New ideas for applying ant colony optimization to the set covering problem

The set covering problem (SCP) is a well known NP-hard problem with many practical applications. In this research, a new approach based on ant colony optimization (ACO) is proposed to solve the SCP. The main differences between it and the existing ACO-based approaches lie in three aspects. First, it adopts a novel method, called single-row-oriented method, to construct solutions. When choosing a new column, it first randomly selects an uncovered row and only considers the columns covering this row, rather than all the unselected columns as candidate solution components. Second, a kind of dynamic heuristic information is used in this approach. It takes into account Lagrangian dual information associated with currently uncovered rows. Finally, a simple local search procedure is developed to improve solutions constructed by ants while keeping their feasibility. The proposed algorithm has been tested on a number of benchmark instances. Computational results show that it is able to produce competitive solutions in comparison with other metaheuristics.

[1]  Thomas Stützle,et al.  A Comparison Between ACO Algorithms for the Set Covering Problem , 2004, ANTS Workshop.

[2]  Thomas Stützle,et al.  Ant Colony Optimization Theory , 2004 .

[3]  Thomas Stützle,et al.  A Racing Algorithm for Configuring Metaheuristics , 2002, GECCO.

[4]  Broderick Crawford,et al.  Integrating Lookahead and Post Processing Procedures with ACO for Solving Set Partitioning and Covering Problems , 2006, ICAISC.

[5]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

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

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

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

[9]  Thomas Stützle,et al.  Exploiting Fitness Distance Correlation of Set Covering Problems , 2002, EvoWorkshops.

[10]  José De Doná,et al.  Lagrangian Duality , 2004 .

[11]  G. Nemhauser,et al.  Integer Programming , 2020 .

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

[13]  Graham Kendall,et al.  A Survey And Analysis Of Diversity Measures In Genetic Programming , 2002, GECCO.

[14]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

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

[16]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[17]  Marco Dorigo,et al.  The hyper-cube framework for ant colony optimization , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Christine Solnon,et al.  An Ant Colony Optimization Meta-Heuristic for Subset Selection Problems , 2006 .

[19]  Guanghui Lan,et al.  On the effectiveness of incorporating randomness and memory into a multi-start metaheuristic with application to the Set Covering Problem , 2006, Comput. Ind. Eng..

[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]  Jack J. Dongarra,et al.  Performance of various computers using standard linear equations software in a FORTRAN environment , 1988, CARN.

[23]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[24]  Ibrahim H. Osman,et al.  A tabu search procedure based on a random Roulette diversification for the weighted maximal planar graph problem , 2006, Comput. Oper. Res..

[25]  Christine Solnon,et al.  A study of ACO capabilities for solving the maximum clique problem , 2006, J. Heuristics.

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

[27]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[28]  W. Gutjahr.  On the Finite-Time Dynamics of Ant Colony Optimization , 2006 .

[29]  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..

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

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

[32]  Michel Gendreau,et al.  Metaheuristics: Progress in Complex Systems Optimization , 2007 .

[33]  Thomas Stützle,et al.  Ant colony optimization: artificial ants as a computational intelligence technique , 2006 .

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

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

[36]  Marco Dorigo,et al.  The ant colony optimization meta-heuristic , 1999 .

[37]  Matteo Fischetti,et al.  Algorithms for the Set Covering Problem , 2000, Ann. Oper. Res..