A Dual Bounding Framework Through Cost Splitting for Binary Quadratic Optimization

Published Online:https://doi.org/10.1287/ijoc.2021.0186

References

  • Adams WP, Forrester RJ (2005) A simple recipe for concise mixed 0-1 linearizations. Oper. Res. Lett. 33(1):55–61.CrossrefGoogle Scholar
  • Adams WP, Sherali HD (1990) Linearization strategies for a class of zero-one mixed integer programming problems. Oper. Res. 38(2):217–226.LinkGoogle Scholar
  • Aloise D, Cafieri S, Caporossi G, Hansen P, Perron S, Liberti L (2010) Column generation algorithms for exact modularity maximization in networks. Phys. Rev. E 82(4):046112.CrossrefGoogle Scholar
  • Amor HB, Desrosiers J, Frangioni A (2004) Stabilization in column generation. Les Cahiers du GERAD 711:2440.Google Scholar
  • Assad A, Xu W (1992) The quadratic minimum spanning tree problem. Naval Res. Logist. 39(3):399–417.CrossrefGoogle Scholar
  • Assari SM, Idrees H, Shah M (2016) Human re-identification in crowd videos using personal, social and environmental constraints. Leibe B, Matas J, Sebe N, Welling M, eds. Computer Vision–ECCV 2016. Lecture Notes in Computer Science, vol. 9906 (Springer, Cham, Switzerland), 119–136.CrossrefGoogle Scholar
  • Barahona F (1983) The max-cut problem on graphs not contractible to K5. Oper. Res. Lett. 2(3):107–111.CrossrefGoogle Scholar
  • Ben-Ameur W, Neto J (2007) Acceleration of cutting-plane and column generation algorithms: Applications to network design. Networks 49(1):3–17.CrossrefGoogle Scholar
  • Bergner M, Caprara A, Ceselli A, Furini F, Lübbecke ME, Malaguti E, Traversi E (2015) Automatic Dantzig-Wolfe reformulation of mixed integer programs. Math. Programming 149(1–2):391–424.CrossrefGoogle Scholar
  • Bettiol E, Bomze I, Létocart L, Rinaldi F, Traversi E (2022) Mining for diamonds—Matrix generation algorithms for binary quadratically constrained quadratic problems. Comput. Oper. Res. 142(C):105735.CrossrefGoogle Scholar
  • Billionnet A, Elloumi S (2001) Best reduction of the quadratic semi-assignment problem. Discrete Appl. Math. 109(3):197–213.CrossrefGoogle Scholar
  • Billionnet A, Soutif É (2004) An exact method based on Lagrangian decomposition for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. 157(3):565–575.CrossrefGoogle Scholar
  • Billionnet A, Elloumi S, Plateau MC (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.CrossrefGoogle Scholar
  • Bonizzoni P, Della Vedova G, Dondi R, Jiang T (2008) On the approximation of correlation clustering and consensus clustering. J. Comput. System Sci. 74(5):671–696.CrossrefGoogle Scholar
  • Booth M, Reinhardt SP, Roy A (2017) Partitioning optimization problems for hybrid classical/quantum execution. GitHub repository URL https://github.com/dwavesystems/qbsolv/blob/master/qbsolv_techReport.pdf.Google Scholar
  • Çela E (2013) The Quadratic Assignment Problem: Theory and Algorithms, vol. 1 (Springer Science & Business Media, Berlin).Google Scholar
  • Charfreitag J, Jünger M, Mallach S, Mutzel P (2022) McSparse: Exact solutions of sparse maximum cut and sparse unconstrained binary quadratic optimization problems. 2022 Proc. Sympos. Algorithm Engrg. Experiments (ALENEX) (SIAM, Philadelphia), 54–66.Google Scholar
  • Chen WA, Zhu Z, Kong N (2018) A Lagrangian decomposition approach to computing feasible solutions for quadratic binary programs. Optim. Lett. 12:155–169.CrossrefGoogle Scholar
  • Chrétienne P (1989) A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints. Eur. J. Oper. Res. 43(2):225–230.CrossrefGoogle Scholar
  • Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper. Res. 8(1):101–111.LinkGoogle Scholar
