Mutation Operator Of Differential Evolution Research Articles

Reinforcement learning-based multi-objective differential evolution algorithm for feature selection

Feature Selection (FS) can be used to determine the optimal subset of features from a raw dataset by reducing dimensionality and improving accuracy. In this study, a reinforcement learning-based multi-objective differential evolution algorithm (RLMODE) for FS is proposed, which is modeled as a multi-objective optimization problem. First, a reinforcement learning-based offspring generation strategy is designed. The offspring generation strategy is based on the Q-learning framework, which considers each individual in the population as an agent. The dominance relationship between an agent and its predecessor is used to encode the state. A well-chosen action set containing three typical differential evolution mutation operators is available for each agent. The reward is used to update the exclusive Q-table. Moreover, a novel Pareto front (PF) relearning strategy is devised to allow adequate communication between individuals on the PF. The PF relearning strategy reevaluates the potential value of all individuals on the PF as a whole. This promotes the propagation of excellent solutions and improves PF diversity. The proposed RLMODE initially demonstrates its strength in benchmarks. The excellent results for 17 datasets demonstrate RLMODE’s merits in terms of dimensionality reduction and accuracy improvement. Therefore, the proposed RLMODE method is a promising FS technique.

Height Sensitive Multi-UAV Deployment Scheme in Edge Data Acquisition System

In data acquisition scenario of edge computing, the optimization of UAV (Unmanned Aerial Vehicle) deployment is of great significance for making use of resources of UAV. We establish an optimization model of UAV cluster deployment in the edge data acquisition system. The model takes the height of UAV as the solving variable, which is more in line with the realistic characteristics. DEVIPSK-SA-FWA is proposed according to the characteristics of this model. The algorithm uses a novel coding mechanism, and uses K-Means to accelerate the convergence process of the algorithm. A variety of differential evolution mutation operators are used to form a self-adaptive strategy pool mechanism to carry out variable scale variation of population, which complete the global search well. Then fireworks algorithm searches the population locally after each round of global search. In our algorithm, global search and local search are well balanced and local optimal is effectively escaped. Finally, experimental results indicate that DEVIPSK-SA-FWA is capable of solving the model with good results, and the superiority of DEVIPSK-SA-FWA is verified through the Wilcoxon rank sum test method. In the best case, the proposed algorithm reduces energy consumption of edge data acquisition system by 32.87[Formula: see text].

Combined knowledge transfer and adaptive coordinate systems approach for evolutionary bilevel optimization

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem.

Learning unified mutation operator for differential evolution by natural evolution strategies

Differential evolution (DE) is one of the widely studied algorithms in evolutionary computation. Recently, many adaptive mechanisms have been proposed for DE including adaptive operator selection and adaptive parameter control. Existing studies consider the two kinds of mechanisms independently. In this paper, we first propose a unified mutation operator with learnable parameters. With different parameter settings, the unified mutation operator degenerates into various classic mutation operators. As a result, by adapting the control parameters of the unified mutation operator, we can realize parameter control and operator selection simultaneously. We then present how to use a neural network to adaptively determine the control parameters. We use natural evolution strategies to train the neural network by modeling the evolutionary process as a Markov decision process. We then embed it into three DEs including classic DE, JADE and LSHADE. Experimental studies show that by embedding the learned unified mutation operator, the performances of these backbone DEs can be improved. Particularly, by embedding the unified mutation operator, LSHADE can perform competitively among state-of-the-art EAs including the winner algorithms in the past CEC competitions. Furthermore, we verify the effectiveness of the unified mutation operator through analyzing the population diversity theoretically.

An efficient annealing-assisted differential evolution for multi-parameter adaptive latent factor analysis

A high-dimensional and incomplete (HDI) matrix is a typical representation of big data. However, advanced HDI data analysis models tend to have many extra parameters. Manual tuning of these parameters, generally adopting the empirical knowledge, unavoidably leads to additional overhead. Although variable adaptive mechanisms have been proposed, they cannot balance the exploration and exploitation with early convergence. Moreover, learning such multi-parameters brings high computational time, thereby suffering gross accuracy especially when solving a bilinear problem like conducting the commonly used latent factor analysis (LFA) on an HDI matrix. Herein, an efficient annealing-assisted differential evolution for multi-parameter adaptive latent factor analysis (ADMA) is proposed to address these problems. First, a periodic equilibrium mechanism is employed using the physical mechanism annealing, which is embedded in the mutation operation of differential evolution (DE). Then, to further improve its efficiency, we adopt a probabilistic evaluation mechanism consistent with the crossover probability of DE. Experimental results of both adaptive and non-adaptive state-of-the-art methods on industrial HDI datasets illustrate that ADMA achieves a desirable global optimum with reasonable overhead and prevails competing methods in terms of predicting the missing data in HDI matrices.

