A New Neighborhood for the QAP

Abstract Local search procedures are popular methods to solve combinatorial problems and neighborhood structures are the main part of those algorithms. This paper presents a new neighborhood for the Quadratic Assignment Problem. The proposed neighborhood is compared with the classical 2-exchange neighborhood.

[1]  Laurence A. Wolsey,et al.  Production Planning by Mixed Integer Programming , 2010 .

[2]  Martin Charles Golumbic,et al.  Graph Sandwich Problems , 1995, J. Algorithms.

[3]  Gilbert Laporte,et al.  Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints , 1991, Oper. Res. Lett..

[4]  Celina M. H. de Figueiredo,et al.  Clique Graph Recognition Is NP-Complete , 2006, WG.

[5]  Mihir Bellare,et al.  On Chromatic Sums and Distributed Resource Allocation , 1998, Inf. Comput..

[6]  D. Bryant.  The Complexity of Calculating Exemplar Distances , 2000 .

[7]  D. Adolphson.  Optimal linear-ordering. , 1973 .

[8]  John M. Lewis,et al.  The Node-Deletion Problem for Hereditary Properties is NP-Complete , 1980, J. Comput. Syst. Sci..

[9]  Jeffrey D. Ullman,et al.  Flow Graph Reducibility , 1972, SIAM J. Comput..

[10]  Jayme Luiz Szwarcfiter,et al.  Computational aspects of the Helly property: a survey , 2006, Journal of the Brazilian Computer Society.

[11]  Hazel Everett,et al.  The Homogeneous Set Sandwich Problem , 1998, Inf. Process. Lett..

[12]  Tibor Szkaliczki,et al.  Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is NP-Complete , 1999, SIAM J. Comput..

[13]  M. Ehrgott,et al.  Heuristics for the K-Cardinality Tree and Subgraph Problems , 1996 .

[14]  Jordi Petit,et al.  Combining Spectral Sequencing and Parallel Simulated Annealing for the MINLA Problem , 2003, Parallel Process. Lett..

[15]  Ewa Kubicka,et al.  An introduction to chromatic sums , 1989, CSC '89.

[16]  Jeffery L. Kennington,et al.  Interfaces in Computer Science and Operations Research , 1997 .

[17]  Martin Farber,et al.  Concerning the achromatic number of graphs , 1986, J. Comb. Theory B.

[18]  Jack Brimberg,et al.  Variable neighborhood search for the vertex weighted k , 2006, Eur. J. Oper. Res..

[19]  S. Hedetniemi,et al.  The achromatic number of a graph , 1970 .

[20]  C. L. Liu.  Elements of Discrete Mathematics , 1985 .

[21]  Celina M. H. de Figueiredo,et al.  On decision and optimization (k, l)-graph sandwich problems , 2004, Discret. Appl. Math..

[22]  Mohammad R. Salavatipour,et al.  On Sum Coloring of Graphs , 2003, Discret. Appl. Math..

[23]  Mike Plantholt.  The chromatic index of graphs with a spanning star , 1981, J. Graph Theory.

[24]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[25]  Bruce A. Reed,et al.  An extremal function for the achromatic number , 1991, Graph Structure Theory.

[26]  Alexandr V. Kostochka,et al.  Acyclic and oriented chromatic numbers of graphs , 1997 .

[27]  Marek Kubale,et al.  A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs , 2002, APPROX.

[28]  Majid Sarrafzadeh,et al.  On the Sum Coloring Problem on Interval Graphs , 1999, Algorithmica.

[29]  André Raspaud,et al.  On the maximum average degree and the oriented chromatic number of a graph , 1999, Discret. Math..

[30]  Hossein Hajiabolhassan,et al.  Minimal coloring and strength of graphs , 2000, Discret. Math..

[31]  Ivan Rival,et al.  A Fixed Point Theorem for Finite Partially Ordered Sets , 1976, J. Comb. Theory, Ser. A.

[32]  Éric Sopena,et al.  Oriented graph coloring , 2001, Discret. Math..

[33]  Mickaël Montassier,et al.  Strong Oriented Chromatic Number of Planar Graphs without Short Cycles , 2008, Discret. Math. Theor. Comput. Sci..

[34]  Cun-Quan Zhang.  Integer Flows and Cycle Covers of Graphs , 1997 .

[35]  Robert Sámal.  Antisymmetric flows and strong oriented coloring of planar graphs , 2003, Discret. Math..

[36]  Maria Axenovich,et al.  Anti-Ramsey numbers for small complete bipartite graphs , 2004, Ars Comb..

[37]  Guy Kortsarz,et al.  Sum Coloring Interval and k-Claw Free Graphs with Application to Scheduling Dependent Jobs , 2003, Algorithmica.

