Standard Differential Evolution Algorithm Research Articles

Meta‐heuristic optimization techniques for scheduling in multiple‐input multiple‐output multiple‐access channel system

SummaryIn a highly dense multiple‐input multiple‐output (MIMO) communication system, proper resource allocation is exceedingly challenging. The simultaneous selection of antennas at the base‐station (BS) and scheduling of users in an uplink multiple access channel (MAC) system add up to the signal processing load in the MIMO wireless system. The method chosen for combining the user scheduling and antenna selection must have a very low computational complexity. However, the exhaustive search algorithm (ESA), which achieves the best sum‐rate capacity in a MIMO‐MAC system, has a very high level of complexity. In this paper, we use a metaheuristic‐based optimization algorithms to optimize the sum‐rate capacity in a MAC system with significantly less computational complexity. First, we use the beluga whale optimization (BWO) metaheuristic method to solve the optimization problem. The BWO is a swarm‐based algorithm that draws inspiration from beluga whale behavior. An improved BWO (iBWO) is also presented and is utilized for the same optimization challenge. The proposed iBWO scheme improves the search capability of the algorithm and thereby ensures better exploration and exploitation capabilities of the beluga whales. We compare the performance of these algorithms with a standard differential evolution (DE) algorithm. The simulation results demonstrate that the proposed iBWO is a very competitive meta‐heuristic algorithm for solving optimization problems. The proposed iBWO algorithm achieves near optimal throughput in a MIMO‐MAC system. Also, the computational complexity related to the suggested optimization technique in a MIMO‐MAC system is found to be very less compared with the complexity related to ESA.

An integrated differential evolution algorithm for reconfigurable manufacturing systems

Product platforms consider an effective strategy to empower mass customization (MC) in a reconfigurable manufacturing system (RMS) to have the capacity to reconfigure the hardware and manage resources at all organisational and functional levels. This enables quick modification of production functions in reaction to unforeseen changes in the market or regulatory requirements. Although several platform formation and assembly line techniques have emerged to satisfy the increased demand for MC and enable the manufacture of products with high variety, they also increase the system’s complexity and make it less cost-efficient as variety increases. This study aims to minimize the complexity of a production system by reducing the number of separate components in different production processes. An efficient approach that integrates the Median-Joining Phylogenetic Networks (MJPN) classification tool and differential evolution (DE) in one unified framework is developed to do that. The proposed framework uses the concept of the package to group separate components that are often employed jointly to produce particular products and allows the use of the ‘all-unit discount policy’, which applies discounts to the purchasing costs of a specific quantity of materials/components. Finally, two case studies are applied to validate the proposed MJPN-DE in different dimensions. The experimental results show that applying the proposed package model saves 57.5% of the purchasing costs of components and 41.35% average setup costs compared to MJPN- and non-platform-based models and increases the postponement effectiveness of the obtained layout by 41.51% and 74.11% compared with two other layout strategies. In algorithmic comparisons, the results of comparing MJPN-DE with standard DE and genetic algorithm (GA) show an enhanced performance of MJPN-DE where the total production cost is reduced in the small case study by 63.34% and 38.52%, and in the large case study by 16.90% and 11.51%, respectively.

Application of adaptive improved DE algorithm based on multi-angle search rotation crossover strategy in multi-circuit testing optimization

Abstract This study based on the standard differential evolution (DE) algorithm was carried out to address the issues of control parameter imprinting, mutation process, and crossover process in the standard DE algorithm as well as the issue of multidimensional circuit testing optimization. A rotation control vector was introduced to expand the search range in the poor strategy to the circumference range of the individual and the parent target individual, and a rotation crossover operator and a binomial poor operator were combined. Finally, an improved adaptive DE algorithm based on a multi-angle search rotation crossover strategy was obtained. The research will improve the DE algorithm to optimize the testing of multidimensional circuits. It can be noted that the improved average precision value is 0.9919 when comparing the precision recall curves of the DE algorithm before and after the change, demonstrating a significant improvement in accuracy and stability. The fitness difference of the 30-dimensional problem is discovered to be between 0.25 × 103 and 0.5 × 103 by comparing the box graphs of the 30-dimensional problem with that of the 50-dimensional problem. On the 50-dimensional problem, when calculating the F4–F10 function, the fitness difference of the improved DE algorithm is 0.2 × 104–0.4 × 104. In summary, the improved DE algorithm proposed in this study compensates for the shortcomings of traditional algorithms in complex problem calculations and has also achieved significant optimization results in multidimensional circuit testing.