Identification of Cancerous Cell from Noisy Images

Abstract: Over the last decades, the incidence of skin cancer, melanoma and non-melanoma,has increased at a continuous rate. In particular for melanoma, the deadliest type of skin cancer, early detection is important to increase patient prognosis. Recently, deep neural networks (DNNs) have become viable to deal with skin cancer detection. In this work, we present a smartphone-based application to assist on skin cancer detection. This application is based on a Convolutional Neural Network (CNN) trained on clinical images and patients demographics, both collected from smartphones. Also, as skin cancer datasets are imbalanced, we present an approach, based on the mutation operator of Differential Evolution (DE) algorithm,to balance data. In this sense, beyond provides a flexible tool to assist doctors on skin cancer screening phase, the method obtains promising results with a balancedaccuracy of 85% and a recall of 96%. Index Terms—skin cancer detection, smartphone application, deep learning, convolutional neural network

An enhanced black widow optimization algorithm for feature selection

Feature selection is an important data processing method to reduce dimension of the raw datasets while preserving the information as much as possible. In this paper, an enhanced version of Black Widow Optimization Algorithm called SDABWO is proposed to solve the feature selection problem. The Black Widow Optimization Algorithm (BWO) is a new population-based meta-heuristic algorithm inspired by the evolution process of spider population. Three main improvements were included into the BWO to overcome the shortcoming of low accuracy, slow convergence speed and being easy to fall into local optima. Firstly, a novel strategy for selecting spouses by calculating the weight of female spiders and the distance between spiders is proposed. By applying the strategy to the original algorithm, it has faster convergence speed and higher accuracy. The second improvement includes the use of mutation operator of differential evolution at mutation phase of BWO which helps the algorithm escape from the local optima. And then, three key parameters are set to adjust adaptively with the increase of iteration times. To confirm and validate the performance of the improved BWO, other 10 algorithms are used to compared with the SDABWO on 25 benchmark functions. The results show that the proposed algorithm enhances the exploitation ability, improves the convergence speed and is more stable when solving optimization problems. Furthermore, the proposed SDABWO algorithm is employed for feature selection. Twelve standard datasets from UCI repository prove that SDABWO-based method has stronger search ability in the search space of feature selection than the other five popular feature selection methods. These results confirm the capability of the proposed method simultaneously improve the classification accuracy while reducing the dimensions of the original datasets. Therefore, SDABWO-based method was found to be one of the most promising for feature selection problem over other approaches that are currently used in the literature.

A hybrid differential evolution and simulated annealing algorithm for global optimization

Differential evolution (DE) is one of the most effective ways to solve global optimization problems. However, considering the traditional DE has lower search efficiency and easily traps into local optimum, a novel DE variant named hybrid DE and simulated annealing (SA) algorithm for global optimization (HDESA) is proposed in this paper. This algorithm introduces the concept of “ranking” into the mutation operation of DE and adds the idea of SA to the selection operation. The former is to improve the exploitation ability and increase the search efficiency, and the latter is to enhance the exploration ability and prevent the algorithm from trapping into the local optimal state. Therefore, a better balance can be achieved. The experimental results and analysis have shown its better or at least equivalent performance on the exploitation and exploration capability for a set of 24 benchmark functions. It is simple but efficient.

