An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating
Published Online:6 May 2019https://doi.org/10.1287/ijoc.2018.0840
References
- (1996) Linear programming for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. 92(2):310–325.Crossref, Google Scholar
- (1995) An algorithm for finding the k-best allocations of a tree structured program. J. Parallel Distributed Comput. 26(2):225–232.Crossref, Google Scholar
- (2001) Best reduction of the quadratic semi-assignment problem. Discrete Appl. Math. 109(3):197–213.Crossref, Google Scholar
- (2009) Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method. Discrete Appl. Math. 157(6):1185–1197.Crossref, Google Scholar
- (2004) An exact method based on Lagrangian decomposition for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. 157(3):565–575.Crossref, Google Scholar
- (2002) The nonlinear knapsack problem—algorithms and applications. Eur. J. Oper. Res. 138(3):459–472.Crossref, Google Scholar
- (1995) A branch and bound algorithm for integer quadratic knapsack problems. INFORMS J. Comput. 7(1):109–116.Link, Google Scholar
- (2013) Separable Non-convex Underestimators for Binary Quadratic Programming (Springer, Berlin, Heidelberg), 236–247.Crossref, Google Scholar
- (1999) Exact solution of the quadratic knapsack problem. INFORMS J. Comput. 11(2):125–137.Link, Google Scholar
- (2015) Iterated responsive threshold search for the quadratic multiple knapsack problem. Annual Oper. Res. 226(1):101–131.Crossref, Google Scholar
- (2016) An evolutionary path relinking approach for the quadratic multiple knapsack problem. Knowledge-Based Syst. 92(C):23–34.Crossref, Google Scholar
- (2006) A memetic heuristic for the generalized quadratic assignment problem. INFORMS J. Comput. 18(4):433–443.Link, Google Scholar
- (2007) The service allocation problem at the Gioia Tauro maritime terminal. Eur. J. Oper. Res. 176(2):1167–1184.Crossref, Google Scholar
- (2000) Approximation algorithms for the multiple knapsack problem with assignment restrictions. J. Combin. Optim. 4(2):171–186.Crossref, Google Scholar
- (2005) Efficient production-distribution system design. Management Sci. 51(7):1151–1164.Link, Google Scholar
- (1996) Solving multiple knapsack problems by cutting planes. SIAM J. Optim. 6(3):858–877.Crossref, Google Scholar
- (2014) A dynamic programming heuristic for the quadratic knapsack problem. INFORMS J. Comput. 26(1):173–182.Link, Google Scholar
- (2005) The multidimensional 0-1 knapsack problem—bounds and computational aspects. Annual Oper. Res. 139(1):195–227.Crossref, Google Scholar
- (1980) Quadratic Knapsack Problems (Springer, Berlin, Heidelberg), 132–149.Crossref, Google Scholar
- (2014a) Strategic oscillation for the quadratic multiple knapsack problem. Comput. Optim. Appl. 58(1):161–185.Crossref, Google Scholar
- (2014b) Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem. Eur. J. Oper. Res. 232(3):454–463.Crossref, Google Scholar
- (1977) On the topological design of distributed computer networks. IEEE Trans. Comm. 25(1):48–60.Crossref, Google Scholar
- (1961) A linear programming approach to the cutting stock problem. Oper. Res. 9(6):849–859.Link, Google Scholar
- (1975) Improved linear integer programming formulations of nonlinear integer problems. Management Sci. 22(4):455–460.Link, Google Scholar
- (2014) Hybrid metaheuristics for solving the quadratic assignment problem and the generalized quadratic assignment problem. 2014 IEEE Internat. Conf. Automation Sci. Engrg. (IEEE, New York), 119–124.Crossref, Google Scholar
- Gurobi Optimization I (2017) Gurobi optimizer reference manual. Accessed April 23, 2019, http://www.gurobi.com.Google Scholar
- (2008) An algorithm for the generalized quadratic assignment problem. Comput. Optim. Appl. 40(3):351–372.Crossref, Google Scholar
- (2006) The quadratic multiple knapsack problem and three heuristic approaches to it. Proc. 8th Annual Conf. Genetic Evolutionary Comput. (ACM, New York), 547–552.Crossref, Google Scholar
- (2006) A variable-grouping based genetic algorithm for large-scale integer programming. Inform. Sci. 176(19):2869–2885.Crossref, Google Scholar
- (1978) An algorithm for 0-1 multiple-knapsack problems. Naval Res. Logist. Quart. 25(3):571–579.Crossref, Google Scholar
- IBM (2017) IBM ILOG CPLEX optimizer. Accessed April 23, 2019, https://www.ibm.com/analytics/cplex-optimizer.Google Scholar
- (2005) Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem. Proc. 7th Annual Conf. Genetic Evolutionary Comput. (ACM, New York), 607–614.Crossref, Google Scholar
- (2004) Knapsack Problems (Springer, New York).Crossref, Google Scholar
- (2006) Investigation of methods for solving new classes of quadratic assignment problems (QAPs). PhD thesis, University of Pennsylvania, Philadelphia.Google Scholar
- (1955) Assignment Problems and the Location of Economic Activities, Cowles Foundation Discussion Papers, no. 4 (Yale University, New Haven, CT), https://EconPapers.repec.org/RePEc:cwl:cwldpp:4.Google Scholar