  • De Fréminville PDLP, Desaulniers G, Rousseau LM, Perron S (2015) A column generation heuristic for districting the price of a financial product. J. Oper. Res. Soc. 66(6):965–978.CrossrefGoogle Scholar
  • Dehghan A, Shah M (2017) Binary quadratic programing for online tracking of hundreds of people in extremely crowded scenes. IEEE Trans. Pattern Anal. Machine Intelligence 40(3):568–581.CrossrefGoogle Scholar
  • Desaulniers G, Desrosiers J, Solomon MM (2006) Column Generation, vol. 5 (Springer Science & Business Media, Berlin).Google Scholar
  • Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math. Programming 91(2):201–213.CrossrefGoogle Scholar
  • Drwal M (2014) Algorithm for quadratic semi-assignment problem with partition size coefficients. Optim. Lett. 8(3):1183–1190.CrossrefGoogle Scholar
  • Du Merle O, Villeneuve D, Desrosiers J, Hansen P (1999) Stabilized column generation. Discrete Math. 194(1):229–237.CrossrefGoogle Scholar
  • Emami P, Pardalos PM, Elefteriadou L, Ranka S (2018) Machine learning methods for solving assignment problems in multi-target tracking. Preprint, submitted February 19, https://arxiv.org/abs/1802.06897.Google Scholar
  • Escoffier B, Hammer PL (2007) Approximation of the quadratic set covering problem. Discrete Optim. 4(3–4):378–386.CrossrefGoogle Scholar
  • Fischer A (2014) An analysis of the asymmetric quadratic traveling salesman polytope. SIAM J. Discrete Math. 28(1):240–276.CrossrefGoogle Scholar
  • Fischer F, Jaeger G, Lau A, Molitor P (2009) Complexity and algorithms for the traveling salesman problem and the assignment problem of second order. Lecture Notes Comput. Sci. 5165:211–224.Google Scholar
  • Furini F, Traversi E, Belotti P, Frangioni A, Gleixner A, Gould N, Liberti L, et al. (2019) QPLIB: A library of quadratic programming instances. Math. Programming Comput. 11(2):237–265.CrossrefGoogle Scholar
  • Glover F, Woolsey E (1974) Converting the 0-1 polynomial programming problem to a 0-1 linear program. Oper. Res. 22(1):180–182.LinkGoogle Scholar
  • Hahn PM, Zhu YR, Guignard M, Hightower WL, Saltzman MJ (2012) A level-3 reformulation-linearization technique-based bound for the quadratic assignment problem. INFORMS J. Comput. 24(2):202–209.LinkGoogle Scholar
  • Hansen P, Lih KW (1992) Improved algorithms for partitioning problems in parallel, pipelined, and distributed computing. IEEE Trans. Comput. 41(6):769–771.CrossrefGoogle Scholar
  • Helmberg C, Rendl F, Weismantel R (2000) A semidefinite programming approach to the Quadratic Knapsack Problem. J. Combin. Optim. 4(2):197–215.CrossrefGoogle Scholar
  • Henschel R, Leal-Taixé L, Cremers D, Rosenhahn B (2018) Fusion of head and full-body detectors for multi-object tracking. Proc. IEEE Conf. Comput. Vision Pattern Recognition Workshops (IEEE, Piscataway, NJ), 1428–1437.Google Scholar
  • Hu H, Sotirov R (2018) Special cases of the quadratic shortest path problem. J. Combin. Optim. 35(3):754–777.CrossrefGoogle Scholar
  • Hu H, Sotirov R (2021) The linearization problem of a binary quadratic problem and its applications. Ann. Oper. Res. 307(1):229–249.CrossrefGoogle Scholar
  • Jünger M, Mallach S (2021) Exact facetial odd-cycle separation for maximum cut and binary quadratic optimization. INFORMS J. Comput. 33(4):1419–1430.AbstractGoogle Scholar
  • Khaniyev T (2018) Data-driven structure detection in optimization: Decomposition, hub location, and brain connectivity. PhD thesis, University of Waterloo, Waterloo, ON.Google Scholar
  • Khaniyev T, Elhedhli S, Erenay FS (2018) Structure detection in mixed-integer programs. INFORMS J. Comput. 30(3):570–587.LinkGoogle Scholar
