In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: This paper presents capabilities of using genetic algorithms to find approximations of function extrema, which cannot be found using analytic ways. To enhance effectiveness of calculations, algorithm has been parallelized using OpenMP library. We gained much increase in speed on platforms using multithreaded processors with shared memory free access. During analysis we used different modifications of genetic operator, using them we obtained varied evolution process of potential solutions. Results allow to choose best methods among many applied in genetic algorithms and observation of acceleration on Yorkfield, Bloomfield, Westmere-EX and most recent Sandy Bridge cores.

Output: GENERATING EXTREMA APPROXIMATION OF ANALYTICALLY INCOMPUTABLE FUNCTIONS THROUGH USAGE OF PARALLEL COMPUTER AIDED GENETIC ALGORITHMS

Input: Consider Input: Multi Expression Programming (MEP) is an evolutionary technique that may be used for solving computationally difficult problems. MEP uses a linear solution representation. Each MEP individual is a string encoding complex expressions (computer programs). A MEP individual may encode multiple solutions of the current problem. In this paper MEP is used for evolving a Traveling Salesman Problem (TSP) heuristic for graphs satisfying triangle inequality. Evolved MEP heuristic is compared with Nearest Neighbor Heuristic (NN) and Minimum Spanning Tree Heuristic (MST) on some difficult problems in TSPLIB. For most of the considered problems the evolved MEP heuristic outperforms NN and MST. The obtained algorithm was tested against some problems in TSPLIB. The results emphasizes that evolved MEP heuristic is a powerful tool for solving difficult TSP instances.

Output: Evolving TSP heuristics using Multi Expression Programming

Input: Consider Input: Markov chain model is widely applied in many fields, especially the field of prediction. The classical Discrete-time Markov chain(DTMC) is a widely used method for prediction. However, the classical DTMC model has some limitation when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain model is proposed by combining Dempster-Shafer evidence theory with Markov chain. In our model, the uncertain data is allowed to be handle in the form of interval number and the basic probability assignment(BPA) is generated based on the distance between interval numbers. The new belief Markov chain model overcomes the shortcomings of classical Markov chain and has an efficient ability in dealing with uncertain information. Moreover, an example of inventory prediction and the comparison between our model and classiCorresponding author at: School of Electronics and Information, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China. Tel: (86-29)88431267. E-mail address: jiangwen@nwpu.edu.cn, jiangwenpaper@hotmail.com Preprint submitted to Elsevier March 7, 2017 cal DTMC model can show the effectiveness and rationality of our proposed model.
Output: A new belief Markov chain model and its application in inventory prediction