[38]  Mysore Ramaswamy,et al.  Using Directed Hypergraphs to Verity Rule-Based Expert Systems , 1997, IEEE Trans. Knowl. Data Eng..

[39]  Sulamita Klein,et al.  List Partitions , 2003, SIAM J. Discret. Math..

[40]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[41]  B. Reed,et al.  Recent advances in algorithms and combinatorics , 2003 .

[42]  J. Szwarcfiter.  A Survey on Clique Graphs , 2003 .

[43]  Robert E. Jamison.  On the edge achromatic numbers of complete graphs , 1989, Discret. Math..

[44]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[45]  Jayme Luiz Szwarcfiter,et al.  On the computation of the hull number of a graph , 2009, Discret. Math..

[46]  Gérard Cornuéjols,et al.  Ideal 0, 1 Matrices , 1994, J. Comb. Theory, Ser. B.

[47]  Kathie Cameron,et al.  The list partition problem for graphs , 2004, SODA '04.

[48]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[49]  Dániel Marx,et al.  The complexity of chromatic strength and chromatic edge strength , 2006, computational complexity.

[50]  L. H. Harper.  Optimal Assignments of Numbers to Vertices , 1964 .

[51]  Celina M. H. de Figueiredo,et al.  Extended skew partition problem , 2006, Discret. Math..

[52]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

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

[54]  É. Taillard.  COMPARISON OF ITERATIVE SEARCHES FOR THE QUADRATIC ASSIGNMENT PROBLEM. , 1995 .

[55]  Éric D. Taillard,et al.  Robust taboo search for the quadratic assignment problem , 1991, Parallel Comput..

[56]  Carsten Lund,et al.  The Approximation of Maximum Subgraph Problems , 1993, ICALP.

[57]  Dushyant Sharma,et al.  Very Large-Scale Neighborhood Search for the Quadratic Assignment Problem , 2007, INFORMS J. Comput..

[58]  Thomas Stützle,et al.  Iterated local search for the quadratic assignment problem , 2006, Eur. J. Oper. Res..

[59]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[60]  Joseph Naor,et al.  Divide-and-conquer approximation algorithms via spreading metrics , 2000, JACM.

[61]  Jayme Luiz Szwarcfiter,et al.  Recognizing Clique-Helly Graphs , 1997, Ars Comb..

[62]  André Luiz Pires Guedes,et al.  Directed hypergraph planarity , 2005 .

[63]  Teresa M. Przytycka,et al.  Decomposition of overlapping protein complexes: A graph theoretical method for analyzing static and dynamic protein associations , 2005, Algorithms for Molecular Biology.

[64]  Satish Rao,et al.  New Approximation Techniques for Some Linear Ordering Problems , 2005, SIAM J. Comput..

[65]  David R. Wood,et al.  Acyclic, Star and Oriented Colourings of Graph Subdivisions , 2005, Discret. Math. Theor. Comput. Sci..

[66]  Éric Sopena.  The chromatic number of oriented graphs , 1997, J. Graph Theory.

[67]  Gerard Sierksma,et al.  Convexities related to path properties on graphs , 2005, Discret. Math..

[68]  Juan José Montellano-Ballesteros,et al.  An Anti-Ramsey Theorem on Cycles , 2005, Graphs Comb..

[69]  Juan José Montellano-Ballesteros,et al.  Tverberg-Type Theorems for Separoids , 2006, Discret. Comput. Geom..

[70]  David Sankoff,et al.  Genome rearrangement with gene families , 1999, Bioinform..

[71]  Ross M. McConnell.  Linear-Time Recognition of Circular-Arc Graphs , 2003, Algorithmica.

[72]  Tao Jiang.  Edge-Colorings with No Large Polychromatic Stars , 2002, Graphs Comb..

[73]  James R. Lee,et al.  An improved approximation ratio for the minimum linear arrangement problem , 2007, Inf. Process. Lett..

[74]  Oleg V. Borodin.  On acyclic colorings of planar graphs , 1979, Discret. Math..

[75]  Erich Prisner.  Convergence of iterated clique graphs , 1992, Discret. Math..

[76]  Michael Hoffmann,et al.  Chordless paths through three vertices , 2006, Theor. Comput. Sci..

[77]  Celina M. H. de Figueiredo,et al.  The sandwich problem for cutsets: Clique cutset, k-star cutset , 2006, Discret. Appl. Math..

[78]  Klaus H. Ecker,et al.  Scheduling Computer and Manufacturing Processes , 2001 .

[79]  Pelayo Melero,et al.  Generalizing the krein-milman property in graph convexity spaces: a short survey , 2006 .

[80]  E. A. Nordhaus,et al.  On Complementary Graphs , 1956 .

[81]  Takeo Yamada,et al.  Upper and lower bounding procedures for minimum rooted k-subtree problem , 2000, Eur. J. Oper. Res..