  • Khaniyev T, Elhedhli S, Erenay FS (2020) Spatial separability in hub location problems with an application to brain connectivity networks. INFORMS J. Optim. 2(4):320–346.LinkGoogle Scholar
  • Kochenberger G, Hao JK, Glover F, Lewis M, Lü Z, Wang H, Wang Y (2014) The unconstrained binary quadratic programming problem: A survey. J. Combin. Optim. 28(1):58–81.CrossrefGoogle Scholar
  • Leal-Taixe L, Pons-Moll G, Rosenhahn B (2012) Branch-and-price global optimization for multi-view multi-target tracking. 2012 IEEE Conf. Comput. Vision Pattern Recognition (IEEE, Piscataway, NJ), 1987–1994.Google Scholar
  • Lemaréchal C, Oustry F (2001) SDP relaxations in combinatorial optimization from a Lagrangian viewpoint. Hadjisavvas N, Pardalos PM, eds. Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol. 54 (Springer, Boston), 119–134.CrossrefGoogle Scholar
  • Liberti L (2007) Compact linearization for binary quadratic problems. 4OR 5(3):231–245.CrossrefGoogle Scholar
  • Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper. Res. 53(6):1007–1023.LinkGoogle Scholar
  • Magirou V, Milis J (1989) An algorithm for the multiprocessor assignment problem. Oper. Res. Lett. 8(6):351–356.CrossrefGoogle Scholar
  • Mallach S (2018) Compact linearization for binary quadratic problems subject to assignment constraints. 4OR 16(3):295–309.CrossrefGoogle Scholar
  • Mallach S (2023) Inductive linearization for binary quadratic programs with linear constraints: A computational study. 4OR, 1–41.Google Scholar
  • Malucelli F (1996) A polynomially solvable class of quadratic semi-assignment problems. Eur. J. Oper. Res. 91(3):619–622.CrossrefGoogle Scholar
  • Mauri GR, Lorena LAN (2011) Lagrangean decompositions for the unconstrained binary quadratic programming problem. Internat. Trans. Oper. Res. 18(2):257–270.CrossrefGoogle Scholar
  • Mauri GR, Lorena LAN (2012) A column generation approach for the unconstrained binary quadratic programming problem. Eur. J. Oper. Res. 217(1):69–74.CrossrefGoogle Scholar
  • Meier JF, Clausen U, Rostami B, Buchheim C (2016) A compact linearisation of Euclidean single allocation hub location problems. Electronic Notes Discrete Math. 52:37–44.CrossrefGoogle Scholar
  • Milan A, Leal-Taixe L, Reid I, Roth S, Schindler K (2016) MOT16: A benchmark for multi-object tracking. Preprint, submitted March 2, https://arxiv.org/abs/1603.00831.Google Scholar
  • O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32(3):393–404.CrossrefGoogle Scholar
  • Pereira DL, da Cunha AS (2018) Polyhedral results, branch-and-cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem. Networks 71(1):31–50.CrossrefGoogle Scholar
  • Pereira DL, da Cunha AS (2020) Dynamic intersection of multiple implicit Dantzig–Wolfe decompositions applied to the adjacent only quadratic minimum spanning tree problem. Eur. J. Oper. Res. 284(2):413–426.CrossrefGoogle Scholar
  • Pereira DL, Gendreau M, Salles da Cunha A (2013) Stronger lower bounds for the quadratic minimum spanning tree problem with adjacency costs. Electronic Notes Discrete Math. 41(5):229–236.CrossrefGoogle Scholar
  • Pereira DL, Gendreau M, Salles da Cunha A (2015) Branch-and-cut and branch-and-cut-and-price algorithms for the adjacent only quadratic minimum spanning tree problem. Networks 65(4):367–379.CrossrefGoogle Scholar
  • Pisinger D (2007) The quadratic knapsack problem—A survey. Discrete Appl. Math. 155(5):623–648.CrossrefGoogle Scholar
  • Punnen AP, Pandey P, Friesen M (2019) Representations of quadratic combinatorial optimization problems: A case study using quadratic set covering and quadratic knapsack problems. Comput. Oper. Res. 112:104769.CrossrefGoogle Scholar
