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.
Algebraic variants of the Differential Evolution (DE) algorithm have been recently proposed to tackle permutation-based optimization problems by means of an algebraic framework, which allows to ...directly encode the solutions as permutations. The algebraic DE in the permutation space can be characterized by considering different neighborhood definitions such as swapping two adjacent items, swapping any two items, shifting an item to a given position. Here we propose the Variable Neighborhood Differential Evolution for Permutations (VNDEP), which adaptively searches the three neighborhoods together based on a method of dynamic reward. We provide an extensive and systematic analysis of the theoretical tools required in VNDEP, by studying the complexity of the proposed algorithmic components and by introducing the possibility to use a scale factor parameter larger than one. Experiments have been held on a widely used benchmark suite for the Linear Ordering Problem with Cumulative Costs, where VNDEP has been compared with four known permutation-based DE schemes and with respect to the state-of-the-art results for the considered instances. The experiments clearly show that VNDEP systematically outperforms the competitor algorithms and, most impressively, 32 new best known solutions, of the 50 most challenging instances, have been obtained.
•Proposing a binary differential evolution algorithm with self-learning strategy, called MOFS-BDE, to solve multi-objective feature selection problems.•Proposing a new binary mutation operator based ...on probability difference to guide the individuals to locate potentially optimal areas fast.•Proposing a new one-bit purifying search operator (OPS) for improving the self-learning capability of elite individuals.•Proposing an efficient non-dominated sorting operator with crowding distance to reduce the time consumption of the selection operator in differential evolution.
Feature selection is an important data preprocessing method. This paper studies a new multi-objective feature selection approach, called the Binary Differential Evolution with self-learning (MOFS-BDE). Three new operators are proposed and embedded into the MOFS-BDE to improve its performance. The novel binary mutation operator based on probability difference can guide individuals to rapidly locate potentially optimal areas, the developed One-bit Purifying Search operator (OPS) can improve the self-learning capability of the elite individuals located in the optimal areas, and the efficient non-dominated sorting operator with crowding distance can reduce the computational complexity of the selection operator in the differential evolution. Experimental results on a series of public datasets show that the effective combination of the binary mutation and OPS makes our MOFS-BDE achieve a trade-off between local exploitation and global exploration. The proposed method is competitive in comparison with some representative genetic algorithm-, particle swarm-, differential evolution-, and artificial bee colony-based feature selection algorithms.
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Due to the increasing complexity of optimization problems, distributed differential evolution (DDE) has become a promising approach for global optimization. However, similar to the centralized ...algorithms, DDE also faces the difficulty of strategies' selection and parameters' setting. To deal with such problems effectively, this article proposes an adaptive DDE (ADDE) to relieve the sensitivity of strategies and parameters. In ADDE, three populations called exploration population, exploitation population, and balance population are co-evolved concurrently by using the master-slave multipopulation distributed framework. Different populations will adaptively choose their suitable mutation strategies based on the evolutionary state estimation to make full use of the feedback information from both individuals and the whole corresponding population. Besides, the historical successful experience and best solution improvement are collected and used to adaptively update the individual parameters (amplification factor <inline-formula> <tex-math notation="LaTeX">{F} </tex-math></inline-formula> and crossover rate CR) and population parameter (population size <inline-formula> <tex-math notation="LaTeX">{N} </tex-math></inline-formula>), respectively. The performance of ADDE is evaluated on all 30 widely used benchmark functions from the CEC 2014 test suite and all 22 widely used real-world application problems from the CEC 2011 test suite. The experimental results show that ADDE has great superiority compared with the other state-of-the-art DDE and adaptive differential evolution variants.
Multimodal optimization problem (MMOP), which targets at searching for multiple optimal solutions simultaneously, is one of the most challenging problems for optimization. There are two general goals ...for solving MMOPs. One is to maintain population diversity so as to locate global optima as many as possible, while the other is to increase the accuracy of the solutions found. To achieve these two goals, a novel dual-strategy differential evolution (DSDE) with affinity propagation clustering (APC) is proposed in this paper. The novelties and advantages of DSDE include the following three aspects. First, a dual-strategy mutation scheme is designed to balance exploration and exploitation in generating offspring. Second, an adaptive selection mechanism based on APC is proposed to choose diverse individuals from different optimal regions for locating as many peaks as possible. Third, an archive technique is applied to detect and protect stagnated and converged individuals. These individuals are stored in the archive to preserve the found promising solutions and are reinitialized for exploring more new areas. The experimental results show that the proposed DSDE algorithm is better than or at least comparable to the state-of-the-art multimodal algorithms when evaluated on the benchmark problems from CEC2013, in terms of locating more global optima, obtaining higher accuracy solution, and converging with faster speed.
•Differential Evolution (DE) approaches in Permutation Flow Shop (PFS) are proposed.•Makespan minimization by three different approaches is conducted.•Discrete DE and two Discrete Self-Adaptive DE ...algorithms are developed.•Four well-known benchmarks are considered.•Discrete Self-Adaptive DE showed better results than Discrete DE in the PFS environment.