Optimal allocation of photovoltaic/wind energy system in distribution network using meta-heuristic algorithm

In this paper, allocation of hybrid photovoltaic panels, wind turbines and battery storage (PV/WT/BA) system in distribution network is presented aimed active losses cost minimization, voltage profile enhancement and minimizing power purchased from the hybrid system by the network. Meta-heuristic improved whale optimizer algorithm (IWOA) is used to determine the optimal location and size of the PV/WT/BA system components as decision variables. The conventional WOA is inspired by social behavior and the hunting of humpback whales and in this study its performance is improved by using crossover and mutation operators of differential evolution (DE) method to avoid getting caught in local optimal and reinforcement to achieve global optimal. The methodology is implemented on IEEE 33 bus network considering seasonal variations. The results indicated that optimal determination of the decision variables in the network minimizes the active losses cost, voltage deviations and cost of power purchased from the hybrid system by the network using IWOA. The superiority of the IWOA is confirmed in benchmark test functions solution with very competitive results and also better results in statistic analysis and higher convergence speed and accuracy in comparison with the WOA, DE and particle swarm optimization (PSO). Also the results showed that the highest losses and better voltage are related to the summer and the lowest values are obtained in autumn season. The solar panels only participate in energy generation in spring and summer seasons, cost of power purchased by the network is highest in summer and lowest in autumn season. Moreover, the network is placed in stable current and voltage condition and the network power losses and voltage deviations are minimized.

An improved adaptive memetic differential evolution optimization algorithms for data clustering problems.

The performance of data clustering algorithms is mainly dependent on their ability to balance between the exploration and exploitation of the search process. Although some data clustering algorithms have achieved reasonable quality solutions for some datasets, their performance across real-life datasets could be improved. This paper proposes an adaptive memetic differential evolution optimisation algorithm (AMADE) for addressing data clustering problems. The memetic algorithm (MA) employs an adaptive differential evolution (DE) mutation strategy, which can offer superior mutation performance across many combinatorial and continuous problem domains. By hybridising an adaptive DE mutation operator with the MA, we propose that it can lead to faster convergence and better balance the exploration and exploitation of the search. We would also expect that the performance of AMADE to be better than MA and DE if executed separately. Our experimental results, based on several real-life benchmark datasets, shows that AMADE outperformed other compared clustering algorithms when compared using statistical analysis. We conclude that the hybridisation of MA and the adaptive DE is a suitable approach for addressing data clustering problems and can improve the balance between global exploration and local exploitation of the optimisation algorithm.

Hybrid multiobjective evolutionary algorithm based on differential evolution for flow shop scheduling problems

This paper proposes a hybrid multiobjective evolutionary algorithm based on differential evolution (HMOEA/DE) to solve the flow shop scheduling problems (FSPs) with the criteria of minimizing the makespan and tardiness simultaneously. Firstly, the hybrid multiobjective evolutionary algorithm (HMOEA) in HMOEA/DE is designed as the global search strategy, which rapidly improves the convergence and distribution performances towards the center and edge regions of Pareto frontier. Secondly, differential evolution (DE) strategy is combined with HMOEA as the local search mechanism to further enhance the convergence and distribution performances on the elite population obtained by HMOEA. Two DE mutation operators are designed for the individuals in the elite population: one is to further improve the performance of each individual and the other serves to much enhance the individual randomly. Numerical comparisons indicate that the efficacy of HMOEA/DE outperforms the traditional multiobjective evolutionary algorithm without DE in convergence and distribution performances on benchmark test problems and FSPs while verifying the advantages and disadvantages of different DE methods.

Review and analysis of three components of the differential evolution mutation operator in MOEA/D-DE

A decomposition-based multi-objective evolutionary algorithm with a differential evolution variation operator (MOEA/D-DE) shows high performance on challenging multi-objective problems (MOPs). The DE mutation consists of three key components: a mutation strategy, an index selection method for parent individuals, and a bound-handling method. However, the configuration of the DE mutation operator that should be used for MOEA/D-DE has not been thoroughly investigated in the literature. This configuration choice confuses researchers and users of MOEA/D-DE. To address this issue, we present a review of the existing configurations of the DE mutation operator in MOEA/D-DE and systematically examine the influence of each component on the performance of MOEA/D-DE. Our review reveals that the configuration of the DE mutation operator differs depending on the source code of MOEA/D-DE. In our analysis, a total of 30 configurations (three index selection methods, two mutation strategies, and five bound handling methods) are investigated on 16 MOPs with up to five objectives. Results show that each component significantly affects the performance of MOEA/D-DE. We also present the most suitable configuration of the DE mutation operator, which maximizes the effectiveness of MOEA/D-DE.

