GRASP: Greedy Randomized Adaptive Search Procedures

GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. An intensification strategy based on path-relinking is frequently used to improve solution quality and to reduce computation times by exploring elite solutions previously found along the search. This chapter describes the basic components of GRASP, successful implementation strategies, and effective hybridizations with path-relinking and other metaheuristics. We also list some tricks to be used in the quest for good implementations. The bibliography is enriched by an account of relevant applications and by links to surveys, software, and additional sources of material.

[1]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[2]  R. Martí.  Arc Crossing Minimization in Graphs with GRASP , 2001 .

[3]  José Luis González Velarde,et al.  A search heuristic for just-in-time scheduling in parallel machines , 1991, J. Intell. Manuf..

[4]  Celso C. Ribeiro,et al.  GRASP with Path-Relinking: Recent Advances and Applications , 2005 .

[5]  Panos M. Pardalos,et al.  A GRASP heuristic for the Cooperative Communication Problem in Ad Hoc Networks , 2005 .

[6]  Panos M. Pardalos,et al.  GRASP with Path-Relinking for the Quadratic Assignment Problem , 2004, WEA.

[7]  Celso C. Ribeiro,et al.  Greedy randomized adaptive search procedures for the Steiner problem in graphs. , 1997 .

[8]  Timothy L. Urban.  Solution procedures for the dynamic facility layout problem , 1998, Ann. Oper. Res..

[9]  Mauricio G. C. Resende,et al.  Computing Approximate Solutions of the Maximum Covering Problem with GRASP , 1998, J. Heuristics.

[10]  Thomas A. Feo,et al.  A grasp for single machine scheduling with sequence dependent setup costs and linear delay penalties , 1996, Comput. Oper. Res..

[11]  Jonathan F. Bard,et al.  Note-Operations Sequencing in Discrete Parts Manufacturing , 1989 .

[12]  José A. Moreno-Pérez,et al.  GRASP-VNS hybrid for the Strip Packing Problem , 2004, Hybrid Metaheuristics.

[13]  Celso C. Ribeiro,et al.  A GRASP heuristic for the capacitated minimum spanning tree problem using a memory-based local search strategy , 2004 .

[14]  Rafael Martí,et al.  GRASP for Seam Drawing in Mosaicking of Aerial Photographic Maps , 1999, J. Heuristics.

[15]  Arvind Rajan,et al.  Using grasp to solve the component grouping problem , 1994 .

[16]  Jonathan F. Bard,et al.  Facility-Wide Planning and Scheduling of Printed Wiring Board Assembly , 1995, Oper. Res..

[17]  Mauricio G. C. Resende,et al.  Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP , 1998, TOMS.

[18]  Alexander J. Robertson,et al.  A Set of Greedy Randomized Adaptive Local Search Procedure (GRASP) Implementations for the Multidimensional Assignment Problem , 2001, Comput. Optim. Appl..

[19]  Panos M. Pardalos,et al.  Network Design: Connectivity and Facilities Location , 1998 .

[20]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[21]  Hugues Delmaire,et al.  REACTIVE GRASP AND TABU SEARCH BASED HEURISTICS FOR THE SINGLE SOURCE CAPACITATED PLANT LOCATION PROBLEM , 1999 .

[22]  Shawki Areibi,et al.  A GRASP clustering technique for circuit partitioning , 1996, Satisfiability Problem: Theory and Applications.

[23]  Thomas Stützle,et al.  On the empirical evaluation of Las Vegas algorithms , 1999 .

[24]  Jonathan F. Bard,et al.  An Enhanced TSP-Based Heuristic for Makespan Minimization in a Flow Shop with Setup Times , 1999, J. Heuristics.

[25]  Jonathan F. Bard,et al.  A GRASP for the Vehicle Routing Problem with Time Windows , 1995, INFORMS J. Comput..

[26]  Mauricio G. C. Resende,et al.  A GRASP for satisfiability , 1993, Cliques, Coloring, and Satisfiability.

[27]  S. Binato,et al.  A GRASP FOR JOB SHOP SCHEDULING , 2001 .

[28]  F. Glover,et al.  Fundamentals of Scatter Search and Path Relinking , 2000 .

[29]  J B Atkinson,et al.  A greedy randomised search heuristic for time-constrained vehicle scheduling and the incorporation of a learning strategy , 1998, J. Oper. Res. Soc..

[30]  Panos M. Pardalos,et al.  Randomized heuristics for the Max-Cut problem , 2002, Optim. Methods Softw..

[31]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[32]  Rafael Martí,et al.  A GRASP for Coloring Sparse Graphs , 2001, Comput. Optim. Appl..

[33]  Sue Abdinnour-Helm,et al.  Tabu search based heuristics for multi-floor facility layout , 2000 .

[34]  Celso C. Ribeiro,et al.  Tabu search for the Steiner problem in graphs , 2000, Networks.

