Differential Evolution Based on Improved Learning Strategy

Social learning differential evolution

Differential Evolution (DE) is an algorithm to solve possibly nonlinear and non-differentiable global optimization problems. Classical Differential Evolution (CDE) employs a synchronous generation-based evolution strategy. We propose a modification of the CDE algorithm by incorporating mutation, crossover and selection operations into an asynchronous strategy. A novel Asynchronous Differential Evolution (ADE) is well suited for parallel optimization. Moreover even in the sequential mode its rate of convergence is competitive to CDE. The performance of the Asynchronous Differential Evolution is reported on a set of benchmark functions.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Differential evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

Differential evolution (DE) is one of the most successful evolutionary algorithms (EAs) for global numerical optimization. Like other EAs, maintaining population diversity is important for DE to escape from local optima and locate a near-global optimum. Using a multi-population algorithm is a representative method to avoid early loss of population diversity. In this paper, we propose a multi-population DE algorithm (MPDE) which manipulates multiple sub-populations. Different sub-populations in MPDE exchange information via a novel mutation operation instead of migration used in most multi-population EAs. The mutation operation is helpful to balance the fast convergence and population diversity of the proposed algorithm. Moreover, the performance of MPDE is further improved by an adaptive parameter control scheme designed based on the multi-population approach. Each sub-population in MPDE evolves with its own set of control parameters, and a learning strategy is used to adaptively adjust the parameter values. A set of benchmark functions is used to test the proposed MPDE algorithm. The experimental results show that MPDE performs better than, or at least comparably, to the classical single population DE with fixed parameter values and three existing state-of-the-art DE variants.

In this paper we present an empirical , comparative performance, analysis of fourteen variants of Differential Evolution (DE) and Multiple Trial Vectors Differential Evolution algorithms to solve unconstrained global optimization problems. The aim is (1) to compare Multiple Trial Vectors DE, which allows each parent vector in the population to generate more than one trial vector, against the classical DE and (2) to identify the competitive variants which perform reasonably well on problems with different features. The DE and Multiple Trial Vectors DE variants are benchmarked on 6 test functions grouped by features --- unimodal separable, unimodal nonseparable, multimodal separable and multimodal non-separable. The analysis identifies the competitive variants and shows that Multiple Trial Vectors DE compares well with the classical DE.

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

Differential Evolution (DE) has become an advanced, robust, and proficient alternative technique for clustering on account of their population-based stochastic and heuristic search manners. Balancing better the exploitation and exploration power of the DE algorithm is important because this ability influences the performance of the algorithm. Besides, keeping superior solutions for the initial population raises the probability of finding better solutions and the rate of convergence. In this paper, an enhanced DE algorithm is introduced for clustering to offer better cluster solutions with faster convergence. The proposed algorithm performs a modified mutation strategy to improve the DE’s search behavior and exploits Quasi-Opposition-based Learning (QBL) to choose fitter initial solutions. This mutation strategy that uses the best solution as a target solution and applies three differentials contributes to avoiding local optima trap and slow convergence. The QBL based initialization method also contributes to increasing the quality of the clustering results and convergence rate. The experimental analysis was conducted on seven real datasets from the UCI repository to evaluate the performance of the proposed clustering algorithm. The obtained results showed that the proposed algorithm achieves more compact clusters and stable solutions than the competing conventional DE variants. Moreover, the performance of the proposed algorithm was compared with the existing state of the art clustering techniques based on DE. The corresponding results also pointed out that the proposed algorithm is comparable to other DE based clustering approaches in terms of the value of the objective functions. Therefore, the proposed algorithm can be regarded as an efficient clustering tool.

Students’ experiences and learning skills are key performance indicators for an institution’s performance. A questionnaire survey was conducted between university business students for a period of one semester to ascertain the role of improved learning strategies which are central to strategic planning. A survey on nearly 400 students was conducted and 95 respondents conformed to the guidelines and were analysed using SPSS. Results showed that the types of learning activities employed are on average okay and less stressful with quiz having the highest percentage. The poorer the student learning experiences and satisfaction, the more vulnerable these institutions are to having sustainable growth and the higher the student satisfaction and satisfactory learning experiences, the more preferable and competitive these institutions become. Students also gain more of knowledge and creative and innovative skills from the learning activities. Therefore, the current learning strategies are largely useful and dependable in building institutional capacity.

