How to cite this paper
Matousek, R., Dobrovsky, L & Kudela, J. (2022). How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem.International Journal of Industrial Engineering Computations , 13(2), 151-164.
Refrences
Abdel-Basset, M., Manogaran, G., El-Shahat, D., & Mirjalili, S. (2018). Integrating the whale algorithm with Tabu search for quadratic assignment problem: A new approach for locating hospital departments. Applied soft computing, 73, 530-546.
Adams, W. P., & Johnson, T. A. (1994). Improved linear programming-based lower bounds for the quadratic assignment problem. DIMACS series in discrete mathematics and theoretical computer science, 16, 43-77.
Adams, W. P., Guignard, M., Hahn, P. M., & Hightower, W. L. (2007). A level-2 reformulation–linearization technique bound for the quadratic assignment problem. European Journal of Operational Research, 180(3), 983-996.
Ahmed, Z. H. (2015). A multi-parent genetic algorithm for the quadratic assignment problem. Opsearch, 52(4), 714-732.
Aksan, Y., Dokeroglu, T., & Cosar, A. (2017). A stagnation-aware cooperative parallel breakout local search algorithm for the quadratic assignment problem. Computers & Industrial Engineering, 103, 105-115.
Anstreicher, K. M., & Brixius, N. W. (2001). A new bound for the quadratic assignment problem based on convex quadratic programming. Mathematical Programming, 89(3), 341-357.
Anstreicher, K. M. (2003). Recent advances in the solution of quadratic assignment problems. Mathematical Programming, 97(1), 27-42.
Benlic, U., & Hao, J. K. (2015). Memetic search for the quadratic assignment problem. Expert Systems with Applications, 42(1), 584-595.
Burkard, R. E., & Rendl, F. (1984). A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operational Research, 17(2), 169-174.
Burkard, R. E., Karisch, S. E., & Rendl, F. (1997). QAPLIB–a quadratic assignment problem library. Journal of Global optimization, 10(4), 391-403.
Burkard, R. E., Dell'Amico, M., & Martello, S. (2012). Assignment problems: revised reprint. Society for Industrial and Applied Mathematics.
Cela, E. (2013). The quadratic assignment problem: theory and algorithms (Vol. 1). Springer Science & Business Media.
Cela, E., Deineko, V., & Woeginger, G. J. (2018). New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices. European journal of operational research, 267(3), 818-834.
Chmiel, W., & Szwed, P. (2016). Bees algorithm for the quadratic assignment problem on CUDA platform. In Man–Machine Interactions 4 (pp. 615-625). Springer, Cham.
Czapiński, M. (2013). An effective parallel multistart tabu search for quadratic assignment problem on CUDA platform. Journal of Parallel and Distributed Computing, 73(11), 1461-1468.
de Klerk, E., & Sotirov, R. (2012). Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Mathematical programming, 133(1), 75-91.
Dell’Amico, M., Diaz, J. C. D., Iori, M., & Montanari, R. (2009). The single-finger keyboard layout problem. Computers & Operations Research, 36(11), 3002-3012.
Dickey, J. W., & Hopkins, J. W. (1972). Campus building arrangement using TOPAZ. Transportation Research, 6(1), 59-68.
Dokeroglu, T. (2015). Hybrid teaching–learning-based optimization algorithms for the quadratic assignment problem. Computers & Industrial Engineering, 85, 86-101.
Dokeroglu, T., & Cosar, A. (2016). A novel multistart hyper-heuristic algorithm on the grid for the quadratic assignment problem. Engineering Applications of Artificial Intelligence, 52, 10-25.
Eschermann, B., & Wunderlich, H. J. (1990). Optimized synthesis of self-testable finite state machines. In 20th international symposium on fault-tolerant computing (FTCS 20).
Fischetti, M., Monaci, M., & Salvagnin, D. (2012). Three ideas for the quadratic assignment problem. Operations research, 60(4), 954-964.
Fleurent, C., & Ferland, J. A. (1994). Genetic hybrids for the quadratic assignment problem. Quadratic assignment and related problems, 16, 173-187.
