Co-evolutionary Differential Evolution Research Articles

Cooperative coevolutionary differential evolution with adjacent intensity matrix with linkage identification for large-scale optimization problems in noisy environments

Cooperative coevolutionary differential evolution with adjacent intensity matrix with linkage identification for large-scale optimization problems in noisy environments

Surrogate-assisted evolutionary optimization for perishable inventory management in multi-echelon distribution systems

Simulation is widely used for analyzing supply chains with complex structures and stochastic nature. However, optimizing supply chain simulation models is usually computationally expensive. This study proposes a surrogate-assisted evolutionary optimization approach to optimize the inventory policies in multi-echelon distribution systems for perishable items under a limited number of evaluations. The random forest algorithm is used to build the surrogate model for a faster estimation of the performance of the inventory policies. A co-evolutionary differential evolution algorithm is proposed to simultaneously evolve the population through multiple searching strategies. The generated solutions are estimated by the low-cost surrogate model to select the promising solutions, which will be evaluated by the inventory model. Moreover, this study also integrates the surrogate model into two classic metaheuristic algorithms, particle swarm optimization and differential evolution. Also, a new performance indicator is proposed to examine the efficiency of the surrogate model in evolutionary computation. Two case studies are used to investigate the performance of the proposed algorithms. The experimental results show that both particle swarm optimization and differential evolution exhibit performance improvements exceeding 55% by using surrogate models under the limited number of function evaluations. Furthermore, the surrogate model reduces computational time for both algorithms by over 34% to achieve equivalent objective values. Finally, the proposed co-evolutionary differential evolution algorithm is compared with 12 algorithms, and the results show that the proposed algorithm consistently outperforms them. These findings confirm the usefulness of the surrogate model in evolutionary algorithms and the effectiveness of the proposed co-evolutionary strategy for solving perishable inventory problems.

Deep reinforcement learning assisted co-evolutionary differential evolution for constrained optimization

Solving constrained optimization problems (COPs) with evolutionary algorithms (EAs) is a popular research direction due to its potential and diverse applications. One of the key issues in solving COPs is the choice of constraint handling techniques (CHTs), as different CHTs can lead to different evolutionary directions. Combining EAs with deep reinforcement learning (DRL) is a promising and emerging approach for solving COPs. Although DRL can help solve the problem of pre-setting operators in EAs, neural networks need to obtain diverse training data within a limited number of evaluations in EAs. Based on the above considerations, this work proposes a DRL assisted co-evolutionary differential evolution, named CEDE-DRL, which can effectively use DRL to help EAs solve COPs. (1) This method incorporates co-evolution into the extraction of training data for the first time, ensuring the diversity of samples and improving the accuracy of the neural network model through information exchange between multiple populations. (2) Multiple CHTs are used for offspring selection to ensure the algorithm’s generality and flexibility. (3) DRL is used to evaluate the population state, taking into account feasibility, convergence, and diversity in the state setting and using the overall degree of improvement as a reward. The neural network selects suitable parent populations and corresponding archives for mutation. Finally, (4) to avoid premature convergence and local optima, an adaptive operator selection and individual archive elimination mechanism is added. Comparisons with state-of-the-art algorithms on benchmark functions CEC2010 and CEC2017 show that the proposed method performs competitively and produced robust solutions. The results of the application test set CEC2020 show that the proposed algorithm is also effective in real-world problems.

Adaptive cooperative coevolutionary differential evolution for parallel feature selection in high-dimensional datasets

In many fields, it is a common practice to collect large amounts of data characterized by a high number of features. These datasets are at the core of modern applications of supervised machine learning, where the goal is to create an automatic classifier for newly presented data. However, it is well known that the presence of irrelevant features in a dataset can make the learning phase harder and, most importantly, can lead to suboptimal classifiers. Consequently, it is becoming increasingly important to be able to select the right subset of features. Traditionally, optimization metaheuristics have been used with success in the task of feature selection. However, many of the approaches presented in the literature are not applicable to datasets with thousands of features because of the poor scalability of optimization algorithms. In this article, we address the problem using a cooperative coevolutionary approach based on differential evolution. In the proposed algorithm, parallelized for execution on shared-memory architectures, a suitable strategy for reducing the dimensionality of the search space and adjusting the population size during the optimization results in significant performance improvements. A numerical investigation on some high-dimensional and medium-dimensional datasets shows that, in most cases, the proposed approach can achieve higher classification performance than other state-of-the-art methods.

