Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification

In this survey we discuss different state-of-the-art approaches of combining exact algorithms and metaheuristics to solve combinatorial optimization problems. Some of these hybrids mainly aim at providing optimal solutions in shorter time, while others primarily focus on getting better heuristic solutions. The two main categories in which we divide the approaches are collaborative versus integrative combinations. We further classify the different techniques in a hierarchical way. Altogether, the surveyed work on combinations of exact algorithms and metaheuristics documents the usefulness and strong potential of this research direction.

[1]  Richard K. Congram Polynomially searchable exponential neighbourhoods for sequencing problems in combinatorial optimisation , 2000 .

[2]  Thomas Stützle,et al.  Combinations of Local Search and Exact Algorithms , 2003, EvoWorkshops.

[3]  James Kennedy,et al.  Proceedings of the 1998 IEEE International Conference on Evolutionary Computation [Book Review] , 1999, IEEE Transactions on Evolutionary Computation.

[4]  Jin-Kao Hao,et al.  A hybrid approach for the 0-1 multidimensional knapsack problem , 2001, IJCAI 2001.

[5]  Nenad Mladenović,et al.  An Introduction to Variable Neighborhood Search , 1997 .

[6]  Itsuo Hatono,et al.  An Approximate Solution Method for Combinatorial Optimization , 1994 .

[7]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[8]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[9]  Martin W. P. Savelsbergh,et al.  Heuristic Optimization: A hybrid AI/OR approach , 1997 .

[10]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[11]  Hisham M. Haddad,et al.  Proceedings of the 2003 ACM Symposium on Applied Computing (SAC), March 9-12, 2003, Melbourne, FL, USA , 2003, SAC.

[12]  David L. Woodruff,et al.  A Chunking Based Selection Strategy for Integrating Meta-Heuristics with Branch and Bound , 1999 .

[13]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[14]  Norman M. Sadeh,et al.  Job-shop-scheduling by a team of asynchronous agents , 1993 .

[15]  Andrea T. Staggemeier,et al.  A hybrid genetic algorithm to solve a lot-sizing and scheduling problem , 2002 .

[16]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[17]  John M. Wilson,et al.  Using a Hybrid Genetic-Algorithm/Branch and Bound Approach to Solve Feasibility and Optimization Integer Programming Problems , 2001, J. Heuristics.

[18]  Luiz Antonio Nogueira Lorena,et al.  Constructive Genetic Algorithm and Column Generation: an Application to Graph Coloring , 2000 .

[19]  Paul M. Thompson,et al.  Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems , 1993, Oper. Res..

[20]  Carlos Cotta,et al.  Embedding Branch and Bound within Evolutionary Algorithms , 2003, Applied Intelligence.

[21]  Peter I. Cowling,et al.  Effective Local and Guided Variable Neighbourhood Search Methods for the Asymmetric Travelling Salesman Problem , 2001, EvoWorkshops.

[22]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[23]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..

[24]  Pablo Moscato,et al.  A Gentle Introduction to Memetic Algorithms , 2003, Handbook of Metaheuristics.

[25]  G. Raidl,et al.  An improved genetic algorithm for the multiconstrained 0-1 knapsack problem , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[26]  Günther R. Raidl,et al.  An improved hybrid genetic algorithm for the generalized assignment problem , 2004, SAC '04.

[27]  Claude Le Pape,et al.  Exploring relaxation induced neighborhoods to improve MIP solutions , 2005, Math. Program..

[28]  Jens Gottlieb,et al.  Evolutionary Computation in Combinatorial Optimization , 2006, Lecture Notes in Computer Science.

[29]  Charalambos Fragakis,et al.  Genetic Programming Applied to Mixed Integer Programming , 2004, EuroGP.

[30]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[31]  Chelsea C. White,et al.  A Hybrid Genetic/Optimization Algorithm for Finite-Horizon, Partially Observed Markov Decision Processes , 2004, INFORMS J. Comput..

[32]  Rama Akkiraju,et al.  Asynchronous Teams , 2003, Handbook of Metaheuristics.

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

[34]  Agnès Plateau,et al.  A hybrid search combining interior point methods and metaheuristics for 0–1 programming , 2002 .

[35]  Günther R. Raidl,et al.  An Evolutionary Algorithm for Column Generation in Integer Programming: An Effective Approach for 2D Bin Packing , 2004, PPSN.

[36]  Gert Smolka Principles and Practice of Constraint Programming-CP97 , 1997, Lecture Notes in Computer Science.

[37]  Matteo Fischetti,et al.  Local branching , 2003, Math. Program..

[38]  Günther R. Raidl,et al.  Solving a Real-World Glass Cutting Problem , 2004, EvoCOP.

[39]  B. Müller,et al.  Solution of the Traveling-Salesman Problem , 1995 .

[40]  Pedro S. de Souza,et al.  Asynchronous Teams: Cooperation Schemes for Autonomous Agents , 1998, J. Heuristics.

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

[42]  Uwe Aickelin Staggemeier A, Clark A and Aickelin U (2002): "A hybrid genetic algorithm to solve a lot-sizing and scheduling problem ", in Sixteenth triennial conference of the International Federation of Operational Research Societies , Edinburgh, UK, 2002. , 2002 .

[43]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[44]  Sunderesh S. Heragu,et al.  A combined branch-and-bound and genetic algorithm based approach for a flowshop scheduling problem , 1996, Ann. Oper. Res..

[45]  Petra Mutzel,et al.  Combining a Memetic Algorithm with Integer Programming to Solve the Prize-Collecting Steiner Tree Problem , 2004, GECCO.

[46]  Jörg Denzinger,et al.  On cooperation between evolutionary algorithms and other search paradigms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[47]  Günther R. Raidl,et al.  Models and algorithms for three-stage two-dimensional bin packing , 2007, Eur. J. Oper. Res..