Gilmore, P. C. (1962). Optimal and suboptimal algorithms for the quadratic assignment problem. Journal of the society for industrial and applied mathematics, 10(2), 305-313.
Hadley, S. W., Rendl, F., & Wolkowicz, H. (1992). A new lower bound via projection for the quadratic assignment problem. Mathematics of Operations Research, 17(3), 727-739.
Hafiz, F., & Abdennour, A. (2016). Particle Swarm Algorithm variants for the Quadratic Assignment Problems-A probabilistic learning approach. Expert Systems with Applications, 44, 413-431.
Haghani, A., & Chen, M. C. (1998). Optimizing gate assignments at airport terminals. Transportation Research Part A: Policy and Practice, 32(6), 437-454.
Hahn, P. M., Zhu, Y. R., Guignard, M., Hightower, W. L., & Saltzman, M. J. (2012). A level-3 reformulation-linearization technique-based bound for the quadratic assignment problem. INFORMS Journal on Computing, 24(2), 202-209.
Hameed, A., Aboobaider, B., Mutar, M., & Choon, N. (2020). A new hybrid approach based on discrete differential evolution algorithm to enhancement solutions of quadratic assignment problem. International Journal of Industrial Engineering Computations, 11(1), 51-72.
Harris, M., Berretta, R., Inostroza-Ponta, M., & Moscato, P. (2015, May). A memetic algorithm for the quadratic assignment problem with parallel local search. In 2015 IEEE congress on evolutionary computation (CEC) (pp. 838-845). IEEE.
Helber, S., Böhme, D., Oucherif, F., Lagershausen, S., & Kasper, S. (2016). A hierarchical facility layout planning approach for large and complex hospitals. Flexible services and manufacturing journal, 28(1), 5-29.
Hoffman, A. J., & Wielandt, H. W. (2003). The variation of the spectrum of a normal matrix. In Selected Papers Of Alan J Hoffman: With Commentary (pp. 118-120).
Hubert, L., & Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. British journal of mathematical and statistical psychology, 29(2), 190-241.
Hussin, M. S., & Stützle, T. (2014). Tabu search vs. simulated annealing as a function of the size of quadratic assignment problem instances. Computers & operations research, 43, 286-291.
Kaufman, L., & Broeckx, F. (1978). An algorithm for the quadratic assignment problem using Bender's decomposition. European Journal of Operational Research, 2(3), 207-211.
Karisch, S. E., Cela, E., Clausen, J., & Espersen, T. (1999). A dual framework for lower bounds of the quadratic assignment problem based on linearization. Computing, 63(4), 351-403.
Koopmans, T. C., & Beckmann, M. (1957). Assignment problems and the location of economic activities. Econometrica: journal of the Econometric Society, 53-76.
Matousek, R., & Zampachova, E. (2011). Promising GAHC and HC12 algorithms in global optimization tasks. Optimization methods and software, 26(3), 405-419.
Matousek, R., Popela, P., & Kudela, J. (2017). Heuristic approaches to stochastic quadratic assignment problem: Var and cvar cases. Mendel, 23(1), 73-78.
Matousek, R., Dobrovsky, L., & Kudela, J. (2019, July). The quadratic assignment problem: metaheuristic optimization using HC12 algorithm. In Proceedings of the Genetic and Evolutionary Computation Conference Companion (pp. 153-154).
Mohammadi, J., Mirzaie, K., & Derhami, V. (2015, November). Parallel genetic algorithm based on GPU for solving quadratic assignment problem. In 2015 2nd International Conference on Knowledge-Based Engineering and Innovation (KBEI) (pp. 569-572). IEEE.
Laporte, G., & Mercure, H. (1988). Balancing hydraulic turbine runners: A quadratic assignment problem. European Journal of Operational Research, 35(3), 378-381.
Lawler, E. L. (1963). The quadratic assignment problem. Management science, 9(4), 586-599.
Li, Y., & Pardalos, P. M. (1992). Generating quadratic assignment test problems with known optimal permutations. Computational Optimization and Applications, 1(2), 163-184.