Cooperative coevolutionary differential evolution with linkage measurement minimization for large-scale optimization problems in noisy environments

Many optimization problems suffer from noise, and the noise combined with the large-scale attributes makes the problem complexity explode. Cooperative coevolution (CC) based on divide and conquer decomposes the problems and solves the sub-problems alternately, which is a popular framework for solving large-scale optimization problems (LSOPs). Many studies show that the CC framework is sensitive to decomposition, and the high-accuracy decomposition methods such as differential grouping (DG), DG2, and recursive DG (RDG) are extremely sensitive to sampling accuracy, which will fail to detect the interactions in noisy environments. Therefore, solving LSOPs in noisy environments based on the CC framework faces unprecedented challenges. In this paper, we propose a novel decomposition method named linkage measurement minimization (LMM). We regard the decomposition problem as a combinatorial optimization problem and design the linkage measurement function (LMF) based on Linkage Identification by non-linearity check for real-coded GA (LINC-R). A detailed theoretical analysis explains why our proposal can determine the interactions in noisy environments. In the optimization, we introduce an advanced optimizer named modified differential evolution with distance-based selection (MDE-DS), and the various mutation strategy and distance-based selection endow MDE-DS with strong anti-noise ability. Numerical experiments show that our proposal is competitive with the state-of-the-art decomposition methods in noisy environments, and the introduction of MDE-DS can accelerate the optimization in noisy environments significantly.

Dynamic hybrid mechanism-based differential evolution algorithm and its application

In order to effectively schedule railway train delay, an adaptive cooperative co-evolutionary differential evolution with dynamic hybrid mechanism of the quantum evolutionary algorithm and genetic algorithm, named QGDECC is designed in this paper. In the QGDECC, the quantum variable decomposition strategy is designed by utilizing qubit string to decompose variables adaptively according to the coevolution performance. Then the increment mutation method is proposed to improve the convergence speed which make full use of searched evolution information. Besides, the parameter adaptive strategy is deeply explored for strengthening the robust of the algorithm. The QGDECC with global search capability is employed to realize a railway train delay scheduling method for effectively eliminating the impact of train delay. Finally, several benchmark functions and actual train operation data are selected to verify the optimization performance of QGDECC. The experimental results show that QGDECC has higher adaptability, faster convergence speed and accuracy. The train delay scheduling method can effectively eliminate the impact of delay on the railway network, and minimize the gap between the rescheduled train schedule and the original train schedule.

Cooperative co-evolutionary differential evolution algorithm applied for parameters identification of lithium-ion batteries

Parameters identification of battery is a significant task for lithium-ion batteries. Some widely used techniques usually simplify the electrical circuit model (ECM) with non-linearity to a linear model or local linear model. However, by using such a methodology, the parameters in ECMs are not globally optimal, since the parameters may be not consistent at different linearized points. To address this issue, this paper proposed a cooperative co-evolution differential evolution (CCDE) algorithm to identify parameters of lithium-ion battery, without any linearization or pre-assumption. First, to describe the dynamic behaviors of battery, we presented a first-order RC equivalent circuit model ECM. Without making any approximation, improved Euler’s numerical method was utilized to solve the differential equations directly. Second, an optimizing objective function was built to minimize errors between the true and optimized terminal voltages. In that optimization model, parameters of battery (R0, RP and CP) and vOCV(t) at each sampling point were considered as variables to be optimized, resulting in a very high-dimension problem. Third, such an optimization problem was transformed into a large scale optimization problem (LSOP). Based on the character of parameters identification, we proposed a new m-decomposition method which is different from general grouping methods for benchmark functions and its corresponding differential evolution (DE) algorithm to solve this LSOP. Comprehensive experimental results demonstrated effectiveness of the proposed framework and methodology, compared with seven state-of-the-art cooperative co-evolution methods.

Multi-strategy co-evolutionary differential evolution for mixed-variable optimization

In real world, engineering design problems have been regarded as common and complex problems which always include non-linear standard functions, many complex constraints and decision variables containing both continuous and discrete variables. Problems with these features also can be named as mixed-variable optimization problems (MVOPs). However, because the decision variables of MVOPs present different spatial distribution features, how to design an effective algorithm to solve MVOPs is still a challenge. In this paper, a new variation of differential evolution (DE), named multi-strategy co-evolutionary differential evolution (MCDEmv) is proposed to solve MVOPs. A mixed-variable co-evolutionary scheme simultaneously considering continuous and discrete variables in MVOPs is utilized. Based on this scheme, a multi-strategy co-evolutionary approach considering a dynamic adaptive selection mechanism and the combination of different characteristic mutation strategies and crossover operators is proposed for adapting to the all-inclusive situations in MVOPs. Furthermore, a statistics-based local search (SBA) specially designed for the optimization of discrete variables in MVOPs is proposed for enhancing the efficiency and flexibility of the MCDEmv. 28 artificial benchmark functions are adopted to verify the effectiveness and efficiency of the proposed algorithm. The experimental results show that our proposed algorithm is more competitive and efficient than other compared similar algorithms, i.e., AEDA, ACOMV, DEMV and PSOmv. Comparing with other similar algorithms in coping with two mixed-variable engineering design problems, MCDEmv also shows higher efficiency and performance.