  • Punnen AP, Walter M, Woods BD (2017) A characterization of linearizable instances of the quadratic traveling salesman problem. Preprint, submitted August 23, https://arxiv.org/abs/1708.07217.Google Scholar
  • Rostami B, Malucelli F (2015) Lower bounds for the quadratic minimum spanning tree problem based on reduced cost computation. Comput. Oper. Res. 64:178–188.CrossrefGoogle Scholar
  • Rostami B, Errico F, Lodi A (2023) A convex reformulation and an outer approximation for a large class of binary quadratic programs. Oper. Res. 71(2):471–486.LinkGoogle Scholar
  • Rostami B, Malucelli F, Belotti P, Gualandi S (2016) Lower bounding procedure for the asymmetric quadratic traveling salesman problem. Eur. J. Oper. Res. 253(3):584–592.CrossrefGoogle Scholar
  • Rostami B, Malucelli F, Frey D, Buchheim C (2015) On the quadratic shortest path problem. Bampis E, ed. Proc. 14th Internat. Sympo. Experiment. Algorithms, SEA 2015 (Springer International Publishing, Cham, Switzerland), 379–390.CrossrefGoogle Scholar
  • Rostami B, Chassein A, Hopf M, Frey D, Buchheim C, Malucelli F, Goerigk M (2018) The quadratic shortest path problem: Complexity, approximability, and solution methods. Eur. J. Oper. Res. 268(2):473–485.CrossrefGoogle Scholar
  • Rousseau LM, Gendreau M, Feillet D (2007) Interior point stabilization for column generation. Oper. Res. Lett. 35(5):660–668.CrossrefGoogle Scholar
  • Sahni S, Gonzalez T (1976) P-complete approximation problems. J. ACM 23(3):555–565.CrossrefGoogle Scholar
  • Saito H, Fujie T, Matsui T, Matuura S (2009) A study of the quadratic semi-assignment polytope. Discrete Optim. 6(1):37–50.CrossrefGoogle Scholar
  • Schüle I, Ewe H, Küfer KH (2009) Finding tight RLT formulations for quadratic semi-assignment problems. Proc. 8th Cologne-Twente Workshop Graphs Combin. Optim. (Ecole Polytechnique and CNAM, Paris), 109–112.Google Scholar
  • Shen H, Huang L, Huang C, Xu W (2018) Tracklet association tracker: An end-to-end learning-based association approach for multi-object tracking. Preprint, submitted August 5, https://arxiv.org/abs/1808.01562.Google Scholar
  • Sherali HD, Adams WP (2013) A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Nonconvex Optimization and Its Applications, vol. 31 (Springer Science & Business Media, Berlin).Google Scholar
  • Sherali HD, Smith JC (2007) An improved linearization strategy for zero-one quadratic programming problems. Optim. Lett. 1(1):33–47.CrossrefGoogle Scholar
  • Silva A, Coelho LC, Darvish M (2021) Quadratic assignment problem variants: A survey and an effective parallel memetic iterated tabu search. Eur. J. Oper. Res. 292(3):1066–1084.CrossrefGoogle Scholar
  • Stone HS (1977) Multiprocessor scheduling with the aid of network flow algorithms. IEEE Trans. Software Engrg. SE-3(1):85–93.CrossrefGoogle Scholar
  • Tang S, Andriluka M, Andres B, Schiele B (2017) Multiple people tracking by lifted multicut and person re-identification. Proc. 30th IEEE Conf. Comput. Vision Pattern Recognition, CVPR 2017 (IEEE, Piscataway, NJ), 3539–3548.Google Scholar
  • Wang S, Wolf S, Fowlkes CC, Yarkony J (2017) Tracking objects with higher order interactions via delayed column generation. Proc. 20th Internat. Conf. Artificial Intelligence Statist. (AISTATS 2017) (PMLR, New York), 1132–1140.Google Scholar
  • Yarkony J, Adulyasak Y, Singh M, Desaulniers G (2020) Data association via set packing for computer vision applications. INFORMS J. Optim. 2(3):167–191.LinkGoogle Scholar
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