Peng, J., Mittelmann, H., & Li, X. (2010). A new relaxation framework for quadratic assignment problems based on matrix splitting. Mathematical Programming Computation, 2(1), 59-77.
Peng, J., Zhu, T., Luo, H., & Toh, K. C. (2015). Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting. Computational Optimization and Applications, 60(1), 171-198.
Popela, P., Matousek, R., & Kudela, J. (2016). Heuristic approaches to stochastic quadratic assignment problem: VO and MM cases. Mendel 22(1), 117-122.
Samanta, S., Philip, D., & Chakraborty, S. (2018). Bi-objective dependent location quadratic assignment problem: Formulation and solution using a modified artificial bee colony algorithm. Computers & Industrial Engineering, 121, 8-26.
Sanhueza, C., Jiménez, F., Berretta, R., & Moscato, P. (2017, June). PasMoQAP: a parallel asynchronous memetic algorithm for solving the multi-objective quadratic assignment problem. In 2017 IEEE congress on evolutionary computation (CEC) (pp. 1103-1110). IEEE.
Steinberg, L. (1961). The backboard wiring problem: A placement algorithm. Siam Review, 3(1), 37-50.
Taillard, É. (1991). Robust taboo search for the quadratic assignment problem. Parallel computing, 17(4-5), 443-455.
Tosun, U. (2015). On the performance of parallel hybrid algorithms for the solution of the quadratic assignment problem. Engineering applications of artificial intelligence, 39, 267-278.
Tsutsui, S., & Fujimoto, N. (2009, July). Solving quadratic assignment problems by genetic algorithms with GPU computation: a case study. In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers (pp. 2523-2530).
Xia, Y., & Yuan, Y. X. (2006). A new linearization method for quadratic assignment problems. Optimisation Methods and Software, 21(5), 805-818.
Zhang, H., Beltran-Royo, C., & Ma, L. (2013). Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers. Annals of Operations Research, 207(1), 261-278.
Zhao, Q., Karisch, S. E., Rendl, F., & Wolkowicz, H. (1998). Semidefinite programming relaxations for the quadratic assignment problem. Journal of Combinatorial Optimization, 2(1), 71-109.
Adams, W. P., & Johnson, T. A. (1994). Improved linear programming-based lower bounds for the quadratic assignment problem. DIMACS series in discrete mathematics and theoretical computer science, 16, 43-77.
Adams, W. P., Guignard, M., Hahn, P. M., & Hightower, W. L. (2007). A level-2 reformulation–linearization technique bound for the quadratic assignment problem. European Journal of Operational Research, 180(3), 983-996.
Ahmed, Z. H. (2015). A multi-parent genetic algorithm for the quadratic assignment problem. Opsearch, 52(4), 714-732.
Aksan, Y., Dokeroglu, T., & Cosar, A. (2017). A stagnation-aware cooperative parallel breakout local search algorithm for the quadratic assignment problem. Computers & Industrial Engineering, 103, 105-115.
Anstreicher, K. M., & Brixius, N. W. (2001). A new bound for the quadratic assignment problem based on convex quadratic programming. Mathematical Programming, 89(3), 341-357.
Anstreicher, K. M. (2003). Recent advances in the solution of quadratic assignment problems. Mathematical Programming, 97(1), 27-42.
Benlic, U., & Hao, J. K. (2015). Memetic search for the quadratic assignment problem. Expert Systems with Applications, 42(1), 584-595.
Burkard, R. E., & Rendl, F. (1984). A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operational Research, 17(2), 169-174.
Burkard, R. E., Karisch, S. E., & Rendl, F. (1997). QAPLIB–a quadratic assignment problem library. Journal of Global optimization, 10(4), 391-403.
Burkard, R. E., Dell'Amico, M., & Martello, S. (2012). Assignment problems: revised reprint. Society for Industrial and Applied Mathematics.
Cela, E. (2013). The quadratic assignment problem: theory and algorithms (Vol. 1). Springer Science & Business Media.
