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: 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: In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 12 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.

Output: Soft Constraints of Difference and Equality


Input: Consider Input: The paper introduces a new method for discrimination of documents given in different scripts. The document is mapped into a uniformly coded text of numerical values. It is derived from the position of the letters in the text line, based on their typographical characteristics. Each code is considered as a gray level. Accordingly, the coded text determines a 1-D image, on which texture analysis by run-length statistics and local binary pattern is performed. It defines feature vectors representing the script content of the document. A modified clustering approach employed on document feature vector groups documents written in the same script. Experimentation performed on two custom oriented databases of historical documents in old Cyrillic, angular and round Glagolitic as well as Antiqua and Fraktur scripts demonstrates the superiority of the proposed method with respect to well-known methods in the state-of-the-art.


Output: Document Image Coding and Clustering for Script Discrimination