@incollection{AbeParRes99a, author = "J. Abello and P.M. Pardalos and M.G.C. Resende", title = "On maximum clique problems in very large graphs", booktitle = "External memory algorithms and visualization", editor = "J. Abello and J. Vitter", series = "{DIMACS} Series on Discrete Mathematics and Theoretical Computer Science", publisher = "American Mathematical Society", volume = "50", pages = "119--130", year = "1999", annote = "An approach for clique and quasi-clique computations in very large multi-digraphs is presented. The authors discuss graph decomposition schemes that break up the original problem into several pieces of manageable dimensions. A semi-external memory {GRASP} is presented to approximately solve the maximum clique problem and maximum quasi-clique problem. The construction phase uses vertex degrees as a guide for construction. The local search uses a simple $(2,1)$-exchange." } @Article{AbeResSud02a, author = {J. Abello and M.G.C. Resende and S. Sudarsky}, title = {Massive quasi-clique detection}, journal = {Lecture Notes in Computer Science}, volume = {2286}, pages = {598--612}, annote = {Detecting dense subgraphs (quasi-cliques) in massive sparse graphs whose vertex set fits in RAM is a hard problem. In this paper, a {GRASP} is designed for extracting dense subgraphs on case of both nonbipartite and bipartite case. In case of nonbipartite graphs, the construction procedure applies a greedy criterion based on a measure of the effect of elements selection on the potential of the other vertices. In the bipartite case, the authors adapt the above greedy criterion to a slight different definition of potential. In both cases, the neighborhood structure used is a $(2,1)$-exchange.}, year = {2002} } @Article{AhuOrlSha01a, author = "R.K. Ahuja and J.B. Orlin and D. Sharma", title = "Multi-exchange neighborhood search structures for the capacitated minimum spanning tree problem", journal = "Mathematical Programming", volume = "91", pages = "71-97", year = "2001", annote = "The main contribute of this paper is the proposal of two very large scale neighborhood search algorithms. The first one uses a node based neighborhood structure, defined by performing multi-exchanges involving several trees, where each tree contributes a subtree. The second algorithm uses instead a tree based neighborhood structure, obtained by allowing multi-exchanges, where each tree contributes a subtree. The authors compare their algorithms with the best state-of-the-art approaches, including a {GRASP}.", } @Article{AhuOrlSha03a, author = {R.K. Ahuja and J.B. Orlin and D. Sharma}, title = {A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem}, journal = {Operations Research Letters}, volume = {31}, number = {3}, pages = {185--194}, annote = {The authors propose a composite neighborhood structure that combines both the node based and the tree based neighborhoods already proposed in Ahuja et al. (2001). They compare their algorithm with the best state-of-art methods, including a {GRASP}.}, year = {2003} } @techreport{AlvGonDeA03a, author = {A.M. \'Alvarez and J. L. Gonz\'alez and K. De-Alba}, title = {Scatter search for a network design problem}, number = {PISIS-2003-02}, institution = {Universidad Aut\'onoma de Nuevo Le\'on, Facultad de Ingenier\'{\i}a Mec\'anica y El\'ectrica, Divisi\'on de Posgrado en Ingenier\'{\i}a de Sistemas, Mexico.}, annote = {The authors propose a Scatter Search (SS) algorithm for solving a fixed charge capacitated multicommodity network design problems on undirected networks. SS is an evolutionary method that constructs new solutions by combining others. It performs the following three basic steps: 1) generation of a population $P$; 2) extraction of a reference set $R$; 3) combination of elements from $R$ and updating of $R$. The different ways SS can be implemented consists in designing several different subroutines, including a Diversification Generation Method (DGM). The DGM proposed in this paper is a {GRASP} with some memory features incorpored. More in detail, in the {GRASP} DGM for each commodity a certain number $q$ of shortest paths between each origin-destination pair are kept as RCL elements. The local search consists basically in sorting the chosen paths and possibly exchange some of them in order to get a better distribution.