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The capacitated min-k-cut problem of hypergraphis the problem of partitioning the vertices into k parts, and each part has a different capacity. The objective is to minimize the weight of cut hyper edges. It is an NP-hard problem which is an important problem with extensive applications to many areas, such as VLSI CAD, image segmentation, etc. Although many heuristic algorithms have been developed,...
This paper presented a randomized local search algorithm for one of the k-means clustering subproblems which requests that each cluster must has at least some points. It is proved that an expected 2-approximation randomized algorithm could be obtained if k centers come from different optimal subsets. A sample set that includes at least one point of each optimal sub-cluster is given in this paper....
Vertex cover is one of the best known NP-hard combinatorial optimization problems. Experimental work has claimed that evolutionary algorithms (EAs) perform fairly well for the problem and can compete with problem-specific ones. A theoretical analysis that explains these empirical results is presented concerning the random local search algorithm and the (1+1)-EA. Since it is not expected that an algorithm...
We studied the multicommodity facility location and a variant K-median problem as well. For the first problem, the pure combinatory strategies are presented. We give a subtle analysis for the nonmetric uncapacitated case and an approximation algorithm for the capacitated case. For the first time, the local search technique is exploited in the variant K-median problem with service installation and...
It is known that the maximum hidden vertex set problem on a given simple polygon is NP-hard (Shermer, 1989), therefore we focused on the development of approximation algorithms to tackle it. We propose four strategies to solve this problem, the first two (based on greedy constructive search) are designed specifically to solve it, and the other two are based on the general metaheuristics simulated...
This paper reviews the different gradient-based schemes and the sources of gradient, their availability, precision and computational complexity, and explores the benefits of using gradient information within a memetic framework in the context of continuous parameter optimization, which is labeled here as memetic gradient search. In particular, we considered a quasi-Newton method with analytical gradient...
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