A Genetic Algorithm for the Constrained Coverage Problem

The coverage problem is one of the most important types of the facility location problems, which belongs in the NP-hard problems. In this paper, we present a genetic algorithm for solving the constrained coverage problem in continuous space. The genetic operators are novel operators and specially designed to solve the coverage problem. The new algorithm has a high convergence rate and finds the global optimum by a high probability. The algorithm is tested by several benchmark problems, the results of which demonstrate the power of algorithm.

[1]  Anthony Man-Cho So,et al.  On Solving Coverage Problems in a Wireless Sensor Network Using Voronoi Diagrams , 2005, WINE.

[2]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[3]  Nimrod Megiddo,et al.  Linear-time algorithms for linear programming in R3 and related problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[4]  Alan T. Murray,et al.  Solving the continuous space p-centre problem: planning application issues , 2006 .

[5]  Doron Chen,et al.  New relaxation-based algorithms for the optimal solution of the continuous and discrete p-center problems , 2009, Comput. Oper. Res..

[6]  Morton E. O'Kelly,et al.  Assessing representation error in point-based coverage modeling , 2002, J. Geogr. Syst..

[7]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[8]  Majid Bagheri,et al.  Efficient k-Coverage algorithms for wireless sensor networks and their applications to early detection of forest fires , 2007 .

[9]  Blas Pelegrín,et al.  A new assignment rule to improve seed points algorithms for the continuous k-center problem , 1998 .

[10]  Morton E. O'Kelly,et al.  Locating Emergency Warning Sirens , 1992 .

[11]  Joseph O'Rourke,et al.  Computational geometry in C (2nd ed.) , 1998 .

[12]  Richard L. Church,et al.  Regional service coverage modeling , 2008, Comput. Oper. Res..

[13]  I. G. Gowda,et al.  Dynamic Voronoi diagrams , 1983, IEEE Trans. Inf. Theory.

[14]  Fan Chung Graham,et al.  Internet and Network Economics, Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings , 2007, WINE.

[15]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[16]  Martine Labbé,et al.  A New Formulation and Resolution Method for the p-Center Problem , 2004, INFORMS J. Comput..

[17]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[18]  Songwu Lu,et al.  PEAS: a robust energy conserving protocol for long-lived sensor networks , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[19]  N. Megiddo Linear-time algorithms for linear programming in R3 and related problems , 1982, FOCS 1982.

[20]  Zvi Drezner,et al.  The p-Centre Problem—Heuristic and Optimal Algorithms , 1984 .

[21]  Wolfgang Maass,et al.  Fast Approximation Algorithms for a Nonconvex Covering Problem , 1987, J. Algorithms.

[22]  Ramesh Govindan,et al.  Understanding packet delivery performance in dense wireless sensor networks , 2003, SenSys '03.

[23]  James Llinas,et al.  Handbook of Multisensor Data Fusion , 2001 .

[24]  Yu-Chee Tseng,et al.  The Coverage Problem in a Wireless Sensor Network , 2005, Mob. Networks Appl..

[25]  Pierre Hansen,et al.  Solving the p‐Center problem with Tabu Search and Variable Neighborhood Search , 2000, Networks.

[26]  Jie Wu,et al.  On Connected Multiple Point Coverage in Wireless Sensor Networks , 2006, Int. J. Wirel. Inf. Networks.