}, year = {2003} } @inproceedings{ArrMarMezOrt01a, author = "E. Arr\'aiz and A. Mart\'{\i}nez and O. Meza and M. Ortega", title = "{GRASP} and tabu search algorithms for computing the forwarding index in a graph", booktitle = "Proceedings of MIC'2001", city = "Porto, Portugal", month = "July 16-20", year = "2001", pages = "367--370", annote = "The forwarding index in a graph is a measure of the load or of the congestion of vertices once the paths between vertices have been computed. For efficiently computing this number, the authors propose a {GRASP} and tabu search algorithms. The {GRASP} greedy choice considers the length of paths connecting nonadjacent nodes, while two different local search strategies are used. The first one replaces a path passing through an internal node with maximum load with another path joining the same endpoints. The second one replaces a path with maximum length." } @techreport{BoeRibBlo03a, author = {M.C. Boeres and C.C. Ribeiro and I. Bloch}, title = {{Randomized algorithms for scene recognition by inexact graph matching}}, institution = {Computer Science Department, Catholic University of Rio de Janeiro}, address = {Rio de Janeiro, Brazil}, annote = {This paper proposes a new algorithm to suboptimally solve non-bijective graph matching for model-based pattern recognition. The algorithm consists of a randomized construction procedure and a local search procedure. In the construction procedure, the used greedy function has two terms representing respectively the node and edge contributions to the measure of the solution quality associated with the corrispondence. Given a feasible solution $x$, the neighborhood structure used during local search considers as neighbors of $x$ all feasible solutions that can be obtained by changing some association.}, year = {2003} } @Article{CanResRib01a, author = "S.A. Canuto and M.G.C. Resende and C.C. Ribeiro", title = "Local search with perturbation for the prize-collecting {Steiner} tree problems in graphs", journal = "Networks", volume = "38", pages = "50--58", year = "2001", annote = "Several local search strategies have been investiged in this paper for solving the prize-collecting {Steiner} tree problems in graphs, including path relinking, VNS, and a {GRASP} that uses some cost perturbations. The greedy choice takes into account the input edge weights, while the local search routine defines as neighborhood of a solution $T(X)$ the set of all minimum spanning trees $T(X')$, where $X'$ differs from $X$ for exactly one node.", } @techreport{FioMal03b, author = "M.S. Fiorenzo Catalano and F. Malucelli", title = "Parallel randomized heuristics for the set covering problem", note = "To appear in International J. of Computer Research", institution = {Transportation and traffic engineering section, Delft U. of Technology, 2600 AG Delft, The Netherlands}, year = "2000", annote = "The authors propose a general scheme to design heuristics for the set covering problem. A first group of procedures randomize the choice of the next element to be added at the solution under construction in a way similar to ant system, while a second set of procedures introduces a random perturbation of the costs of the problem instance. The second set includes also a {GRASP} and seems to be more efficient than competitors from the first set of algorithms.", } @Article{CorMarSan02a, author = "A. Corber\'an and R. Mart\'{\i} and J.M. Sanch\'{\i}s", title = "A {GRASP} heuristic for the mixed {C}hinese postman problem", journal = "European Journal of Operational Research", volume = "142", pages = "70--80", year = "2002", annote = "Given a strongly connected mixed graph $G(V,E,A,c)$, where $V$ is the node set, $E$ is the set of undirected edges, $A$ is the set of directed arcs, and $c$ is a nonnegative cost function defined in $E\cup A$, then the mixed {C}hinese postman problem consists in finding a minimum cost tour passing through each link $e\in E\cup A$ at least once. The construction phase of the proposed {GRASP} uses a greedy function based on the definition of the degree of a node in terms of both incident oriented arcs and incident undirected edges. Each iteration of the local search procedure selects a pair of vertices $u,v\in V$ that are candidates for the move if they are joined by a path of duplications.", } @Incollection{SouDuhRib03a, author = "M.C. de Souza and C. Duhamel and C.C. Ribeiro", title = "A {GRASP} heuristic for the capacitated minimum spanning tree problem using a memory-based local search strategy", booktitle = "Metaheuristics: Computer decision-making", editor = "M.G.C. Resende and J.P. de Sousa", publisher = {Kluwer Academic Publishers}, pages = "627--658", year = "2003", annote = "In this paper, the authors propose a novel local search that applies reduction techniques to speed up the search and uses a new path-based neighborhood structure, defined by path exchanges. Each edge $e$ having extremities into two different components of $T$ is considered a candidate for being inserted into the current tree, but immediately discarded (reduction strategy) if it does not respect some conditions that depend on three criteria and that, if verified, ensure that it is unlikely that the involved edge can be part of an improving move. One criterion is based on the relative cost $r(e)$ of the edge $e$, i.e. the difference between the weight of a minimum spanning tree and the weight of a constrained spanning tree in which the presence of $e$ is enforced. Another criterion is based on the decomposition of the cost of a move defined by the