Genetic Algorithm with Fast Greedy Heuristic for Clustering and Location Problems

Authors propose new genetic algorithm for solving the planar p-median location problem and k-means clustering problem. The ideas of the algorithm are based on the genetic algorithm with greedy heuristic for the p-median problem on networks and information bottleneck (IB) clustering algorithms. The proposed algorithm uses the standard k-means procedure or any other similar algorithm for local search. The efficiency of the proposed algorithm in comparison with known algorithms was proved by experiments on large-scale location and clustering problems.

[1]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[2]  Franziska Abend,et al.  Facility Location Concepts Models Algorithms And Case Studies , 2016 .

[3]  L. Kazakovtsev.  Wireless Coverage Optimization Based on Data Provided by Built-In Measurement Tools , 2013 .

[4]  G. O. Wesolowsky,et al.  A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem , 1972 .

[5]  James G. Morris,et al.  Convergence of the Weiszfeld Algorithm for Weber Problems Using a Generalized "Distance" Function , 1981, Oper. Res..

[6]  James C. French,et al.  Clustering large datasets in arbitrary metric spaces , 1999, Proceedings 15th International Conference on Data Engineering (Cat. No.99CB36337).

[7]  Zeinab Azarmand,et al.  Location Allocation Problem , 2009 .

[8]  Zvi Drezner,et al.  An Efficient Genetic Algorithm for the p-Median Problem , 2003, Ann. Oper. Res..

[9]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

[10]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[11]  Sudipto Guha,et al.  Streaming-data algorithms for high-quality clustering , 2002, Proceedings 18th International Conference on Data Engineering.

[12]  Ahmed Wasif Reza,et al.  A comprehensive study of optimization algorithm for wireless coverage in indoor area , 2014, Optim. Lett..

[13]  Cabot A.Victor,et al.  A Network Flow Solution to a Rectilinear Distance Facility Location Problem , 1970 .

[14]  Amit Kumar,et al.  A Simple D2-Sampling Based PTAS for k-Means and Other Clustering Problems , 2012, Algorithmica.

[15]  Leonard Pitt,et al.  Sublinear time approximate clustering , 2001, SODA '01.

[16]  Christian Sohler,et al.  StreamKM++: A clustering algorithm for data streams , 2010, JEAL.

[17]  Artur Czumaj,et al.  Sublinear-Time Approximation for Clustering Via Random Sampling , 2004, ICALP.

[18]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[19]  Pierre Hansen,et al.  Analysis of Global k-Means, an Incremental Heuristic for Minimum Sum-of-Squares Clustering , 2005, J. Classif..

[20]  L. Cooper.  Location-Allocation Problems , 1963 .

[21]  Celso C. Ribeiro,et al.  Scatter Search and Path-Relinking: Fundamentals, Advances, and Applications , 2010 .

[22]  Kenneth D. Bailey,et al.  Numerical Taxonomy and Cluster Analysis , 1994 .

[23]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[24]  George O. Wesolowsky,et al.  THE WEBER PROBLEM: HISTORY AND PERSPECTIVES. , 1993 .

[25]  T. Ibaraki,et al.  The Computational Complexity of the m -Center Problems on the Plane , 1981 .

[26]  Amit Kumar,et al.  A Simple D 2-Sampling Based PTAS for k-Means and other Clustering Problems , 2012, COCOON.

[27]  Zvi Drezner,et al.  A Trajectory Method for the Optimization of the Multi-Facility Location Problem With lp Distances , 1978 .

[28]  Flávio Keidi Miyazawa,et al.  A continuous facility location problem and its application to a clustering problem , 2008, SAC '08.

[29]  William Bialek,et al.  Geometric Clustering Using the Information Bottleneck Method , 2003, NIPS.

[30]  Christopher R. Houck,et al.  Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems , 1996, Comput. Oper. Res..

[31]  Sergei Vassilvitskii,et al.  k-means++: the advantages of careful seeding , 2007, SODA '07.

[32]  Tian Zhang,et al.  BIRCH: an efficient data clustering method for very large databases , 1996, SIGMOD '96.

[33]  Ujjwal Maulik,et al.  Genetic algorithm-based clustering technique , 2000, Pattern Recognit..

[34]  Alan M. Frieze,et al.  Clustering Large Graphs via the Singular Value Decomposition , 2004, Machine Learning.

[35]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[36]  V. A. Trubin,et al.  Effective algorithm for the weber problem with a rectangular metric , 1978 .

[37]  Pierre Hansen,et al.  The p-median problem: A survey of metaheuristic approaches , 2005, Eur. J. Oper. Res..

[38]  I. Osinuga,et al.  On the Minimum Norm Solution to Weber Problem , 2008 .

[39]  Diansheng Guo,et al.  A Clustering‐Based Approach to the Capacitated Facility Location Problem 1 , 2008, Trans. GIS.

[40]  Pierre Hansen,et al.  NP-hardness of Euclidean sum-of-squares clustering , 2008, Machine Learning.

[41]  M. N. Neema,et al.  New Genetic Algorithms Based Approaches to Continuous p-Median Problem , 2011 .

[42]  Bodo Manthey,et al.  k-Means Has Polynomial Smoothed Complexity , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[43]  E. Correa,et al.  A genetic algorithm for the P-median problem , 2001 .

[44]  Lev Kazakovtsev,et al.  Random Search Algorithm for the p-Median Problem , 2013, Informatica.

[45]  Leszek Gasieniec,et al.  Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms , 2007, SODA 2007.

[46]  Zvi Drezner.  The fortified Weiszfeld algorithm for solving the Weber problem , 2015 .

[47]  Cun-Hui Zhang,et al.  A modified Weiszfeld algorithm for the Fermat-Weber location problem , 2001, Math. Program..

[48]  M. Resende.  Metaheuristic Hybridization with Greedy Randomized Adaptive Search Procedures , 2008 .

[49]  M. Goodchild,et al.  Discrete space location-allocation solutions from genetic algorithms , 1986 .

[50]  M. Narasimha Murty,et al.  Genetic K-means algorithm , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[51]  Pierre Hansen,et al.  Solving large p-median clustering problems by primal–dual variable neighborhood search , 2009, Data Mining and Knowledge Discovery.

[52]  Leon Cooper,et al.  AN EXTENSION OF THE GENERALIZED WEBER PROBLEM , 1968 .