[82]  Facultad De Ciencias Exactas,et al.  UNIVERSIDAD NACIONAL DE ROSARIO , 1997 .

[83]  Francisco Larrión,et al.  On clique divergent graphs with linear growth , 2002, Discret. Math..

[84]  Matteo Fischetti,et al.  Weighted k-cardinality trees: Complexity and polyhedral structure , 1994, Networks.

[85]  Marek Kubale,et al.  Edge-chromatic sum of trees and bounded cyclicity graphs , 2000, Inf. Process. Lett..

[86]  JOSEP DÍAZ,et al.  A survey of graph layout problems , 2002, CSUR.

[87]  Chengbin Chu.  A faster polynomial algorithm for 2-cyclic robotic scheduling , 2006, J. Sched..

[88]  Nair Maria Maia de Abreu,et al.  A survey for the quadratic assignment problem , 2007, Eur. J. Oper. Res..

[89]  V. N. Bhave.  On the pseudoachromatic number of a graph , 1979 .

[90]  André Raspaud,et al.  Good and Semi-Strong Colorings of Oriented Planar Graphs , 1994, Inf. Process. Lett..

[91]  Daniele Pretolani,et al.  On Some Path Problems on Oriented Hypergraphs , 1998, RAIRO Theor. Informatics Appl..

[92]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[93]  Ian Holyer,et al.  The NP-Completeness of Edge-Coloring , 1981, SIAM J. Comput..

[94]  D. Quillen,et al.  Homotopy properties of the poset of nontrivial p-subgroups of a group , 1978 .

[95]  Vasek Chvátal,et al.  Star-cutsets and perfect graphs , 1985, J. Comb. Theory, Ser. B.

[96]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[97]  M. Farber,et al.  Convexity in graphs and hypergraphs , 1986 .

[98]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .

[99]  Giorgio Gallo,et al.  Directed Hypergraphs and Applications , 1993, Discret. Appl. Math..

[100]  Zvi Drezner,et al.  Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods , 2005, Ann. Oper. Res..

[101]  Robin Thomas,et al.  The Four-Colour Theorem , 1997, J. Comb. Theory, Ser. B.

[102]  Ilya Safro,et al.  Graph minimum linear arrangement by multilevel weighted edge contractions , 2006, J. Algorithms.

[103]  Jayme Luiz Szwarcfiter,et al.  On clique-complete graphs , 1998, Discret. Math..

[104]  Guy Kortsarz,et al.  Minimum Color Sum of Bipartite Graphs , 1998, J. Algorithms.

[105]  André Raspaud,et al.  Colored Homomorphisms of Colored Mixed Graphs , 2000, J. Comb. Theory, Ser. B.

[106]  John Gimbel.  Some Remarks on the Convexity Number of a Graph , 2003, Graphs Comb..

[107]  Zoltán Füredi.  Covering the complete graph by partitions , 1989, Discret. Math..

[108]  László Lovász,et al.  Approximating Min Sum Set Cover , 2004, Algorithmica.

[109]  R. Hamelink.  A partial characterization of clique graphs , 1968 .

[110]  Giorgio Gambosi,et al.  Complexity and approximation: combinatorial optimization problems and their approximability properties , 1999 .

[111]  E. Welzl,et al.  Convex Quadrilaterals and k-Sets , 2003 .

[112]  Andrea Vietri.  The complexity of arc-colorings for directed hypergraphs , 2004, Discret. Appl. Math..

[113]  Santosh S. Vempala,et al.  Flow metrics , 2004, Theor. Comput. Sci..

[114]  P. Bonizzoni,et al.  Exemplar Longest Common Subsequence , 2006, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[115]  Jin-Kao Hao,et al.  An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem , 2008, Comput. Oper. Res..

[116]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[117]  David Défossez.  Coloration d'hypergraphes et clique-coloration , 2006 .

[118]  Fred Glover,et al.  Tabu Search and Adaptive Memory Programming — Advances, Applications and Challenges , 1997 .

[119]  Celina M. H. de Figueiredo,et al.  The graph sandwich problem for 1-join composition is NP-complete , 2002, Discret. Appl. Math..

[120]  N. Alon,et al.  Homomorphisms of Edge-Colored Graphs and Coxeter Groups , 1998 .

[121]  Edward F. Schmeichel,et al.  On the cost chromatic number of outerplanar, planar, and line graphs , 1997, Discuss. Math. Graph Theory.

[122]  P. Seymour,et al.  The Strong Perfect Graph Theorem , 2002, math/0212070.

[123]  Celina M. H. de Figueiredo,et al.  Stable skew partition problem , 2004, Discret. Appl. Math..

[124]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[125]  Christian Blum,et al.  Local Search Algorithms for the k-cardinality Tree Problem , 2003, Discret. Appl. Math..