candidate edge $e$ for insertion and by a candidate path $(p--q)$ (from $p$ to $q$) for removal. The cost $\Delta$ of such a move can be written as $\Delta=\Delta_1+\Delta_2$, where $\Delta_1$ is associated with the edge exchanges that will generate the component containing $e$ in the new solution, while $\Delta_2$ is given by the reconnection of the remaining elements along the candidate path $(p--q)$. The third criterion does not compute $\Delta_2$ and uses a lower bound $\delta\leq \delta_1$: a candidate edge $e$ is discarded if $\delta\geq 0$ for each possible candidate path $(p--q)$ that can be used in conjunction with $e$. The authors also propose a {GRASP} that uses the same neighborhood structure as the previously described local search and some short term memory elements of tabu search and that implements a randomized version of a savings heuristic in the construction phase. A post-optimization phase is realized by applying a path-relinking procedure.", } @Article{FeoRes89a, author = "T.A. Feo and M.G.C. Resende", title = "A probabilistic heuristic for a computationally difficult set covering problem", journal = "Operations Research Letters", volume = "8", pages = "67--71", year = "1989", annote = "{GRASP} is proposed for set covering. A value based restricted candidate list is used to construct solutions of difficult set covering problems that arise in computing the $1$-width of the incidence matrix of Steiner triple systems. The local search is based on the elimination of redundant elements in the cover.", } @Article{FeoResSmi94a, author = "T.A. Feo and M.G.C. Resende and S.H. Smith", title = "A greedy randomized adaptive search procedure for maximum independent set", journal = "Operations Research", volume = "42", pages = "860--878", year = "1994", annote = "A {GRASP} for approximately solving the maximum independent set problem is described. The greedy function chosen orders admissible vertices with respect to the minimum admissible vertex degree. The adjective admissible is referred to a vertex that is not adjacent to any vertex in the current independent set. The neighborhood definition used in the local search is $(2,1)$-exchange, where two nonadjacent vertices can be added to the current solution if a single vertex from the solution is removed. The proposed heuristic can be easily implemented in parallel by decomposing the problem into smaller subproblems, each defined by conditioning on vertices being in the solution. An implementation of this algorithm was tested on a MIMD computer with up to eight processors. Average linear speedup is observed.", } @Article{FesParResRib02a, author = "P. Festa and P.M. Pardalos and M.G.C. Resende and C.C. Ribeiro", title = "Randomized heuristics for the {MAX-CUT} problem", journal = "Optimization Methods and Software", volume = "7", pages = {1033--1058}, year = "2002", annote = {Given an undirected graph with edge weights, the max-cut problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. For solving this well-known NP-hard problem, the authors propose and test a {GRASP}, a variable neighborhood search (VNS), a path relinking intensification heuristic, and new hybrid heuristics that combine {GRASP}, VNS, and path relinking. The greedy function of the pure {GRASP} is related to the sum of the weights of the edges in each cut. Let $(S,\bar S)$ be the current cut solution and let $v\in V$ be a vertex, then the pure {GRASP} local search associates to $v$ either the neighbor $(S \setminus \{v\}, \bar S\cup \{v\})$ if $v \in S$, or the neighbor $(S \cup \{v\}, \bar S \setminus \{v\})$ otherwise. Computational results indicate that the proposed randomized heuristics find near-optimal solutions. On a set of standard test problems, new best known solutions were produced for many of the instances.}, } @Article{HamRad01a, author = "P.L. Hammer and D.J. {Rader,~Jr.}", title = "Maximally disjoint solutions of the set covering problem", journal = "Journal of Heuristics", volume = "7", pages = "131--144", year = "2001", annote = "This paper describes the problem of finding two solutions of a set covering problem that have a minimum number of common variables. It is proved that this problem is NP-complete and three heuristics are proposed for solving it. Two of these algorithms find the solutions sequentially. One of them is a {GRASP}. The third algorithm finds solutions simultaneously. Each proposed heuristic is a variant of the standard greedy method for set covering problems, whose greedy choice favors unselected variables that maximize the number of uncovered rows that become covered. To reduce the overlap of any pair of solutions, a local search algorithm is used that swaps at each iteration parts of the solution found with a set of variables not in it.", } @incollection{HolMigPar98a, author = "K. Holmqvist and A. Migdalas and P.M. Pardalos", title = "A {GRASP} algorithm for the single source uncapacitated minimum concave-cost network flow problem", booktitle = "Network design: {C}onnectivity and facilities location", editor = "P.M. Pardalos and D.