In this work we consider the problem of Stochastic Submodular Maximization, in which we would like to maximize the value of a monotone and submodular objective function, subject to the fact that the values of this fun...
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Quantum computers are designed to outperform standard computers by running quantum algorithms. Fields in which quantum algorithms can be applied include cryptography, search and optimization, simulation of quantum sys...
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The paper considers the application of mathematical methods in the problems of territorial design on the example of designing the development of oil fields. The application of the method of sequential calculations for...
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We study the problem of multicommodity flow and multicut in treewidth-2 graphs and prove bounds on the multiflow-multicut gap. In particular, we give a primal-dual algorithm for computing multicommodity flow and multi...
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Fitness approximation methods have been widely employed in evolutionary algorithms to reduce the number of fitness evaluations in solving expensive optimization problems. As a simple and efficient approximation approa...
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ISBN:
(纸本)9781728145693
Fitness approximation methods have been widely employed in evolutionary algorithms to reduce the number of fitness evaluations in solving expensive optimization problems. As a simple and efficient approximation approach, k-nearest neighbors (kNN) estimates the fitness value of an unknown solution by combining the fitness values of its nearest neighbors according to a similarity measure. kNN generally adopts the Euclidean distance as the similarity measure, which may limit its performance as the solution distribution information is underutilized in the approximation process. Aiming at this issue, this study proposes a Mahalanobis distance-based k-nearest neighbors (MkNN) to improve the approximation accuracy by utilizing the distribution information. Compared to the Euclidean distance-based kNN (EkNN), MkNN adopts the Mahalanobis distance to measure the similarity between solutions, which is capable of capturing the distribution information of solutions and thus can improve the approximation efficiency. Furthermore, considering that the main idea of estimation of distribution algorithms (EDAs) is also to learn the distribution information of solutions, the proposed MkNN as well as EkNN are combined with an EDA and two new algorithms named EDA-MkNN and EDA-EkNN, respectively, are developed for expensive optimization. The performances of EDA-MkNN and EDA-EkNN were comprehensively tested on a set of 28 benchmark functions and compared with that of a typical EDA. Experimental results demonstrate that MkNN and EkNN could effectively improve the performance of EDA in solving different kinds of expensive optimization problems and MkNN can have an edge over EkNN on condition that the distribution information is well captured.
We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected...
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We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning subgraph (2-ECSS) of minimum cost. We first present a reduction of any givenMAP instance to a collection of well-structured MAP instances such that the approximation guarantee is preserved. Then we present a 7/4 approximation algorithm for awell-structuredMAPinstance. The algorithm starts with amin-cost 2-edge cover and then applies ear-augmentation steps. We analyze the cost of the ear-augmentations using an approach similar to the one proposed by Vempala and Vetta for the (unweighted) min-size 2-ECSS problem (in: Jansen and Khuller (eds.) approximationalgorithms forCombinatorialOptimization, Third InternationalWorkshop, APPROX2000, Proceedings, LNCS1913, pp.262-273, Springer, Berlin, 2000).
This study's purpose is to analyze channel members' local buckling behavior based on the energy method. A mechanical model and displacement functions that simulate the local buckling behavior were proposed. An...
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The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ϵ ⊆ E or vertices ν ⊆ V whose removal G ∖ ϵ, G ∖ ν makes a given multi-digraph G=(V, E) acyc...
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In this paper we consider three problems of searching for disjoint subsets among a finite set of points in an Euclidean space. In all three problems, it is required to maximize the size of the minimal cluster so that ...
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In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the f...
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In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved;also the form of the optimized result as a TFS is guaranteed. We regard the optimized TFS as the "skeleton" (blueprint) of the original fuzzy set. Based on this skeleton, we further extend the TFS to a higher type, that is, an interval type-2 TFS (IT2 TFS), so that more information about the original fuzzy set could be captured but the number of the parameters used to describe the original fuzzy set is still maintained low (nine parameters are required for an IT2 TFS). The principle of justifiable granularity is used to ensure that the formed type-2 information granule exhibits a sound interpretation. Both synthetic fuzzy sets and those constructed by the fuzzy C-means algorithm applied to the publicly available data have been used to demonstrate the usefulness of the proposed approximation methods.
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