power point tracking (MPPT) methods are easy to get in the local maximum power point (LMPP) and fail. Based on the standard differential evolution (DE) algorithm, the mutation strategy, scaling factor F, and cross factor CR of the algorithm are optimized. Also, the population position variance δ 2 is used to prevent falling into LMPP. Finally, the conditions for algorithm termination and restart are set. It is verified by simulation that the method has fast convergence speed, high accuracy, and can adapt well to changes in the external environment. The improved DE algorithm has a great advantage in MPPT.

Rethinking the differential evolution algorithm

Selection operation plays a significant role in differential evolution algorithm. A new differential evolution algorithm based on an improved selection process is presented in this work. It was studied that there was neither a practical method to maintain the distribution of population nor a correction to the variables out of bounds in mutation process in a standard differential evolution algorithm. The fast non-dominated sorting approach and the spatial distance algorithm which were applied to the beginning of the selection process, as well as a method to fix the transboundary variables in the mutation process, were adopted to optimize the differential evolution algorithm. The reformative algorithm could obtain a uniformly distributed and effective Pareto-optimal sets when applied to the classical multi-objective test functions; it performed prominently in the experiment of optimizing the quality, the cost and the time in a construction project compared with the previous work.

Power optimization method for wireless power transmission system based on improved differential evolution algorithm

In this paper, we proposes a power optimization algorithm in view of the Differential Evolution algorithm (DE) in order to reduce the transmission power due to the frequency split of the electromagnetic coupling resonant radio energy transmission system in the over-coupled state. Simulation experiments in MATLAB environment verify the effectiveness of the algorithm for power optimization of transmission system. Simulation experiments show that compared with the standard Differential Evolution algorithm and adaptive control parameter Differential Evolution algorithm (JDE), a new adaptive Differential Evolution algorithm (NDE) is improved based on the standard Differential Evolution algorithm. The new algorithm enables the system to find the optimal load power faster, which is conducive to increasing the output power of the system.

A modified Boltzmann Annealing Differential Evolution algorithm for inversion of directional resistivity logging-while-drilling measurements

Being introduced in the last decade for proactive geosteering, directional resistivity logging-while-drilling (DRLWD) measurements have been used to predict and invert formation boundary, which provides more confidence to geosteering engineers in steering a well towards reservoirs’ sweet spots. However, the strong non-uniqueness of the inversion problems in the data processing in the DRLWD measurements requires a robust algorithm having a global optimization capability. We propose a modified Boltzmann Annealing Differential Evolution (BADE) algorithm to optimize the inversion problem in the DRLWD measurements. The algorithm combines a multi-population Differential Evolution (DE) algorithm with an annealing strategy. Controlled by the annealing temperature, a bad solution may be accepted probabilistically to avoid the local minima. Moreover, different differential strategies are employed at different stages of annealing to improve the convergence as well as to save computation time. The proposed algorithm is suitable for parallel implementation and it can be accelerated drastically. Synthetic and field examples are presented to showcase the effectiveness and accuracy of the BADE algorithm. Compared to the standard DE algorithm, the modified algorithm converges faster and finds global optimization easier. Combined with a multi-layer model, the BADE algorithm can be used to predict multiple formation boundaries and to evaluate the anisotropic formation resistivities, which will be of great help for proactive geosteering and well placement.

Elite Representative Based Individual Adaptive Regeneration Framework for Differential Evolution

Differential evolution (DE) is a popular optimization algorithm which attracts numerous research studies and is applied widely. To address the problem of population stagnation in DE, this paper proposes an elite representative based individual adaptive regeneration framework (EIR) that can be incorporated into any DE variant easily. EIR is able to renovate stagnated individuals to regions centering around the weighted value of the individuals themselves and the elite representatives based on the Gaussian distribution with distinct crossover rates. Elite representatives are sampled from dynamically varied elite swarms for different individuals. A less greedy substitution mechanism considering the proximity of fitness values is introduced to avoid exclusion of some valuable information from inferior solutions. The whole regeneration and substitution mechanism is dynamically adapted according to the evolutionary process and the fitness ranking status of current individuals to balance between exploitation and exploration capability. Experimental results on CEC 2014 benchmark functions of $30D$ , $50D$ , $100D$ and two real world optimization problems show that the proposed EIR framework can significantly improve the performance of two standard DEs and six state-of-the-art DE algorithms.

Analysis of New Distributed Differential Evolution Algorithm with Best Determination Method and Species Evolution

This is a new semi-distributed differential evolution algorithm with best determination method and species evolution (DESBS). This algorithm is based on fact- evolution of species around niche. In DESBS, the best determination method determines the best individuals of population. These best individuals act as niches and the species are evolved around these best individuals. Over the period of time, each species evolved separately, using standard differential evolution algorithm. The evolving efficiency of each species evaluated separately and inefficient species are merge to nearby species. The scale-up study is performed to find out best parameter setting and the results are compared with other state-of-art algorithms like CoDE, EPSDE and standard differential evolution algorithm. The results show that the DESBS perform better than SDE in multimodal functions and CoDE, EPSDE in rotating optimization function