-Z. Du", series = "{DIMACS} Series on Discrete Mathematics and Theoretical Computer Science", publisher = "American Mathematical Society", volume = "40", pages = "131--142", year = "1998", annote = "This paper is concerned with the single source uncapacitated version of the minimum concave-cost network flow problem, that requires establishing a minimum cost flow through a given network from a single source to a set of sinks. The authors propose a {GRASP} that can be trivially implemented on parallel processors. The construction phase iteratively builds a tree starting from the source node. The elements of the restricted candidate list are end nodes of arcs with a cost close to the best one. The local search phase applies either of the two local search variants proposed by Guisewite and Pardalos (1990)." } @inproceedings{KumSriWanLanRam01a, author = {K. Kumaran and A. Srinivasan and Q. Wang and S. Lanning and K.G. Ramakrishnan}, title = {Efficient algorithms for location and sizing problems in network design}, booktitle = {Global Telecommunications Conference, 2001 (GLOBECOM '01)}, publisher = {IEEE}, volume = {4}, annote = {The authors develop algorithms based on linear programming and a slight modified {GRASP}, in which the costruction phase is performed at random. Given an initial solution, the local search procedure exhaustively evaluate objective function value for all possible single location changes.}, year = {2001}, pages = {2586--2590} } @Article{LagMar01b, author = "M. Laguna and R. Mart\'{\i}", title = "A {GRASP} for coloring sparse graphs", journal = "Computational Optimization and Applications", volume = "19", pages = "165--178", year = "2001", annote = "A {GRASP} for graph coloring is presented. The {GRASP} construction phase constructs the next coloring, one color at time. The greedy function chooses the vertex having the maximum degree among the uncolored vertices adjacent to at least one colored vertex. At each step, the local search combines the two smallest cardinality color classes into one and tries to find a valid color for each violating vertex.", } @techreport{MacSou97b, author = "E.M. Macambira and C.C. de Souza", title = "The edge-weighted clique problem: {V}alid inequalities, facets and polyhedral computations", number = "IC-97-14", institution = "Instituto de Computa\c c\~ao, Universidade Estadual de Campinas", address = "Campinas, Brazil", annote = "Given a complete undirected graph $K_n=(V,E)$ with weights $c_e$ associated to edges in $E$, the edge-weighted clique problem consists in finding a subclique $C=(U,F)$ of $K_n$ such that the sum of the weights of the edges in $F$ is maximized and $\vert U\vert\leq b$, for some $b\in \{1,2,\ldots,n\}$. In this paper, the facial structure of the polytope associated to the problem is studied and new classes of facies are introduced. To obtain initial lower bounds, the authors used a {GRASP}.", year = "1997" } @inproceedings{MacSou97a, author = "E.M. Macambira and C.C. de Souza", title = "A {GRASP} for the maximum clique problem with weighted edges", booktitle = "Proceedings of the XXIX Brazilian Symposium on Operations Research", month = "October", year = "1997", pages = "70", annote = "The authors propose a branch-and-cut algorithm for the maximum clique problem with weighted edges. The initialization phase of the algorithm uses a {GRASP} to generate good starting solutions. The greedy function minimizes the sum of weights of the edges outgoing from vertices in the partition. The local search uses the exchange of one element in the current partition with one not in it." } @techreport{MacMen98a, author = "E.M. Macambira and C.N. Meneses", title = "A {GRASP} algorithm for the maximum weighted edge subgraph problem", institution = "Department of Statistics and Computation, University of Cear\'a", address = "Fortaleza, CE 60740-000 Brazil", year = "1998", annote = " {GRASP} for the maximum weighted edge subgraph problem is proposed to overcome the difficulties encountered by local search methods. The greedy function of the construction phase favors the vertices corresponding to the maximum sum of the weights associated with its outgoing edges. The local search tries to improve the actual solution by simply swapping one element in the solution set with one not belonging to the solution. In Portuguese." } @techreport{MarMig03a, author = "Y. Marinakis and A. Migdalas", title = "Expading neighborhood {GRASP} for the {T}raveling {S}alesman {P}roblem", institution = "Technical University of Crete", address = "Chania 73100, Greece", annote = {For the traveling salesman problem the authors of this paper propose a {GRASP} that includes tour improvement methods. One among the simplest tour improvement method is the nearest neighbor in which at each step the salesman moves to the city nearest to the current one.