Solving the Set Covering Problem with a Shuffled Frog Leaping Algorithm

In this paper we design and evaluate a shuffled frog leaping algorithm that solves the set covering problem. The shuffled frog leaping algorithm is a novel metaheuristic inspired by natural memetics. It consists of an individual memetic evolution and a global memetic information exchange between a population of virtual frogs representing possible solutions of a problem at hand. The experimental results show the effectiveness of our approach which produces competitive results solving a portfolio of set covering problems from the OR-Library.

[1]  Paolo Toth,et al.  An electromagnetism metaheuristic for the unicost set covering problem , 2010, Eur. J. Oper. Res..

[2]  Antonio Sassano,et al.  A Lagrangian-based heuristic for large-scale set covering problems , 1998, Math. Program..

[3]  G B Gharehpetian,et al.  Unit Commitment Problem Solution Using Shuffled Frog Leaping Algorithm , 2011, IEEE Transactions on Power Systems.

[4]  Francis J. Vasko,et al.  Using a facility location algorithm to solve large set covering problems , 1984 .

[5]  J. Beasley.  A lagrangian heuristic for set‐covering problems , 1990 .

[6]  Kevin E Lansey,et al.  Optimization of Water Distribution Network Design Using the Shuffled Frog Leaping Algorithm , 2003 .

[7]  Francis J. Vasko,et al.  Optimal Selection of Ingot Sizes Via Set Covering , 1987, Oper. Res..

[8]  Chen Fang,et al.  An effective shuffled frog-leaping algorithm for resource-constrained project scheduling problem , 2012, Comput. Oper. Res..

[9]  Marco Caserta,et al.  Tabu Search-Based Metaheuristic Algorithm for Large-scale Set Covering Problems , 2007, Metaheuristics.

[10]  Abhijit Chakrabarti,et al.  Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valve-point effect , 2013, Appl. Soft Comput..

[11]  Egon Balas,et al.  A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering , 1992, Oper. Res..

[12]  Broderick Crawford,et al.  A Hybrid Soft Computing Approach for Subset Problems , 2013 .

[13]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[14]  S. Balachandar,et al.  A Meta-Heuristic Algorithm for Vertex Covering Problem Based on Gravity , 2010 .

[15]  Andrew Lewis,et al.  S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization , 2013, Swarm Evol. Comput..

[16]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[17]  Min-Rong Chen,et al.  Improved Shuffled Frog Leaping Algorithm and its multi-phase model for multi-depot vehicle routing problem , 2014, Expert Syst. Appl..

[18]  Sarada Prasad Sarmah,et al.  Shuffled frog leaping algorithm and its application to 0/1 knapsack problem , 2014, Appl. Soft Comput..

[19]  M. Fisher,et al.  Optimal solution of set covering/partitioning problems using dual heuristics , 1990 .

[20]  Efthymios Housos,et al.  Automatic Optimization of Subproblems in Scheduling Airline Crews , 1997 .

[21]  Matteo Fischetti,et al.  A Heuristic Method for the Set Covering Problem , 1999, Oper. Res..

[22]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[23]  J. Beasley,et al.  A genetic algorithm for the set covering problem , 1996 .

[24]  Zhi-Gang Ren,et al.  New ideas for applying ant colony optimization to the set covering problem , 2010, Comput. Ind. Eng..

[25]  Michael J. Brusco,et al.  A morphing procedure to supplement a simulated annealing heuristic for cost‐ andcoverage‐correlated set‐covering problems , 1999, Ann. Oper. Res..

[26]  Yang Ye,et al.  Solving TSP with Shuffled Frog-Leaping Algorithm , 2008 .

[27]  Muzaffar Eusuff,et al.  Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization , 2006 .