A Hybridization of Cuckoo Search and Differential Evolution for the Logistics Distribution Center Location Problem

The location selection of logistics distribution centers is a crucial issue in the modern urban logistics system. In order to achieve a more reasonable solution, an effective optimization algorithm is indispensable. In this paper, a new hybrid optimization algorithm named cuckoo search-differential evolution (CSDE) is proposed for logistics distribution center location problem. Differential evolution (DE) is incorporated into cuckoo search (CS) to improve the local searching ability of the algorithm. The CSDE evolves with a coevolutionary mechanism, which combines the Lévy flight of CS with the mutation operation of DE to generate solutions. In addition, the mutation operation of DE is modified dynamically. The mutation operation of DE varies under different searching stages. The proposed CSDE algorithm is tested on 10 benchmarking functions and applied in solving a logistics distribution center location problem. The performance of the CSDE is compared with several metaheuristic algorithms via the best solution, mean solution, and convergence speed. Experimental results show that CSDE performs better than or equal to CS, ICS, and some other metaheuristic algorithms, which reveals that the proposed CSDE is an effective and competitive algorithm for solving the logistics distribution center location problem.

Hybrid Harris Hawk Optimization Based on Differential Evolution (HHODE) Algorithm for Optimal Power Flow Problem

Harri’s Hawk Optimization (HHO) algorithm manifests as a new meta-heuristic algorithm in literature. When we look at studies that have used with this algorithm, we can see that its results in test functions and in the solutions of some test functions in IEEE Congress on Evolutionary Computation (CEC) are much better compared to other heuristic and meta heuristic algorithm results. In this study, an algorithm has been developed which has been hybridized with the mutation operators of Differential Evolution (DE) to further improve the HHO algorithm. This algorithm is named as Hybrid Harris Hawk Optimization based on Differential Evolution (HHODE). Performance of the proposed HHODE algorithm has been first compared with HHO and then compared with the results of other algorithms which have been most commonly used in the literature. In this comparison process, the most commonly used test functions in the literature and some of the other test functions in CEC2005 and CEC2017 as a new application field, have been solved. When the results of the comparison of HHODE with other algorithms are analyzed, it is observed that the balance between the exploratory tendency and exploitative tendency of the algorithm is well consistent. Formula 1 ranking method is used in the order of HHODE according to HHO and other algorithms. When a general evaluation of HHODE was performed, it was found to be an even more powerful algorithm as a result of the combination of strong features of both HHO and DE. The optimal power flow (OPF) problem is one of the most important problems of the modern power system. The HHODE algorithm is proposed to solve the OPF problem, which is considered without valve-point effect and prohibited zones (1) and with prohibited zones (2) in this paper. The effectiveness of the HHODE hybrid algorithm is tested on modified IEEE 30-bus test system. The result of HHODE algorithms are compared with other optimization algorithms in the literature.

Adaptive Differential Evolution Based on Simulated Annealing for Large-Scale Dynamic Economic Dispatch with Valve-Point Effects

Dynamic economic dispatch (DED) that considers valve-point effects is a complex nonconvex and nonsmooth optimization problem in power systems. Over the past few decades, multiple approaches have been developed to solve this problem. In this paper, an adaptive differential evolution based on simulated annealing algorithm is proposed to solve the DED problem with valve-point effects. Simulated annealing (SA) algorithm is employed to carry out an adaptive selection mechanism in which the mutation operators of differential evolution (DE) are selected adaptively based on their historical performance. A mutation operator pool consisting of five operators is built to make each operator show its strength at different stages of the evolutionary process. Moreover, a heuristic strategy is introduced to transform infeasible solutions towards feasible ones to enhance the convergence rate of the proposed algorithm. The effectiveness of the proposed methods is demonstrated first on 10 popular benchmark functions with 100 dimensions, in comparison with the classic DE and five variants. Then, it is used to solve four DED problems with 10, 15, 30, and 54 units, which consider the valve-point effects, transmission loss, and prohibited operating zones. The simulation results are compared with those of state-of-the-art algorithms to clarify the significance of the proposed method and verify its performance. Three systems with 100-500 generators are also tested to confirm the advantages of the proposed method on large-scale DED problem.