Cela, E., Deineko, V., & Woeginger, G. J. (2018). New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices. European journal of operational research, 267(3), 818-834.
Chmiel, W., & Szwed, P. (2016). Bees algorithm for the quadratic assignment problem on CUDA platform. In Man–Machine Interactions 4 (pp. 615-625). Springer, Cham.
Czapiński, M. (2013). An effective parallel multistart tabu search for quadratic assignment problem on CUDA platform. Journal of Parallel and Distributed Computing, 73(11), 1461-1468.
de Klerk, E., & Sotirov, R. (2012). Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Mathematical programming, 133(1), 75-91.
Dell’Amico, M., Diaz, J. C. D., Iori, M., & Montanari, R. (2009). The single-finger keyboard layout problem. Computers & Operations Research, 36(11), 3002-3012.
Dickey, J. W., & Hopkins, J. W. (1972). Campus building arrangement using TOPAZ. Transportation Research, 6(1), 59-68.
Dokeroglu, T. (2015). Hybrid teaching–learning-based optimization algorithms for the quadratic assignment problem. Computers & Industrial Engineering, 85, 86-101.
Dokeroglu, T., & Cosar, A. (2016). A novel multistart hyper-heuristic algorithm on the grid for the quadratic assignment problem. Engineering Applications of Artificial Intelligence, 52, 10-25.
Eschermann, B., & Wunderlich, H. J. (1990). Optimized synthesis of self-testable finite state machines. In 20th international symposium on fault-tolerant computing (FTCS 20).
Fischetti, M., Monaci, M., & Salvagnin, D. (2012). Three ideas for the quadratic assignment problem. Operations research, 60(4), 954-964.
Fleurent, C., & Ferland, J. A. (1994). Genetic hybrids for the quadratic assignment problem. Quadratic assignment and related problems, 16, 173-187.
Gilmore, P. C. (1962). Optimal and suboptimal algorithms for the quadratic assignment problem. Journal of the society for industrial and applied mathematics, 10(2), 305-313.
Hadley, S. W., Rendl, F., & Wolkowicz, H. (1992). A new lower bound via projection for the quadratic assignment problem. Mathematics of Operations Research, 17(3), 727-739.
Hafiz, F., & Abdennour, A. (2016). Particle Swarm Algorithm variants for the Quadratic Assignment Problems-A probabilistic learning approach. Expert Systems with Applications, 44, 413-431.
Haghani, A., & Chen, M. C. (1998). Optimizing gate assignments at airport terminals. Transportation Research Part A: Policy and Practice, 32(6), 437-454.
Hahn, P. M., Zhu, Y. R., Guignard, M., Hightower, W. L., & Saltzman, M. J. (2012). A level-3 reformulation-linearization technique-based bound for the quadratic assignment problem. INFORMS Journal on Computing, 24(2), 202-209.
Hameed, A., Aboobaider, B., Mutar, M., & Choon, N. (2020). A new hybrid approach based on discrete differential evolution algorithm to enhancement solutions of quadratic assignment problem. International Journal of Industrial Engineering Computations, 11(1), 51-72.
Harris, M., Berretta, R., Inostroza-Ponta, M., & Moscato, P. (2015, May). A memetic algorithm for the quadratic assignment problem with parallel local search. In 2015 IEEE congress on evolutionary computation (CEC) (pp. 838-845). IEEE.
Helber, S., Böhme, D., Oucherif, F., Lagershausen, S., & Kasper, S. (2016). A hierarchical facility layout planning approach for large and complex hospitals. Flexible services and manufacturing journal, 28(1), 5-29.
Hoffman, A. J., & Wielandt, H. W. (2003). The variation of the spectrum of a normal matrix. In Selected Papers Of Alan J Hoffman: With Commentary (pp. 118-120).
Hubert, L., & Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. British journal of mathematical and statistical psychology, 29(2), 190-241.
Hussin, M. S., & Stützle, T. (2014). Tabu search vs. simulated annealing as a function of the size of quadratic assignment problem instances. Computers & operations research, 43, 286-291.