MLFS-CCDE: multi-objective large-scale feature selection by cooperative coevolutionary differential evolution

Feature selection is a pre-processing procedure of choosing the optimal feature subsets for constructing model, yet it is difficult to satisfy the requirements of reducing number of features and maintaining classification accuracy. Towards this problem, we propose novel multi-objectives large-scale cooperative coevolutionary algorithm for three-objectives feature selection, termed MLFS-CCDE. Firstly, a cooperative searching framework is designed for efficiently and effectively seeking for the optimal feature subset. Secondly, in the framework, three objectives, feature’s number, classification accuracy and total information gain are established for guiding the evolution of features’ combination. Thirdly, in framework’s decomposition process, cluster-based decomposition strategy is elaborated for reducing the computation; in framework’s coevolution process, dual indicator-based representatives are elaborated for balancing the representative solution’ convergence and diversity. Finally, to verify framework’s practicability, a heart disease diagnosis system based on MLFS-CCDE framework is constructed in cardiology. Numerical experiments demonstrate that the proposed MLFS-CCDE outperforms its competitors in terms of both classification accuracy and metrics of features’ number.

MPPCEDE: Multi-population parallel co-evolutionary differential evolution for parameter optimization

In this paper, a novel multi-population parallel co-evolutionary differential evolution, named MPPCEDE, is proposed to optimize parameters of photovoltaic (PV) models and enhance conversion efficiency of solar energy. In the MPPCEDE, the reverse learning mechanism is employed to generate the initial several subpopulations to enhance the convergence velocity and keep the population diversity. A new multi-population parallel control strategy is developed to maintain the search efficiency in subpopulations. The co-evolutionary mutation strategy with elite population and three mutation strategies is proposed to reduce computing resources and balance the exploration and exploration capability through the cooperative mechanism, improve the convergence speed, realize the information exchange. Then the MPPCEDE is employed to effectively optimize parameters of PV models under various conditions and environments to obtain a parameter values of PV models. Finally, the effectiveness of the proposed method is tested by different PV models and manufacturer's datasheet. The experimental and comparative results demonstrate that the MPPCEDE exhibits higher accuracy and reliability, and has fast convergence speed by comparing with several methods in extracting parameters of PV models.

Design of an Helical Spring using Single-solution Simulated Kalman Filter Optimizer


 
 
 
 Optimization is one of the important process in solving engineering problems. Regrettably, there are numerous problems in practical optimization that cannot be solved flawlessly within reasonable computational effort. Thus, metaheuristic approach is often useful to get near-optimal solution when the best solution is not achievable. This paper demonstrates the usefullness of a metaheuristic algorithm called single-solution simulated Kalman filter (ssSKF) in helical spring design, which is an example of structural engineering design problem. The ssSKF is a single agent-based optimization algorithm based on the Kalman filtering. The solution obtained by the ssSKF is compared againsts the genetic algorithm, co-evolutionary particle swarm optimization, co-evolutionary differential evolution, bat algorithm, and artificial bee colony.
 
 
 

Differential evolution with subpopulations for high‐dimensional seismic inversion

ABSTRACTSeismic inversion has drawn the attention of researchers due to its capability of building an accurate earth model. Such a model will need to be discretised finely, and the dimensions of the inversion problem will be very high. In this paper, we propose an efficient differential evolution algorithm and apply it to high‐dimensional seismic inversion. Our method takes into account the differences among individuals, which are disregarded in conventional differential evolution methods, resulting to a better balance between exploration and exploitation. We divide the entire population into three subpopulations and propose a novel mutation strategy with two phases. Furthermore, we optimise the crossover operator by applying the components having the best objective function values into the crossover operator. We embed this strategy into a cooperative coevolutionary differential evolution and propose a new differential evolution algorithm referred to as a differential evolution with subpopulations. Then, we apply our scheme to both synthetic and field data; the results of high‐dimensional seismic inversion have shown that the proposed differential evolution with subpopulations achieves faster convergence and a higher‐quality solution for seismic inversion.