Joint decision-making of virtual module formation and scheduling considering queuing time

Formation and scheduling are the most important decisions in the virtual modular manufacturing system; however, the global performance optimization of the system may be sacrificed via the superposition of two independent decision-making results. The joint decision of formation and scheduling is very important for system design. Complex and discrete manufacturing enterprises such as shipbuilding and aerospace often comprise multiple tasks, processes, and parallel machines, resulting in complex routes. The queuing time of parts in front of machines may account for 90% of the production cycle time. This study established a weighted allocation model of a formation-scheduling joint decision problem considering queuing time in system. To solve this nondeterministic polynomial (NP) problem, an adaptive differential evolution-simulated annealing (ADE-SA) algorithm is proposed. Compared with the standard differential evolution (DE) algorithm, the adaptive mutation factor overcomes the disadvantage that the scale of DE’s differential vector is difficult to control. The selection strategy of the SA algorithm compensates for the deficiency that DE’s greedy strategy may fall into a local optimal solution. The comparison results of four algorithms of a series of random examples demonstrate that the overall performance of ADE-SA is superior to the genetic algorithm, and average iteration, maximum completion time, and move time are 24%, 11%, and 7% lower than the average of other three algorithms, respectively. The method can generate the joint decision-making scheme with better overall performance, and effectively identify production bottlenecks through quantitative analysis of queuing time.

Convolutional neural network optimized by differential evolution for electrocardiogram classification.

The Coronavirus disease 2019, or COVID-19, has shifted the medical paradigm from face-to-face to telehealth. Telehealth has become a vital resource to contain the virus spread and ensure the continued care of patients. In terms of preventing cardiovascular diseases, automating electrocardiogram (ECG) classification is a promising telehealth intervention. The healthcare service ensures that patient care is appropriate, comfortable, and accessible. Convolutional neural networks (CNNs) have demonstrated promising results in ECG categorization, which require high accuracy and short training time to ensure healthcare quality. This study proposes a one-dimensional-CNN (1D-CNN) arrhythmia classification based on the differential evolution (DE) algorithm to optimize the accuracy of ECG classification and training time. The performance of 1D-CNNs of different activation functions are optimized based on the standard DE algorithm. Finally, based on MIT-BIH and SCDH arrhythmia databases, the performances of optimized and unoptimized 1D-CNN are compared and analysed. Results show that the 1D-CNN optimized by the DE has higher accuracy in heartbeats classification. The optimized 1D-CNN improves from 97.6% to 99.5% on MIT-BIH and from 80.2% to 88.5% on SCDH. Therefore, the optimized 1D-CNN shows improvements of 1.9% and 8.3% in the two datasets, respectively. In addition, compared with the unoptimized 1D-CNN based on the same parameter settings, the optimized 1D-CNN has less training time. Under the conditions of ReLU function and 10 epochs, the training takes 9.22s on MIT-BIH and 10.35s on SCDH, reducing training time by 67.2% and 64.2%, respectively.

An optimal design of current conveyors using a hybrid-based metaheuristic algorithm

<span lang="EN-US">This paper focuses on the optimal sizing of a positive second-generation current conveyor (CCII+), employing a hybrid algorithm named DE-ACO, which is derived from the combination of differential evolution (DE) and ant colony optimization (ACO) algorithms. The basic idea of this hybridization is to apply the DE algorithm for the ACO algorithm’s initialization stage. Benchmark test functions were used to evaluate the proposed algorithm’s performance regarding the quality of the optimal solution, robustness, and computation time. Furthermore, the DE-ACO has been applied to optimize the CCII+ performances. SPICE simulation is utilized to validate the achieved results, and a comparison with the standard DE and ACO algorithms is reported. The results highlight that DE-ACO outperforms both ACO and DE.</span>

RESEARCH ON FUZZY SCHEDULING OF CLOUD COMPUTING TASKS BASED ON HYBRID SEARCH ALGORITHMS AND DIFFERENTIAL EVOLUTION

In the process of task scheduling, due to the large search space of resources, it takes a long time to allocate appropriate resources for tasks, which results in the increase of execution time and execution cost of algorithms. For this reason, this paper proposes a cloud computing task fuzzy scheduling strategy based on hybrid search algorithm and differential evolution, which incorporates the classification based on normal distribution and a variety of mutation strategies on the basis of standard differential evolution algorithm. In mutation strategy, the individual difference vector assigns priority to each task and arranges tasks according to resource allocation rules. It improves the slow convergence speed and easy to fall into local optimum of standard difference algorithm, and can effectively solve the task scheduling problem of cloud computing. A cloud computing task scheduling algorithm with time and cost constraints is designed and tested in a simulation environment. The experimental results show that the algorithm can not only shorten the task processing time and reduce the execution cost, but also fully satisfy the users’ actual quality of service requirements by adjusting the weights of time and cost factors.

