Opposition-Based Learning in Compact Differential Evolution

Artificial Intelligence Review, 2010

Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving various engineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon DE by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimensional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within both macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which includes some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Thus, a limited employment of these alternative moves appears to be the best option in successfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the introduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE functioning.

2007 IEEE Congress on Evolutionary Computation, 2007

In this paper, an enhanced version of the Opposition-Based Differential Evolution (ODE) is proposed. ODE utilizes opposite numbers in the population initialization and generation jumping to accelerate Differential Evolution (DE). Instead of opposite numbers, in this work, quasi opposite points are used. So, we call the new extension Quasi-Oppositional DE (QODE). The proposed mathematical proof shows that in a black-box optimization problem quasi-opposite points have a higher chance to be closer to the solution than opposite points. A test suite with 15 benchmark functions has been employed to compare performance of DE, ODE, and QODE experimentally. Results confirm that QODE performs better than ODE and DE in overall. Details for the proposed approach and the conducted experiments are provided.

This paper presents a comparison of various strategies of differential evolution. Differential evolution (DE) is a simple and powerful optimization method, which is mainly applied to numerical optimization and many other problems (for example: neural network train, filter design or image analysis). The comparison of various modifications (named strategies) of DE algorithm allows to choose the algorithm version, which is best adjusted to desirable requirements. Three parameters are tested: speed, accuracy and completeness. The first section presents general optimization problem, and says little about methods used to function optimization. The next section describes a method of differential evolution – basic algorithm is presented. Two different crossover methods, process of initial population creation and basic mutation schema are described. The third section contains chosen by authors different mutation strategies (called DE strategies), and their variations. Every strategy is descr...

Latest Survey Paper of DEs, 2014

Over the past few years, differential Evolution (DE) is generally considered as a reliable, accurate and robust population based evolutionary algorithm (EA). It is capable of handling non-differentiable, nonlinear, multi-modal and constrained optimization problems. However, it suffers from slow convergence rate and takes large computational time for optimizing the computationally expensive objective functions including problems dimensionality, several local and global optimums. Over the last few years, several attempts have been made to overcome these drawbacks of simple DE by employing the key features of some existing evolutionary algorithms either self-adaptively and have been formed in the forms of enhanced versions of DEs. This paper reviews those efforts and gathered state-of-the-art survey of the DEs that included some novel self-adaptive mechanisms, different ensemble techniques, efficient local search optimizers and various constrained handling techniques.

Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new candidate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made-unless specific mechanisms for diversity preservation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely " DE/rand/1/bin " and " DE/rand/1/exp " , and a rotation-invariant strategy, " DE/current-to-random/1 " , with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that " DE/rand/1/exp " preserves the population diversity the most, whereas " DE/current-to-random/1 " preserves diversity the least.

Applied Sciences, 2018

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based metaheuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. In particular, we present a state-of-the-art survey of the literature on DE and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques.

Communications in computer and information science, 2012

In recent decades, new optimization algorithms have attracted much attention from researchers in both gradientand evolution-based optimal methods. Many strategy techniques are employed to enhance the effectiveness of optimal methods. One of the newest techniques is opposition-based learning (OBL), which shows more power in enhancing various optimization methods. This research presents a new edition of the Differential Evolution (DE) algorithm in which the OBL technique is applied to investigate the opposite point of each candidate of selfadaptive control parameters. In comparison with conventional optimal methods, the proposed method is used to solve benchmark-test optimal problems and applied to real optimizations. Simulation results show the effectiveness and improvement compared with some reference methodologies in terms of the convergence speed and stability of optimal results.

2011 IEEE Congress of Evolutionary Computation (CEC), 2011

Differential Evolution is a population based stochastic algorithm with less number of parameters to tune. However, the performance of DE is sensitive to the mutation and crossover strategies and their associated parameters. To obtain optimal performance, DE requires time consuming trial and error parameter tuning. To overcome the computationally expensive parameter tuning different adaptive/self-adaptive techniques have been proposed. Recently the idea of ensemble strategies in DE has been proposed and favorably compared with some of the state-of-the-art self-adaptive techniques.

Evolutionary algorithms have been shown to be powerful for solving multi-objective optimization problems, where non-dominated sorting is a widely adopted selection method. Differential Evolution (DE) is a simple and efficient population-based EA that has been reported in several studies for its high robustness, fast convergence speed, and good solution quality, making it a very popular EA in the evolutionary computing community. In this paper, a new two stage hybridized multi-objective differential evolution algorithm MODE based on opposition learning OBL is proposed, which balances exploration and exploitation capabilities as found in the original differential evolution DE, as well as OBL that brings higher selection pressure. in this developed approach, two stage are evolved. Firstly, MODE based on ranking mutation is applied using non-dominated sorting and crowding distance. Secondly, jumping probability is used in second stage in order to meet the objective of balancing the precision of the solution and the rate of convergence while maintaining the diversity of the population by opposition-based learning technique. Through the validation of MODE-OBL using a suite of carefully selected test reference problems for continuous multi-objective optimization, it is observed that MODE-OBL achieves overall better performance in terms of convergence and diversity compared to other algorithms of literature. In addition, MODE-OBL can be recommended to solve large portfolio optimization problems as well as problems with complex Pareto sets, as evidenced by its superior optimization performance in these types of problems.

Studies in Computational Intelligence, 2008

In this chapter we present an overview of the major applications areas of differential evolution. In particular we pronounce the strengths of DE algorithms in tackling many difficult problems from diverse scientific areas, including single and multiobjective function optimization, neural network training, clustering, and real life DNA microarray classification. To improve the speed and performance of the algorithm we employ distributed computing architectures and demonstrate how parallel, multi-population DE architectures can be utilised in single and multiobjective optimization. Using data mining we present a methodology that allows the simultaneous discovery of multiple local and global minimizers of an objective function. At a next step we present applications of DE in real life problems including the training of integer weight neural networks and the selection of genes of DNA microarrays in order to boost predictive accuracy of classification models. The chapter concludes with a discussion on promising future extensions of the algorithm, and presents novel mutation operators, that are the result of a genetic programming procedure, as very interesting future research direction.