Kaufman, L., & Broeckx, F. (1978). An algorithm for the quadratic assignment problem using Bender's decomposition. European Journal of Operational Research, 2(3), 207-211.
Karisch, S. E., Cela, E., Clausen, J., & Espersen, T. (1999). A dual framework for lower bounds of the quadratic assignment problem based on linearization. Computing, 63(4), 351-403.
Koopmans, T. C., & Beckmann, M. (1957). Assignment problems and the location of economic activities. Econometrica: journal of the Econometric Society, 53-76.
Matousek, R., & Zampachova, E. (2011). Promising GAHC and HC12 algorithms in global optimization tasks. Optimization methods and software, 26(3), 405-419.
Matousek, R., Popela, P., & Kudela, J. (2017). Heuristic approaches to stochastic quadratic assignment problem: Var and cvar cases. Mendel, 23(1), 73-78.
Matousek, R., Dobrovsky, L., & Kudela, J. (2019, July). The quadratic assignment problem: metaheuristic optimization using HC12 algorithm. In Proceedings of the Genetic and Evolutionary Computation Conference Companion (pp. 153-154).
Mohammadi, J., Mirzaie, K., & Derhami, V. (2015, November). Parallel genetic algorithm based on GPU for solving quadratic assignment problem. In 2015 2nd International Conference on Knowledge-Based Engineering and Innovation (KBEI) (pp. 569-572). IEEE.
Laporte, G., & Mercure, H. (1988). Balancing hydraulic turbine runners: A quadratic assignment problem. European Journal of Operational Research, 35(3), 378-381.
Lawler, E. L. (1963). The quadratic assignment problem. Management science, 9(4), 586-599.
Li, Y., & Pardalos, P. M. (1992). Generating quadratic assignment test problems with known optimal permutations. Computational Optimization and Applications, 1(2), 163-184.
Peng, J., Mittelmann, H., & Li, X. (2010). A new relaxation framework for quadratic assignment problems based on matrix splitting. Mathematical Programming Computation, 2(1), 59-77.
Peng, J., Zhu, T., Luo, H., & Toh, K. C. (2015). Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting. Computational Optimization and Applications, 60(1), 171-198.
Popela, P., Matousek, R., & Kudela, J. (2016). Heuristic approaches to stochastic quadratic assignment problem: VO and MM cases. Mendel 22(1), 117-122.
Samanta, S., Philip, D., & Chakraborty, S. (2018). Bi-objective dependent location quadratic assignment problem: Formulation and solution using a modified artificial bee colony algorithm. Computers & Industrial Engineering, 121, 8-26.
Sanhueza, C., Jiménez, F., Berretta, R., & Moscato, P. (2017, June). PasMoQAP: a parallel asynchronous memetic algorithm for solving the multi-objective quadratic assignment problem. In 2017 IEEE congress on evolutionary computation (CEC) (pp. 1103-1110). IEEE.
Steinberg, L. (1961). The backboard wiring problem: A placement algorithm. Siam Review, 3(1), 37-50.
Taillard, É. (1991). Robust taboo search for the quadratic assignment problem. Parallel computing, 17(4-5), 443-455.
Tosun, U. (2015). On the performance of parallel hybrid algorithms for the solution of the quadratic assignment problem. Engineering applications of artificial intelligence, 39, 267-278.
Tsutsui, S., & Fujimoto, N. (2009, July). Solving quadratic assignment problems by genetic algorithms with GPU computation: a case study. In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers (pp. 2523-2530).
Xia, Y., & Yuan, Y. X. (2006). A new linearization method for quadratic assignment problems. Optimisation Methods and Software, 21(5), 805-818.
Zhang, H., Beltran-Royo, C., & Ma, L. (2013). Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers. Annals of Operations Research, 207(1), 261-278.
Zhao, Q., Karisch, S. E., Rendl, F., & Wolkowicz, H. (1998). Semidefinite programming relaxations for the quadratic assignment problem. Journal of Combinatorial Optimization, 2(1), 71-109.