Opposition-Based Differential Evolution

Evolutionary algorithms (EAs) are well-established techniques to approach those problems which for the classical optimization methods are difficult to solve. Tackling problems with mixed-type of variables, many local optima, undifferentiable or non-analytical functions are some examples to highlight the outstanding capabilities of the evolutionary algorithms. Among the various kinds of evolutionary algorithms, differential evolution (DE) is well known for its effectiveness and robustness. Many comparative studies confirm that the DE outperforms many other optimizers. Finding more accurate solution(s), in a shorter period of time for complex black-box problems, is still the main goal of all evolutionary algorithms. The opposition concept, on the other hand, has a very old history in philosophy, set theory, politics, sociology, and physics. But, there has not been any opposition-based contribution to optimization. In this thesis, firstly, the opposition-based optimization (OBO) is constituted. Secondly, its advantages are formally supported by establishing mathematical proofs. Thirdly, the opposition-based acceleration schemes, including opposition-based population initialization and generation jumping, are proposed. Fourthly, DE is selected as a parent algorithm to verify the acceleration effects of proposed schemes. Finally, a comprehensive set of well-known complex benchmark functions is employed to experimentally compare and analyze the algorithms. Results confirm that opposition-based DE (ODE) performs better than its parent (DE), in terms of both convergence speed and solution quality. The main claim of this thesis is not defeating DE, its numerous versions, or other optimizers, but to introduce a new notion into nonlinear continuous optimization via innovative metaheuristics, namely the notion of opposition. Although, ODE has been compared with six other optimizers and outperforms them overall. Furthermore, both presented experimental and mathematical results conform with each other and demonstrate that opposite points are more beneficial than pure random points for black-box problems; this fundamental knowledge can serve to accelerate other machine learning approaches as well (such as reinforcement learning and neural networks). And perhaps in future, it could replace the pure randomness with random-opposition model when there is no a priori knowledge about the solution/problem. Although, all conducted experiments utilize DE as a parent algorithm, the proposed schemes are defined at the population level and, hence, have an inherent potential to be utilized for acceleration of other DE extensions or even other population-based algorithms, such as genetic algorithms (GAs). Like many other newly introduced concepts, ODE and the proposed opposition-based schemes still require further studies to fully unravel their benefits, weaknesses, and limitations

Evolutionary Neuro-Computing Approaches to System Identification

System models are essentially required for analysis, controller design and future prediction. System identification is concerned with developing models of physical system. Although linear system identification got enriched with several useful classical methods, nonlinear system identification always remained active area of research due to the reason that most of the real world systems are nonlinear in nature and moreover, having non-unique models. Among the several conventional system identification techniques, the Volterra series, Hammerstein-Wiener and polynomial model identification involve considerable computational complexities. The other techniques based on regression models such as nonlinear autoregressive exogenous (NARX) and nonlinear autoregressive moving average exogenous (NARMAX), also suffer from dfficulty in choosing regressors

Applying Mean-field Approximation to Continuous Time Markov Chains

The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and uid model checking analysis techniques

Improved scheme of e-mail spam classification using meta-heuristics feature selection and support vector machine

With the technological revolution in the 21st century, time and distance of communication are decreased by using electronic mail (e-mail). Furthermore, the growing use of e-mail has led to the emergence and further growth problems caused by unsolicited bulk e-mails, commonly referred to as spam e-mail. Many of the existing supervised algorithms like the Support Vector Machine (SVM) were developed to stop the spam e-mail. However, the problem of dealing with large data and high dimensionality of feature space can lead to high execution-time and low accuracy of spam e-mail classification. Nowadays, removing the irrelevant and redundant features beside finding the optimal (or near-optimal) subset of features significantly influences the performance of spam e-mail classification; this has become one of the important challenges. Therefore, in order to optimize spam e-mail classification accuracy, dimensional reduction issues need to be solved. Feature selection schemes become very important in order to reduce the dimensionality through selecting a proper subset feature to facilitate the classification process. The objective of this study is to investigate and improve schemes to reduce the execution time and increase the accuracy of spam e-mail classification. The methodology of this study comprises of four schemes: one-way ANOVA f-test, Binary Differential Evolution (BDE), Opposition Differential Evolution (ODE) and Opposition Particle Swarm Optimization (OPSO), and combination of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The four schemes were used to improve the spam e-mail classification accuracy. The classification accuracy of the proposed schemes were 95.05% with population size of 50 and 1000 number of iterations in 20 runs and 41 features. The experiment of the proposed schemes were carried out using spambase and spamassassin benchmark dataset to evaluate the feasibility of proposed schemes. The experimental findings demonstrate that the improved schemes were able to efficiently reduce the number of features as well as improving the e-mail classification accuracy

An Improved Water Strider Algorithm for Optimal Design of Skeletal Structures

Water Strider Algorithm (WSA) is a new metaheuristic method that is inspired by the life cycle of water striders. This study attempts to enhance the performance of the WSA in order to improve solution accuracy, reliability, and convergence speed. The new method, called improved water strider algorithm (IWSA), is tested in benchmark mathematical functions and some structural optimization problems. In the proposed algorithm, the standard WSA is augmented by utilizing an opposition-based learning method for the initial population as well as a mutation technique borrowed from the genetic algorithm. By employing Generalized Space Transformation Search (GSTS) as an opposition-based learning method, more promising regions of the search space are explored; therefore, the precision of the results is enhanced. By adding a mutation to the WSA, the method is helped to escape from local optimums which is essential for engineering design problems as well as complex mathematical optimization problems. First, the viability of IWSA is demonstrated by optimizing benchmark mathematical functions, and then it is applied to three skeletal structures to investigate its efficiency in structural design problems. IWSA is compared to the standard WSA and some other state-of-the-art metaheuristic algorithms. The results show the competence and robustness of the IWSA as an optimization algorithm in mathematical functions as well as in the field of structural optimization

Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems

An Enhanced Differential Evolution Algorithm Based on Multiple Mutation Strategies

Differential evolution algorithm is a simple yet efficient metaheuristic for global optimization over continuous spaces. However, there is a shortcoming of premature convergence in standard DE, especially in DE/best/1/bin. In order to take advantage of direction guidance information of the best individual of DE/best/1/bin and avoid getting into local trap, based on multiple mutation strategies, an enhanced differential evolution algorithm, named EDE, is proposed in this paper. In the EDE algorithm, an initialization technique, opposition-based learning initialization for improving the initial solution quality, and a new combined mutation strategy composed of DE/current/1/bin together with DE/pbest/bin/1 for the sake of accelerating standard DE and preventing DE from clustering around the global best individual, as well as a perturbation scheme for further avoiding premature convergence, are integrated. In addition, we also introduce two linear time-varying functions, which are used to decide which solution search equation is chosen at the phases of mutation and perturbation, respectively. Experimental results tested on twenty-five benchmark functions show that EDE is far better than the standard DE. In further comparisons, EDE is compared with other five state-of-the-art approaches and related results show that EDE is still superior to or at least equal to these methods on most of benchmark functions