}, year = "2003" } @Article{Mar01a, author = "R. Mart\'{\i}", title = "Arc crossing minimization in graphs with {GRASP}", journal = "IIE Transactions", volume = "33", pages = "913--919", year = "2001", annote = "A {GRASP} for minimizing straight-line crossings in hierarchical graphs is presented. {GRASP} is shown to be faster than more complex heuristics but produces lower-quality solutions. It is not as fast as simple heuristics, but finds better-quality solutions. Hence, it is a candidate for practical implementation in graph drawing systems.", } @Article{MarEst01a, author = "R. Mart\'{\i} and V. Estruch", title = "Incremental bipartite drawing problem", journal = "Computers and Operations Research", volume = "28", pages = "1287--1298", year = "2001", annote = "The goal of limiting the number of arc crossings is a well accepted criterion of how well a graph is drawn. Incremental graph drawing supports interactive updates by users. A {GRASP} is proposed for the incremental arc crossing minimization problem for bipartite graphs. Computational experiments are done on 450 instances and results are compared with a branch and bound algorithm.", } @article{MarLag03a, author = "R. Mart\'{\i} and M. Laguna", title = "Heuristics and meta-heuristics for $2$-layer straight line crossing minimization", journal = {Discrete Applied Mathematics}, volume = {127}, pages = {665-678}, year = "2003", annote = "Extensive computational results are presented using 12 heuristics and two meta-heuristics for the $2$-layer straight line crossing minimization problem. On dense graphs, a tabu search meta-heuristic does best with {GRASP} a close second. On low-density graphs, {GRASP} outperforms all other approaches." } @incollection{MarParResRib99a, author = "S.L. Martins and P.M. Pardalos and M.G.C. Resende and C.C. Ribeiro", title = "Greedy randomized adaptive search procedures for the {Steiner} problem in graphs", booktitle = "Randomization methods in algorithmic design", editor = "P.M. Pardalos and S. Rajasekaran and J. Rolim", series = "{DIMACS} Series on Discrete Mathematics and Theoretical Computer Science", publisher = "American Mathematical Society", volume = "43", pages = "133--145", year = "1999", annote = "Four versions of a {GRASP} for approximately solving general instances of the Steiner problem in graphs are proposed. One is implemented and tested. The construction phase is based on the distance network heuristic. A distance network corresponding to the original graph is built. Associated with each edge of the distance network is a weight that takes into account the shortest distances in the original graph. With respect to the new weight distribution, Kruskal's algorithm is used to solve the minimum spanning tree (MST) problem and the edges in the MST so computed are replaced by the edges in the corresponding shortest paths in the original graph. The local search is based on insertions and eliminations of nodes to and from the current solution." } @Article{MarResRibPar00b, author = "S.L. Martins and M.G.C. Resende and C.C. Ribeiro and P.M. Pardalos", title = "A parallel {GRASP} for the {Steiner} tree problem in graphs using a hybrid local search strategy", journal = "Journal of Global Optimization", volume = "17", year = "2000", pages = "267--283", annote = "This paper presents a {GRASP} for the Steiner problem in graphs. The construction phase is based on the Mehlhorn distance network heuristic, which consists of computing the modified distance network graph and using Kruskal's algorithm to solve the minimum spanning tree problem for the resulting graph. The local search is done by using a combination of key-path based local search and node based local search.", } @incollection{MarRibSou98a, author = "S.L. Martins and C.C. Ribeiro and M.C. Souza", title = "A parallel {GRASP} for the {S}teiner problem in graphs", booktitle = "Proceedings of {IRREGULAR}'98 -- 5th {I}nternational {S}ymposium on {S}olving {I}rregularly {S}tructured {P}roblems in {P}arallel", editor = "A. Ferreira and J. Rolim", series = "Lecture Notes in Computer Science", publisher = "Springer-Verlag", volume = "1457", pages = "285--297", year = "1998", annote = "A parallelization of a sequential {GRASP} for the Steiner minimal tree problem is proposed. The procedure implemented is one of the procedures described in Martins, Pardalos, Resende, and Ribeiro (1999). The parallelization is accomplished by distributing the {GRASP} iterations among the processors on a demand-driven basis." } @inproceedings{MotOchMar01a, author = "L. Motta and L.S. Ochi and C. Martinhon", title = {{GRASP} metaheuristics to the generalized covering tour problem}, booktitle = "Proceedings of MIC'2001", city = "Porto, Portugal", month = "July 16-20", pages = "387--391", annote = {Let $G(V\cup W,E)$ be an undirected graph, where $V\cup W=\{1,2,\ldots,n\}$ is the node set, and $E=\{(i,j)\vert i,j\in V\cup W,\ i