Topic
Discrete optimization
About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.
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TL;DR: In this paper, the authors used multidimensional Z transforms and the discrete form of the Volterra series to analyze a large class of nonlinear sampled-data systems and nonlinear difference equations, presenting the solution in terms of the kernels of the VOLTERRA series.
Abstract: By utilizing multidimensional Z transforms and the discrete form of the Volterra series it is shown how to analyze a large class of nonlinear sampled-data systems and nonlinear difference equations, presenting the solution in terms of the kernels of the Volterra series. The method is shown to be just as applicable when the discrete system is not quiescent with the interaction between the initial conditions and the driving function evidenced by means of the transition matrix. Several illustrative examples are given, and applications of the method are suggested.
98 citations
01 Jan 2004
TL;DR: The novel optimization method based on Differential Evolution algorithm is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.
Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The Part 1 of the article describes a novel optimization method based on Differential Evolution algorithm. The required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. In Part 2 of the article a mechanical engineering design related numerical example, design of a coil spring, is given to illustrate the capabilities and the practical use of the method. It is demonstrated that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.
98 citations
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TL;DR: This framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions, and easily incorporates robustness to different kinds of outliers through the choice of the loss function.
98 citations
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TL;DR: In this chapter a review of recent results on robust discrete optimization is presented, and the most popular discrete and interval uncertainty representations are discussed.
Abstract: In this chapter a review of recent results on robust discrete optimization is presented. The most popular discrete and interval uncertainty representations are discussed. Various robust concepts are presented, namely the traditional minmax (regret) approach with some of its recent extensions, and several two-stage concepts. A special attention is paid to the computational properties of the robust problems considered.
98 citations
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01 Jan 2018
TL;DR: This work intends to analyze nature-inspired algorithms both qualitatively and quantitatively, and briefly outline the links between self-organization and algorithms, and then analyze algorithms using Markov chain theory, dynamic system and other methods.
Abstract: Nature-inspired algorithms are a class of effective tools for solving optimization problems and these algorithms have good properties such as simplicity, flexibility and high efficiency. Despite their popularity in practice, a mathematical framework is yet to be developed to analyze these algorithms theoretically. This work intends to analyze nature-inspired algorithms both qualitatively and quantitatively. We briefly outline the links between self-organization and algorithms, and then analyze algorithms using Markov chain theory, dynamic system and other methods. This can serve as a basis for building a multidisciplinary framework for algorithm analysis.
98 citations