This paper aims to prove the efficiency of an adapted computationally intelligence-based behavior of cats called the cat swarm optimization algorithm, that solves the open shop scheduling problem, classified as NP-hard which its importance appears in several industrial and manufacturing applications. The cat swarm optimization algorithm was applied to solve some benchmark instances from the literature. The computational results, and the comparison of the relative percentage deviation of the proposed metaheuristic with other's existing in the literature, show that the cat swarm optimization algorithm yields good results in reasonable execution time.
The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.
Performing the shape derivative (Sokolowski and Zolesio, 1992) and using the maximum principle, we show that the so-called Quadrature Surfaces free boundary problemhas a solution which contains strictly the support of f if and only ifWhere C is the convex hull of the support of f . We also give a necessary and sufficient condition of existence for the problem Q S ( f, k) where the term source f is a uniform density supported by a segment.
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