An improved multi-population ensemble differential evolution

Adaptive Operator Selection (AOS) is an approach that controls discrete parameters of an Evolutionary Algorithm (EA) during the run. In this paper, we propose an AOS method based on Double Deep Q-Learning (DDQN), a Deep Reinforcement Learning method, to control the mutation strategies of Differential Evolution (DE). The application of DDQN to DE requires two phases. First, a neural network is trained offline by collecting data about the DE state and the benefit (reward) of applying each mutation strategy during multiple runs of DE tackling benchmark functions. We define the DE state as the combination of 99 different features and we analyze three alternative reward functions. Second, when DDQN is applied as a parameter controller within DE to a different test set of benchmark functions, DDQN uses the trained neural network to predict which mutation strategy should be applied to each parent at each generation according to the DE state. Benchmark functions for training and testing are taken from the CEC2005 benchmark with dimensions 10 and 30. We compare the results of the proposed DE-DDQN algorithm to several baseline DE algorithms using no online selection, random selection and other AOS methods, and also to the two winners of the CEC2005 competition. The results show that DE-DDQN outperforms the non-adaptive methods for all functions in the test set; while its results are comparable with the last two algorithms.

Differential evolution (DE) is a simple, powerful optimization algorithm, which has been widely used in many areas.However, the choices of the best mutation and search strategies are difficult for the specific issues. To alleviate thesedrawbacks and enhance the performance of DE, in this paper, the hybrid framework based on the adaptive mutationand Wrapper Local Search (WLS) schemes, is proposed to improve searching ability to efficiently guide the evolutionof the population toward the global optimum. Furthermore, the effective particle encoding representation namedParticle Segment Operation-Machine Assignment (PSOMA) that we previously published is applied to always producefeasible candidate solutions for solving the Flexible Job-shop Scheduling Problem (FJSP). Experiments wereconducted on comprehensive set of complex benchmarks including the unimodal, multimodal and hybrid compositionfunction, to validate performance of the proposed method and to compare with other state-of-the art DE variants suchas jDE, JADE, MDE_pBX etc. Meanwhile, the hybrid DE model incorporating PSOMA is used to solve differentrepresentative instances based on practical data for multi-objective FJSP verifications. Simulation results indicate thatthe proposed method performs better for the majority of the single-objective scalable benchmark functions in terms ofthe solution accuracy and convergence rate. In addition, the wide range of Pareto-optimal solutions and more Ganttchart decision-makings can be provided for the multi-objective FJSP combinatorial optimizations.

The Algebraic Differential Evolution (ADE) is a recently proposed combinatorial evolutionary scheme which mimics the behaviour of the classical Differential Evolution (DE) in discrete search spaces which can be represented as finitely generated groups. ADE has been successfully applied to both permutation and binary optimization problems. However, in the previous works, the relationship between ADE and the classical continuous DE has been only intuitively sketched without any theoretical or experimental proof. Here, we fill this gap by providing both theoretical and experimental justifications proving that ADE is a full-fledged generalization of DE which works across different search spaces. First, we formally prove that there exists a concrete implementation of ADE's algebraic operations converging to the classical vector operations of DE, then we propose a real-vector implementation of ADE and we experimentally prove that its behaviour is statistically equivalent to DE. As conclusion, we also pave the way for further applications of the original DE idea to mixed discrete/continuous search spaces.

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.

In this paper, a novel hybrid intelligent algorithm, integrating with differential evolution (DE) and particle swarm optimization (PSO), is proposed. Initially, all individual in the population are divided into three groups (in increasing order of function value): inferior group, mid-group, and superior group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method uses DE-PSO-DE, then it is denoted by DPD. At present, many mutation strategies of DE are reported. Every mutation strategy has its own pros and cons, so which one of them should be selected is critical for DE. Therefore, over 8 mutation strategies, the best one is investigated for both DEs used in DPD. Moreover, two strategies, namely elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality), have been employed in DPD cycle. Combination of 8 mutation strategies generated 64 different variants of DPD. Top 4 DPDs are investigated through solving a set of constrained benchmark functions. Based on the ‘performance,’ best DPD is reported and further used in solving engineering design problem.