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.
Papers published on a yearly basis
Papers
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TL;DR: Two classes of discrete quasiconvex functions are introduced by generalizing the concepts of M- and L-convexity due to Murota, and it is shown that various greedy algorithms work for the minimization of quasi M-
37 citations
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TL;DR: A model of a forced circulation solar water heating system for supplying a hot water at a required temperature for an aquaculture system using genetic algorithm, which is one of the modern optimization techniques because of their evolutionary nature.
37 citations
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TL;DR: This work revisits the continuous max-flow problem and shows that the analogous discrete formulation is different from the classical max- flow problem, and applies an appropriate combinatorial optimization technique to find a null-divergence solution that exhibits no metrication artifacts.
Abstract: Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cut algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching, and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit metrication artifacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous max-flow (CCMF) problem to find a null-divergence solution that exhibits no metrication artifacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the max-flow and the total variation problems are not always equivalent.
37 citations
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03 Apr 2005TL;DR: This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program, or a generalized geometric program (GGP).
Abstract: This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program (GP), or a generalized geometric program (GGP). These nonlinear, constrained optimization problems can be transformed to convex optimization problems, and then solved (globally) very efficiently.
37 citations
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TL;DR: Theoretical analysis and experiment results show that the minimum near-convex decomposition (MNCD) outperforms the state-of-the-art results without introducing redundant parts and thus leads to robust shape representation.
Abstract: Shape decomposition is a fundamental problem for part-based shape representation. We propose the minimum near-convex decomposition (MNCD) to decompose arbitrary shapes into minimum number of "near-convex" parts. The near-convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of nonintersecting cuts. Two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition. With the degree of near-convexity a user-specified parameter, our decomposition is robust to local distortions and shape deformation. The optimization can be efficiently solved via binary integer linear programming. Both theoretical analysis and experiment results show that our approach outperforms the state-of-the-art results without introducing redundant parts and thus leads to robust shape representation.
37 citations