Journal•ISSN: 0096-3003

# Applied Mathematics and Computation

About: Applied Mathematics and Computation is an academic journal. The journal publishes majorly in the area(s): Numerical analysis & Nonlinear system. It has an ISSN identifier of 0096-3003. Over the lifetime, 22432 publication(s) have been published receiving 430482 citation(s).

Topics: Numerical analysis, Nonlinear system, Differential equation, Boundary value problem, Partial differential equation

##### Papers published on a yearly basis

##### Papers

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TL;DR: Results show that the performance of the ABC is better than or similar to those of other population-based algorithms with the advantage of employing fewer control parameters.

Abstract: Artificial Bee Colony (ABC) algorithm is one of the most recently introduced swarm-based algorithms. ABC simulates the intelligent foraging behaviour of a honeybee swarm. In this work, ABC is used for optimizing a large set of numerical test functions and the results produced by ABC algorithm are compared with the results obtained by genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and evolution strategies. Results show that the performance of the ABC is better than or similar to those of other population-based algorithms with the advantage of employing fewer control parameters.

2,544 citations

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TL;DR: The impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented and the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods.

Abstract: This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm has been successfully applied to various benchmarking and standard engineering optimization problems. Numerical results reveal that the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems.

1,626 citations

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TL;DR: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet.

Abstract: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet. Two rules, the rule of solution expression and the rule of coefficient ergodicity, are proposed, which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering. An explicit analytic solution is given for the first time, with recursive formulas for coefficients. This analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem.

1,477 citations

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TL;DR: The result reveals that the first order of approximation obtained by the proposed method is valid uniformly even for very large parameter, and is more accurate than the perturbation solutions.

Abstract: In this paper, a new perturbation method is proposed. In contrast to the traditional perturbation methods, this technique does not require a small parameter in an equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter [email protected]?[0,1] is constructed, and the imbedding parameter is considered as a ''small parameter'', so the method is called the homotopy perturbation method, which can take the full advantages of the traditional perturbation methods and homotopy techniques. To illustrate its effectiveness and its convenience, a Duffing equation with high order of nonlinearity is used; the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter, and is more accurate than the perturbation solutions.

1,343 citations

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TL;DR: A novel version of the method (augmented @e-constraint method - AUGMECON) is proposed that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations.

Abstract: As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a posteriori methods convey much more information to the decision maker. Especially, the a posteriori (or generation) methods give the whole picture (i.e. the Pareto set) to the decision maker, before his/her final choice, reinforcing thus, his/her confidence to the final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The present work is an effort to effectively implement the @e-constraint method for producing the Pareto optimal solutions in a MOMP. We propose a novel version of the method (augmented @e-constraint method - AUGMECON) that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations. The method AUGMECON has been implemented in GAMS, a widely used modelling language, and has already been used in some applications. Finally, an interactive approach that is based on AUGMECON and eventually results in the most preferred Pareto optimal solution is also proposed in the paper.

1,149 citations