Differential Evolution Algorithm with Hierarchical Fair Competition Model

This paper presents the study of differential evolution algorithm with hierarchical fair competition model (HFC-DE). HFC model is based on the fair competition of societal system found in natural world. In this model, the population is split into hierarchy and the competition is allowed between the hierarchical members. During evolution, the population members are allowed to move within the hierarchy levels. The standard differential evolution algorithm is used for population evolution. Experimentation has carried out to define the parameter for proposed model on test suit having unimodal problems and multi-model problems. After analyzing the results, the two variants of HFC-DE are proposed, named hierarchical fair competition model in differential evolution algorithm with replacement, I,e, HFCDE-R and hierarchical fair competition model in differential evolution algorithm without replacement, I,e, HFCDE-wR. The problem-solving capabilities of both algorithms are checked and the results are compared with differential evolution algorithm (DE) and other variants of DE. The early results are encouraging and motivating.

Overall Dynamic Optimization of Metal Mine Technical Indicators Considering Spatial Distribution of Ore Grade Using AADE

In optimizing the production of a metal mine, either the overall dynamic relations between technical indicators or the spatial distribution of the ore grade are usually considered, but few studies have considered both factors together. These two factors in combination have a greater effect on the optimization of mine production in terms of economic benefit and resource utilization than they do individually. We proposed an overall dynamic optimization model of technical indicators of metal mine production that considers the spatial distribution of the ore grade to better optimize the technical indicators and improve sustainable development of mineral resources. We incorporated an adaptive mutation strategy and adaptive control parameters into a differential evolution algorithm (AADE) in order to overcome the drawbacks of the differential evolution algorithm in solving this optimization model. The adaptive mutation strategy and adaptive control parameters were used to increase the rate of convergence and improve the search for a global maximum. To assess the performance of AADE, we used a real case and four test functions (the Sphere, Griewank, Rastrigin and Rosenbrock functions) in tests that compared AADE with a standard genetic algorithm, a standard differential evolution algorithm and the recently developed adaptive differential evolution algorithm. The results indicate that the optimization model we created is better aligned with mine production processes than current optimization models. In optimizing the technical indicators of metal mine production to maximize economic benefits, AADE performed significantly better than the other three algorithms tested in terms of convergence rate and global search ability.

Convergence Track Based Adaptive Differential Evolution Algorithm (CTbADE)

One of the challenging problems with evolutionary computing algorithms is to maintain the balance between exploration and exploitation capability in order to search global optima. A novel convergence track based adaptive differential evolution (CTbADE) algorithm is presented in this research paper. The crossover rate and mutation probability parameters in a differential evolution algorithm have a significant role in searching global optima. A more diverse population improves the global searching capability and helps to escape from the local optima problem. Tracking the convergence path over time helps enhance the searching speed of a differential evolution algorithm for varying problems. An adaptive powerful parameter-controlled sequences utilized learning period-based memory and following convergence track over time are introduced in this paper. The proposed algorithm will be helpful in maintaining the equilibrium between an algorithm's exploration and exploitation capability. A comprehensive test suite of standard benchmark problems with different natures, i.e., unimodal/multimodal and separable/non-separable, was used to test the convergence power of the proposed CTbADE algorithm. Experimental results show the significant performance of the CTbADE algorithm in terms of average fitness, solution quality, and convergence speed when compared with standard differential evolution algorithms and a few other commonly used state-of-the-art algorithms, such as jDE, CoDE, and EPSDE algorithms. This algorithm will prove to be a significant addition to the literature in order to solve real time problems and to optimize computational models with a high number of parameters to adjust during the problem-solving process.

Application of Improved Differential Evolution Algorithm in Solving Equations

The problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.

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 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.

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.

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.