- (2014) Improved semidefinite bounding procedure for solving max-cut problems to optimality. Math. Programming 143(1):61–86.Crossref, Google Scholar
- (2016) Computational results of a semidefinite branch-and-bound algorithm for k-cluster. Comput. Oper. Res. 66:153–159.Crossref, Google Scholar
- (2017) Biqcrunch: A semidefinite branch-and-bound method for solving binary quadratic problems. ACM Trans. Math. Software 43(4):32:1–32:23.Crossref, Google Scholar
- (1963) The quadratic assignment problem. Management Sci. 9(4):586–599.Link, Google Scholar
- (2004) The generalized quadratic assignment problem. Research report, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto.Google Scholar
- (1989) An algorithm for the multiprocessor assignment problem. Oper. Res. Lett. 8(6):351–356.Crossref, Google Scholar
- (1992) An improved partial solution to the task assignment and multiway cut problems. Oper. Res. Lett. 12(1):3–10.Crossref, Google Scholar
- (2013) On the bridge between combinatorial optimization and nonlinear optimization: A family of semidefinite bounds for 0–1 quadratic problems leading to quasi-Newton methods. Math. Programming 140(1):99–124.Crossref, Google Scholar
- (1981) Heuristic algorithms for the multiple knapsack problem. Computing 27(2):93–112.Crossref, Google Scholar
- (2011) Grasp with path-relinking for the generalized quadratic assignment problem. J. Heuristics 17(5):527–565.Crossref, Google Scholar
- (1896) On the partition of numbers. Proc. London Math. Soc. s1–28(1):486–490Crossref, Google Scholar
- (1983) A branch and search algorithm for a class of nonlinear knapsack problems. Oper. Res. Lett. 2(4):155–160.Crossref, Google Scholar
- (2017) A tabu search heuristic for a generalized quadratic assignment problem. J. Indust. Production Engrg. 34(3):221–231.Crossref, Google Scholar
- (1993) Lagrangean methods for 0–1 quadratic problems. Discrete Appl. Math. 42(2):257–269.Crossref, Google Scholar
- (2014) Entropy-based optimization of nonlinear separable discrete decision models. Management Sci. 60(3):695–707.Link, Google Scholar
- (2010) Algorithms for the generalized quadratic assignment problem combining lagrangean decomposition and the reformulation-linearization technique. Eur. J. Oper. Res. 206(1):54–63.Crossref, Google Scholar
- (1999) An exact algorithm for large multiple knapsack problems. Eur. J. Oper. Res. 114(3):528–541.Crossref, Google Scholar
- (2007) The quadratic knapsack problem—a survey. Discrete Appl. Math. 155(5):623–648.Crossref, Google Scholar
- (2007) Solution of large quadratic knapsack problems through aggressive reduction. INFORMS J. Comput. 19(2):280–290.Link, Google Scholar
- (2009) An Artificial Bee Colony Algorithm for the Quadratic Knapsack Problem (Springer, Berlin, Heidelberg), 196–205.Crossref, Google Scholar
- (2016) Hybridization of tabu search with feasible and infeasible local searches for the quadratic multiple knapsack problem. Comput. Oper. Res. 66(February):199–214.Crossref, Google Scholar
- (2012) 0-1 quadratic knapsack problems: An exact approach based on a t-linearization. SIAM J. Optim. 22(4):1449–1468.Crossref, Google Scholar
- (1975) A branch and bound algorithm for the generalized assignment problem. Math. Programming 8(1):91–103.Crossref, Google Scholar
- (2004) From linear to semidefinite programming: An algorithm to obtain semidefinite relaxations for bivalent quadratic problems. J. Combin. Optim. 8(4):469–493.Crossref, Google Scholar
- (2014) Generalized quadratic multiple knapsack problem and two solution approaches. Comput. Oper. Res. 43(1):78–89.Crossref, Google Scholar
- (2007) A new grouping genetic algorithm for the quadratic multiple knapsack problem. Cotta C, van Hemert J, eds. Evolutionary Comput. Combinatorial Optimization: Proc. 7th Eur. Conf. (Springer, Berlin, Heidelberg), 210–218.Crossref, Google Scholar
- (2012) A memetic algorithm for the quadratic multiple container packing problem. Appl. Intelligence 36(1):119–135.Crossref, Google Scholar
- (1992) The process allocation problem: A survey of the application of graph-theoretic and integer programming approaches. J. Oper. Res. Soc. 43(5):407–413.Crossref, Google Scholar
- (2010) A swarm intelligence approach to the quadratic multiple knapsack problem. Wong KW, Mendis BSU, Abdesselam B, eds. ICONIP: International Conf. Neural Inform. Processing: Theory Algorithms, Sydney, Australia, November 22–25. (Springer, Berlin, Heidelberg), 626–633.Crossref, Google Scholar
- (2016) An iterated variable neighborhood descent hyperheuristic for the quadratic multiple knapsack problem. Lee R, ed. Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Studies in Computational Intelligence (Springer, New York), 245–251.Google Scholar
- (2016) On linearization techniques for budget-constrained binary quadratic programming problems. Oper. Res. Lett. 44(6):702–705.Crossref, Google Scholar

