Abstract.The Multiple-Choice Multi-Dimension Knapsack Problem (MMKP) is a variant of the 0-1 Knapsack Problem, an NP-Hard problem. Hence algorithms for finding the exact solution of MMKP are not suitable for application in real time decision-making applications, like quality adaptation and admission control of an interactive multimedia system. This paper presents two new heuristic algorithms, M-HEU and I-HEU for solving MMKP. Experimental results suggest that M-HEU finds 96% optimal solutions on average with much reduced computational complexity and performs favorably relative to other heuristic algorithms for MMKP. The scalability property of I-HEU makes this heuristic a strong candidate for use in real time applications.

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We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

A generalized and improved(G′/G)-expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.

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The modified simple equation (MSE) method is promising for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this letter, we investigate solutions of the (2 + 1)-dimensional Zoomeron equation and the (2 + 1)-dimensional Burgers equation by using the MSE method and the Exp-function method. The competence of the methods for constructing exact solutions has been established.Ó 2013 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

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