Scheduling problems (SP) in the permutation flow shop (PFS) environment are present in many intermittent production industries, consisting of to determinate the processing order of n jobs in m sequential machines, with the purpose to optimize some performance criterion. In this paper, three optimization algorithms based on discrete differential evolution (DE) metaheuristics are applied to PFS scheduling problems, to minimize the makespan, are proposed, that are Discrete Differential Evolution, and Discrete Self-Adaptive Differential Evolution for SP in PFS named DDE-PFS, DSADE-PFS1 and DSADE-PFS2, respectively. The Carlier (CB), Heller (HB), Reeves (RB), and Taillard (TB) numerical benchmarks were adopted to test the proposed optimization algorithms. The performance of the optimization algorithms was evaluated regarding relative percentage error (RPE) criterion, convergence, standard deviation (Std), statistical tests of Friedman and post hoc Nemenyi. For TB, the DSADE-PFS1 algorithm presented a better performance in terms of RPE and Std measures. For CB and HB, the DSADE-PFS1 and DSADE-PFS2 algorithms presented a better performance in RPE, and the DSADE-PFS2 algorithm in terms of Std. For RB, the DSADE-PFS2 algorithm presented a better performance in RPE, while the DSADE-PFS1 algorithm was achieved in Std. Considering the processing time for each algorithm the DSADE-PFS2 approach achieved better results than CB, HB, and RB. Overall the results have shown that the optimization approaches proposed in this paper are promising for the SP in PFS, with highly competitive results in terms of average performance values.
Differential evolution (DE) is a popular evolutionary algorithm inspired by Darwin’s theory of evolution and has been studied extensively to solve different areas of optimisation and engineering ...applications since its introduction by Storn in 1997. This study aims to review the massive progress of DE in the research community by analysing the 192 articles published on this subject from 1997 to 2021, particularly studies in the past five years. The methodology used to search for relevant DE papers and an overview of the original DE are firstly explained. Recent advances in the modifications proposed to enhance the effectiveness and efficiency of the original DE are reviewed by analysing the strengths and weaknesses of each published work, followed by the potential applications of these DE variants in solving different real-world engineering problems. In contrast to most existing DE review papers, additional analyses are performed in this survey by investigating the impacts of various parameter settings on given DE variants to identify their optimal values required for solving certain problem classes. The qualities of modifications incorporated into selected DE variants are also evaluated by measuring the performance gains achieved in terms of search accuracy and/or efficiency against the original DE. The additional surveys conducted in this study are anticipated to provide more insightful perspectives for both beginners and experts of DE research, enabling their better understanding about current research trends and new motivations to outline appropriate strategic planning for future development works.
•An aeDE is proposed for optimization of truss structures with discrete design variables.•The aeDE algorithm is a newly improved adaptive version of DE with three modifications.•Three improvements ...relate to the mutation phase, selection phase and rounding technique.•The numerical results for six benchmark problems illustrate the effectiveness of aeDE.
This paper proposes an adaptive elitist differential evolution (aeDE) for optimization of truss structures with discrete design variables. The aeDE algorithm is a newly improved version of the differential evolution (DE) algorithm with three modifications. Firstly, in the mutation phase, an adaptive technique based on the deviation of objective function between the best individual and the whole population in the previous generation is proposed to select a suitable mutation operator. This technique helps preserve the balance between global and local searching abilities in the DE. Secondly, in the selection phase, an elitist selection technique which helps choose the best individuals for the next generation is utilized to increase the convergence rate. Finally, a rounding technique is integrated into the aeDE for solving optimization problems with discrete design variables. The efficiency and reliability of the proposed method are demonstrated through six optimization problems of truss structures with discrete design variables. Numerical results reveal that in most of the test cases, the aeDE is more efficient than the DE and some other methods in the literature in terms of the quality of solution and convergence rate.
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•Multi-layer perceptron is hybridized through two optimizers.•Optimizers are particle swarm optimization and differential evolution algorithms.•MLP-PSODE is used to model suspended ...sediment load of Mahabad river.•MLP-PSODE is found superior to its alternatives in extreme values estimation.•MLP-PSODE is a parsimonious model, possessing less number of input parameters.
River suspended sediment load (SSL) estimation is of importance in water resources engineering and hydrological modeling. In this study, a novel hybrid approach is recommended for SSL estimation in which multi-layer perceptron (MLP) is hybridized with particle swarm optimization (PSO) and then, integrated with differential evolution algorithm (DE) called as MLP-PSODE. The hybrid MLP-PSODE model is implemented to model the SSL of Mahabad river located at northwest of Iran. For the sake of examination of the MLP-PSODE model performance, several techniques including multi-layer perceptron (MLP), multi-layer perceptron integrated with particle swarm optimization (MLP-PSO), radial basis function (RBF) and support vector machine (SVM) are selected as benchmarks. For this purpose, five different scenarios are considered for the modeling. The results indicated that the new hybrid model of MLP-PSODE is successful in estimating SSL by considering single input of discharge (Q) with high accuracy as compared to its alternatives with RMSE = 1794.4 ton·day−1, MAPE = 41.50% and RRMSE = 107.09%, which were much lower than those of MLP based model with RMSE = 3133.7 ton·day−1, MAPE = 121.40% and RRMSE = 187.03%. The developed MLP-PSODE model, not only outperforms its counterparts in terms of accuracy in extreme values estimation, but also it is found as a parsimonious model that incorporates lower number of input parameters in its structure for SSL estimation.
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