Abstract: One of the global combinatorial optimization
problems in machine learning is feature selection. It concerned with
removing the irrelevant, noisy, and redundant data, along with
keeping the original meaning of the original data. Attribute reduction
in rough set theory is an important feature selection method. Since
attribute reduction is an NP-hard problem, it is necessary to
investigate fast and effective approximate algorithms. In this paper,
we proposed two feature selection mechanisms based on memetic
algorithms (MAs) which combine the genetic algorithm with a fuzzy
record to record travel algorithm and a fuzzy controlled great deluge
algorithm, to identify a good balance between local search and
genetic search. In order to verify the proposed approaches, numerical
experiments are carried out on thirteen datasets. The results show that
the MAs approaches are efficient in solving attribute reduction
problems when compared with other meta-heuristic approaches.
Abstract: The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.
Abstract: A key element of many distribution systems is the
routing and scheduling of vehicles servicing a set of customers. A
wide variety of exact and approximate algorithms have been
proposed for solving the vehicle routing problems (VRP). Exact
algorithms can only solve relatively small problems of VRP, which is
classified as NP-Hard. Several approximate algorithms have proven
successful in finding a feasible solution not necessarily optimum.
Although different parts of the problem are stochastic in nature; yet,
limited work relevant to the application of discrete event system
simulation has addressed the problem. Presented here is optimization
using simulation of VRP; where, a simplified problem has been
developed in the ExtendSimTM simulation environment; where,
ExtendSimTM evolutionary optimizer is used to minimize the total
transportation cost of the problem. Results obtained from the model
are very satisfactory. Further complexities of the problem are
proposed for consideration in the future.
Abstract: The Far From Most Strings Problem (FFMSP) is to obtain a string which is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are said to be far if their hamming distance is greater than or equal to a given positive integer. FFMSP belongs to the class of sequences consensus problems which have applications in molecular biology. The problem is NP-hard; it does not admit a constant-ratio approximation either, unless P = NP. Therefore, in addition to exact and approximate algorithms, (meta)heuristic algorithms have been proposed for the problem in recent years. On the other hand, in the recent years, hybrid algorithms have been proposed and successfully used for many hard problems in a variety of domains. In this paper, a new metaheuristic algorithm, called Constructive Beam and Local Search (CBLS), is investigated for the problem, which is a hybridization of constructive beam search and local search algorithms. More specifically, the proposed algorithm consists of two phases, the first phase is to obtain several candidate solutions via the constructive beam search and the second phase is to apply local search to the candidate solutions obtained by the first phase. The best solution found is returned as the final solution to the problem. The proposed algorithm is also similar to memetic algorithms in the sense that both use local search to further improve individual solutions. The CBLS algorithm is compared with the most recent published algorithm for the problem, GRASP, with significantly positive results; the improvement is by order of magnitudes in most cases.
Abstract: Frequent pattern discovery over data stream is a hard
problem because a continuously generated nature of stream does not
allow a revisit on each data element. Furthermore, pattern discovery
process must be fast to produce timely results. Based on these
requirements, we propose an approximate approach to tackle the
problem of discovering frequent patterns over continuous stream.
Our approximation algorithm is intended to be applied to process a
stream prior to the pattern discovery process. The results of
approximate frequent pattern discovery have been reported in the
paper.
Abstract: We consider the methods of construction simple
polygons for a set S of n points and applying them for searching the
minimal area polygon. In this paper we propose the approximate
algorithm, which generates the simple polygonalizations of a fixed
set of points and finds the minimal area polygon, in O (n3) time and
using O(n2) memory.