[35]  Celso C. Ribeiro,et al.  A GRASP with path‐relinking for private virtual circuit routing , 2003, Networks.

[36]  Celso C. Ribeiro,et al.  A Parallel Grasp for the Steiner Tree Problem in Graphs Using a Hybrid Local Search Strategy , 2000, J. Glob. Optim..

[37]  T. Feo,et al.  An algorithm for the manufacturing equipment selection problem , 1991 .

[38]  P. Pardalos,et al.  Greedy Randomized Adaptive Search for a Location Problem with Economies of Scale , 1997 .

[39]  Celso C. Ribeiro,et al.  Heuristics for the Phylogeny Problem , 2002, J. Heuristics.

[40]  S. Binato,et al.  A Greedy Randomized Adaptive Search Procedure for Transmission Expansion Planning , 2001 .

[41]  John Baxter,et al.  Local Optima Avoidance in Depot Location , 1981 .

[42]  Sandra Sudarsky,et al.  Massive Quasi-Clique Detection , 2002, LATIN.

[43]  Panos M. Pardalos,et al.  Algorithm 815: FORTRAN subroutines for computing approximate solutions of feedback set problems using GRASP , 2001, TOMS.

[44]  Edward W. Felten,et al.  Large-Step Markov Chains for the Traveling Salesman Problem , 1991, Complex Syst..

[45]  Fred Glover,et al.  Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory , 1999, INFORMS J. Comput..

[46]  Panos M. Pardalos,et al.  A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem , 1998, J. Comb. Optim..

[47]  Celso C. Ribeiro,et al.  Local search with perturbations for the prize‐collecting Steiner tree problem in graphs , 2001, Networks.

[48]  Celso C. Ribeiro,et al.  A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs , 2002, INFORMS J. Comput..

[49]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[50]  Celso C. Ribeiro,et al.  Applications and Parallel Implementations of Metaheuristics in Network Design and Routing , 2004, AACC.

[51]  Peter L. Hammer,et al.  Maximally Disjoint Solutions of the Set Covering Problem , 2001, J. Heuristics.

[52]  Panos M. Pardalos,et al.  Algorithm : FORTRAN Subroutines for Approximate Solution of Dense Quadratic Assignment Problems using GRASP , 2008 .

[53]  Jonathan F. Bard,et al.  A GRASP for scheduling printed wiring board assembly , 1996 .

[54]  Panos M. Pardalos,et al.  A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem , 1997, Network Design: Connectivity and Facilities Location.

[55]  Silvio Binato,et al.  A Reactive Grasp for Transmission Network Expansion Planning , 2002 .

[56]  Panos M. Pardalos,et al.  A Parallel Grasp Implementation for the Quadratic Assignment Problem , 1995 .

[57]  Panos M. Pardalos,et al.  Approximate solution of weighted MAX-SAT problems using GRASP , 1996, Satisfiability Problem: Theory and Applications.

[58]  Manuel Laguna,et al.  A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem , 1994, Oper. Res..

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

[60]  Aravind Srinivasan,et al.  Optimal design of signaling networks for Internet telephony , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[61]  Panos M. Pardalos,et al.  Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP , 1996, TOMS.

[62]  Thomas Stützle,et al.  Evaluating Las Vegas Algorithms: Pitfalls and Remedies , 1998, UAI.

[63]  Celso C. Ribeiro,et al.  Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment , 2000, INFORMS J. Comput..

[64]  Celso C. Ribeiro,et al.  Algorithm 797: Fortran subroutines for approximate solution of graph planarization problems using GRASP , 1999, TOMS.

[65]  Renata M. Aiex,et al.  Parallel GRASP with path-relinking for job shop scheduling , 2003, Parallel Comput..

[66]  Celso C. Ribeiro,et al.  A GRASP/VND heuristic for the phylogeny problem using a new neighborhood structure , 2005, Int. Trans. Oper. Res..

[67]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[68]  Joaquín A. Pacheco,et al.  Solving two location models with few facilities by using a hybrid heuristic: a real health resources case , 2005, Comput. Oper. Res..

[69]  Edoardo Amaldi,et al.  Planning UMTS base station location: optimization models with power control and algorithms , 2003, IEEE Trans. Wirel. Commun..

[70]  Isaac Plana,et al.  GRASP and path relinking for the matrix bandwidth minimization , 2004, Eur. J. Oper. Res..

[71]  Panos M. Pardalos,et al.  A GRASP algorithm for the single source uncapacitated minimum concave-cost network flow problem , 1997, Network Design: Connectivity and Facilities Location.

[72]  M. Resende,et al.  A GRASP for graph planarization , 1997, Networks.

[73]  Celso C. Ribeiro,et al.  Parallel Greedy Randomized Adaptive Search Procedures , 2005 .

