Heuristic Feasibility and Preprocessing for a Set Covering Solver Based on Firefly Optimization

The set covering problem is a classic benchmark that has many real applications such as positioning of communications systems, logical analysis, steel production, vehicle routing, and service allocation in general. In this paper, we present an improved firefly algorithm to the efficient resolution of this problem. The firefly algorithm is a recent metaheuristic based on the flashing characteristics of fireflies that attract each other by using their brightness. We improve this approach by incorporating pre-processing and an heuristic feasibility operator resulting in an interesting solver able to clearly outperform the previously reported results obtained from firefly algorithms.

[1]  Broderick CRAWFORD,et al.  Dynamic selection of enumeration strategies for solving constraint satisfaction problems , 2012 .

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

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

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

[5]  Broderick Crawford,et al.  A Binary Firefly Algorithm for the Set Covering Problem , 2014, CSOC.

[6]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[7]  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..

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

[9]  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..

[10]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

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

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

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

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

[15]  Roman Senkerik,et al.  Modern Trends and Techniques in Computer Science - 3rd Computer Science On-line Conference 2014 (CSOC 2014) , 2014, CSOC.

[16]  Narayana Prasad Padhy,et al.  Binary real coded firefly algorithm for solving unit commitment problem , 2013, Inf. Sci..

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

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

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

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