A Non-Dominated Sorting Cooperative Co-Evolutionary Differential Evolution Algorithm for Multi-Objective Layout Optimization

Different from traditional multi-objective evolutionary algorithms (MOEAS), multi-objective cooperative co-evolutionary algorithms (MOCCEAs) divide the decision variables into several subproblems to optimize. Solutions of each subproblem are evaluated by complete solutions formed through combining representative solutions from all subproblems. Therefore, the combination of representative solutions is a key issue in MOCCEAs. To improve the capability of MOCCEAs to complex multi-objective optimization problems, we propose a non-dominated sorting cooperative co-evolutionary differential evolution algorithm (NSCCDE). The proposed NSCCDE uses an external archive for storing complete solutions to establish a new collaboration mechanism, which forms a complete solution by combining collaborators from each subpopulation as well as from the external archive. On the one hand, the external archive is updated continuously through non-dominated sorting of complete solutions, which is conducive to speeding up the convergence. On the other hand, the external archive evolves itself through spatial dispersal and mutation operation to increase the diversity. The performance of proposed NSCCDE is then evaluated on a suite of satellite module layout optimization problem. Experimental results demonstrate that the proposed algorithm outperforms NSCCGA and NSGA- II.

Cooperative coevolutionary differential evolution with improved augmented Lagrangian to solve constrained optimisation problems

In constrained optimisation, the augmented Lagrangian method is considered as one of the most effective and efficient methods. This paper studies the behaviour of augmented Lagrangian function (ALF) in the solution space and then proposes an improved augmented Lagrangian method. We have shown that our proposed method can overcome some of the drawbacks of the conventional augmented Lagrangian method. With the improved augmented Lagrangian approach, this paper then proposes a cooperative coevolutionary differential evolution algorithm for solving constrained optimisation problems. The proposed algorithm is evaluated on a set of 24 well-known benchmark functions and five practical engineering problems. Experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art algorithms with respect to solution quality as well as efficiency.

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.

A Cooperative Coevolutionary Differential Evolution Algorithm with Adaptive Subcomponents

The performance of cooperative co-evolutionary (CC) algorithms for large-scale continuous optimization is significantly affected by the adopted decomposition of the search space. According to the literature, a typical decomposition in case of separable problems consists of adopting equally sized subcomponents for the whole optimization process (i.e. static decomposition). Such an approach is also often used for non-separable problems, together with a random-grouping strategy. More advanced methods try to determine the optimal size of subcomponents during the optimization process using reinforcement-learning techniques. However, the latter approaches are not always suitable in this case because of the non-stationary and history-dependent nature of the learning environment. This paper investigates a new CC algorithm, based on Differential Evolution, in which several decompositions are applied in parallel during short learning phases. The experimental results on a set of large-scale optimization problems show that the proposed method can lead to a reliable estimate of the suitability of each subcomponent size. Moreover, in some cases it outperforms the best static decomposition.

Dual-system Cooperative Coevolutionary Differential Evolution Algorithm for Solving Nonseparable Function Optimization

Dual-system Cooperative Coevolutionary Differential Evolution Algorithm for Solving Nonseparable Function Optimization

Parallel Dual-system Cooperative Co-evolutionary Differential Evolution Algorithm with Human-computer Cooperation for Multi-cabin Satellite Layout Optimization

Parallel Dual-system Cooperative Co-evolutionary Differential Evolution Algorithm with Human-computer Cooperation for Multi-cabin Satellite Layout Optimization

Opposition-based Cooperative Coevolutionary Differential Evolution Algorithm With Gaussian Mutation for Simplified Satellite Module Optimization

Opposition-based Cooperative Coevolutionary Differential Evolution Algorithm With Gaussian Mutation for Simplified Satellite Module Optimization

A co-evolutionary differential evolution algorithm for solving min–max optimization problems implemented on GPU using C-CUDA

Several areas of knowledge are being benefited with the reduction of the computing time by using the technology of graphics processing units (GPU) and the compute unified device architecture (CUDA) platform. In case of evolutionary algorithms, which are inherently parallel, this technology may be advantageous for running experiments demanding high computing time. In this paper, we provide an implementation of a co-evolutionary differential evolution (DE) algorithm in C-CUDA for solving min–max problems. The algorithm was tested on a suite of well-known benchmark optimization problems and the computing time has been compared with the same algorithm implemented in C. Results demonstrate that the computing time can significantly be reduced and scalability is improved using C-CUDA. As far as we know, this is the first implementation of a co-evolutionary DE algorithm in C-CUDA.