[74]  Danuta Sosnowska,et al.  Optimization of a simplified Fleet Assignment Problem with metaheuristics: Simulated Annealing and GRASP , 2000 .

[75]  Mauricio G. C. Resende,et al.  Grasp: An Annotated Bibliography , 2002 .

[76]  Celso C. Ribeiro,et al.  Strategies for the Parallel Implementation of Metaheuristics , 2002 .

[77]  Ramón Alvarez-Valdés,et al.  A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems , 2005, J. Oper. Res. Soc..

[78]  Ashish Tiwari,et al.  A greedy genetic algorithm for the quadratic assignment problem , 2000, Comput. Oper. Res..

[79]  Jonathan F. Bard,et al.  Flight Scheduling and Maintenance Base Planning , 1989 .

[80]  Panos M. Pardalos,et al.  GRASP with Path Relinking for Three-Index Assignment , 2005, INFORMS J. Comput..

[81]  Celso C. Ribeiro,et al.  Probability Distribution of Solution Time in GRASP: An Experimental Investigation , 2002, J. Heuristics.

[82]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[83]  J. G. Klincewicz,et al.  Avoiding local optima in thep-hub location problem using tabu search and GRASP , 1993, Ann. Oper. Res..

[84]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Path Relinking , 2001 .

[85]  E. T RIANTAPHYLLOU,et al.  A Greedy Randomized Adaptive Search Procedure ( GRASP ) for Inferring Logical Clauses from Examples in Polynomial Time and some Extensions , 1998 .

[86]  Ángel Corberán,et al.  A GRASP heuristic for the mixed Chinese postman problem , 2002, Eur. J. Oper. Res..

[87]  Hanan Luss,et al.  Design of Stacked Self-Healing Rings Using a Genetic Algorithm , 2000, J. Heuristics.

[88]  Bernard T. Han,et al.  A Grasp Heuristic For Solving An Extended Capacitated Concentrator Location Problem , 2003, Int. J. Inf. Technol. Decis. Mak..

[89]  Gang Yu,et al.  A Grasp for Aircraft Routing in Response to Groundings and Delays , 1997, J. Comb. Optim..

[90]  Mauricio G. C. Resende,et al.  POWER TRANSMISSION NETWORK DESIGN BY A GREEDY RANDOMIZED ADAPTIVE PATH RELINKING APPROACH , 2022 .

[91]  Rafael Martí,et al.  GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization , 1999, INFORMS J. Comput..

[92]  Panos M. Pardalos,et al.  A GRASP for the biquadratic assignment problem , 1998, Eur. J. Oper. Res..

[93]  Panos M. Pardalos,et al.  A Parallel GRASP for MAX-SAT Problems , 1996, PARA.

[94]  Ibrahim H. Osman,et al.  A greedy random adaptive search procedure for the weighted maximal planar graph problem , 2003, Comput. Ind. Eng..

[95]  Celso C. Ribeiro,et al.  A Parallel GRASP Heuristic for the 2-Path Network Design Problem (Research Note) , 2002, Euro-Par.

[96]  Mats Carlsson,et al.  Constraint Solving for Inkjet Print Mask Design , 1999, Journal of Imaging Science and Technology.

[97]  Panos M. Pardalos,et al.  Approximate solutions to the turbine balancing problem , 2001, Eur. J. Oper. Res..

[98]  Panos M. Pardalos,et al.  A Parallel Grasp for the Data Association Multidimensional Assignment Problem , 1999 .

[99]  Richard L. Church,et al.  A GRASP and Path Relinking Heuristic for Rural Road Network Development , 2005, J. Heuristics.

[100]  Panos M. Pardalos,et al.  On maximum clique problems in very large graphs , 1999, External Memory Algorithms.

[101]  Fred Glover,et al.  Multi-Start and Strategic Oscillation Methods - Principles to Exploit Adaptive Memory , 2000 .

[102]  Steve Y. Chiu,et al.  Effective Heuristic Procedures for a Field Technician Scheduling Problem , 2001, J. Heuristics.

[103]  Wen-Chyuan Chiang,et al.  The integrated machine allocation and layout problem , 2000 .

[104]  Dushyant Sharma,et al.  Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem , 2001, Math. Program..

[105]  Panos M. Pardalos,et al.  A Greedy Randomized Adaptive Search Procedure for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[106]  Mauricio G. C. Resende,et al.  A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set , 1994, Oper. Res..

[107]  Daniel Serra,et al.  Consumer choice in competitive location models: Formulations and heuristics , 1998 .

[108]  Jonathan F. Bard,et al.  Heuristics for the flow line problem with setup costs , 1998, Eur. J. Oper. Res..

[109]  Celso C. Ribeiro,et al.  A Parallel GRASP for the Steiner Problem in Graphs , 1998, IRREGULAR.

[110]  Mauricio G. C. Resende,et al.  A Hybrid Heuristic for the p-Median Problem , 2004, J. Heuristics.