A Parallel Surrogate Model Assisted Evolutionary Algorithm for Electromagnetic Design Optimization

Optimization efficiency is a major challenge for electromagnetic (EM) device, circuit, and machine design. Although both surrogate model-assisted evolutionary algorithms (SAEAs) and parallel computing are playing important roles in addressing this challenge, there is little research that investigates their integration to benefit from both techniques. In this paper, a new method, called parallel SAEA for electromagnetic design (PSAED), is proposed. A state-of-the-art SAEA framework, surrogate model-aware evolutionary search, is used as the foundation of PSAED. Considering the landscape characteristics of EM design problems, three differential evolution mutation operators are selected and organized in a particular way. A new SAEA framework is then proposed to make use of the selected mutation operators in a parallel computing environment. PSAED is tested by a micromirror and a dielectric resonator antenna as well as four mathematical benchmark problems of various complexity. Comparisons with state-of-the-art methods verify the advantages of PSAED in terms of efficiency and optimization capacity.

Differential evolution mutation operators for constrained multi-objective optimization

Many real-world optimization problems belong to constrained multi-objective optimization problems (CMOPs). Handling constraints and optimizing objectives are two equally important goals. With effective and efficient population-based meta-heuristics in mind, how to generate the offspring with good convergence and diversity properties is a problem to be solved. Competitive algorithms based on different evolution (DE) metaphors have been proposed to solve CMOPs over years as the performance of the DE is attractive. The creative idea of the proposed algorithm is to design a novel mutation mechanism for handling infeasible solutions and feasible solutions respectively. The mechanism can produce well distributed Pareto optimal front while satisfying all concerning constraints. The performance of the algorithm is evaluated on nineteen benchmark functions. Compared with three representative constraint handling techniques and latest optimization algorithms, experimental results have indicated that the proposed algorithm is an effective candidate for real-world problems. At last, the proposed method is used to solve combined economic emission dispatch (CEED) problem. The experiment results have further validated the efficiency of the method.

Ranking-Based Differential Evolution for Large-Scale Continuous Optimization

Large-scale continuous optimization has gained considerable attention in recent years. Differential evolution (DE) is a simple yet efficient global numerical optimization algorithm, which has been successfully used in diverse fields. Generally, the vectors in the DE mutation operators are chosen randomly from the population. In this paper, we employ the ranking-based mutation operators for the DE algorithm to improve DE's performance. In the ranking-based mutation operators, the vectors are selected according to their rankings in the current population. The ranking-based mutation operators are general, and they are integrated into the original DE algorithm, GODE, and GaDE to verify the enhanced performance. Experiments have been conducted on the large-scale continuous optimization problems. The results indicate that the ranking-based mutation operators are able to enhance the overall performance of DE, GODE, and GaDE in the large-scale continuous optimization problems.

Multi-objective differential evolution with performance-metric-based self-adaptive mutation operator for chemical and biochemical dynamic optimization problems

Each mutation operator of differential evolution (DE) algorithm is generally suitable for certain specific types of multi-objective optimization problems (MOPs) or particular stages of the evolution. To automatically select an appropriate mutation operator for solving MOPs in different phases of the evolution, a multi-objective differential evolution with performance-metric-based self-adaptive mutation operator (MODE-PMSMO) is proposed in this study. In MODE-PMSMO, a modified inverted generational distance (IGD) is utilized to evaluate the performance of each mutation operator and guide the evolution of mutation operators. The proposed MODE-PMSMO is then compared with seven multi-objective evolutionary algorithms (MOEAs) on five bi-objective and five tri-objective optimization problems. Generally, MODE-PMSMO exhibits the best average performance among all compared algorithms on ten MOPs. Additionally, MODE-PMSMO is employed to solve four typical multi-objective dynamic optimization problems in chemical and biochemical processes. Experimental results indicate that MODE-PMSMO is suitable for solving these actual problems and can provide a set of nondominated solutions for references of decision makers.

Adaptive Multimodal Continuous Ant Colony Optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization (ACO) algorithms in preserving high diversity, this paper intends to extend ACO algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ACO algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima.