Metaheuristics: Some Principles for an Efficient Design

Many optimization problems (from academia or industry) require the use of a metaheuristic to find a satisfying solution in a reasonable amount of time, even if optimality is not guaranteed. Metaheuristics can be roughly partitioned in two groups: local search methods (e.g., simulated annealing, tabu search, and variable neighborhood search) and population based algorithms (e.g., genetic algorithms, ant colonies, and scatter search). The reader is assumed to be familiar with the most popular metaheuristics. Even if there exist convergence theorems for some metaheuristics, they usually do not help to develop an efficient metaheuristic. The goal of this paper is to propose general rules which are useful when designing metaheuristics in order to produce good performance according to several criteria, independently of the class of metaheuristics employed. The discussion is illustrated for three well-known optimization problems: graph coloring, vehicle routing and job-shop scheduling.

[1]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[2]  Alain Hertz,et al.  Guidelines for the use of meta-heuristics in combinatorial optimization , 2003, Eur. J. Oper. Res..

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

[4]  Paolo Toth,et al.  A survey on vertex coloring problems , 2010, Int. Trans. Oper. Res..

[5]  Paolo Toth,et al.  A Metaheuristic Approach for the Vertex Coloring Problem , 2008, INFORMS J. Comput..

[6]  Gilbert Laporte,et al.  Metaheuristics: A bibliography , 1996, Ann. Oper. Res..

[7]  Egon Balas,et al.  Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm , 1969, Oper. Res..

[8]  Holger H. Hoos,et al.  Stochastic Local Search-Methods , 1998 .

[9]  Craig A. Morgenstern.  Distributed coloration neighborhood search , 1993, Cliques, Coloring, and Satisfiability.

[10]  Mitsuo Gen,et al.  A tutorial survey of job-shop scheduling problems using genetic algorithms—I: representation , 1996 .

[11]  Sheik Meeran,et al.  Deterministic job-shop scheduling: Past, present and future , 1999, Eur. J. Oper. Res..

[12]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

[13]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[14]  Günther R. Raidi.  A unified view on hybrid metaheuristics , 2006 .

[15]  Thomas Stützle,et al.  The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances , 2003 .

[16]  Alain Hertz,et al.  Using tabu search techniques for graph coloring , 1987, Computing.

[17]  John Shawe-Taylor,et al.  Ants and Graph Coloring , 2001 .

[18]  Alain Hertz,et al.  Ants can colour graphs , 1997 .

[19]  Egon Balas,et al.  Guided Local Search with Shifting Bottleneck for Job Shop Scheduling , 1998 .

[20]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[21]  Fred W. Glover,et al.  Tabu search and finite convergence , 2002, Discret. Appl. Math..

[22]  Ching-Jong Liao,et al.  Ant colony optimization combined with taboo search for the job shop scheduling problem , 2008, Comput. Oper. Res..

[23]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[24]  D. Werra,et al.  Some experiments with simulated annealing for coloring graphs , 1987 .

[25]  Christian Bessiere,et al.  Arc-Consistency and Arc-Consistency Again , 1993, Artif. Intell..

[26]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[27]  J. Culberson.  Iterated Greedy Graph Coloring and the Difficulty Landscape , 1992 .

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

[29]  R. Jonker,et al.  The symmetric traveling salesman problem and edge exchanges in minimal 1-trees , 1983 .

[30]  Masahito Yamamoto,et al.  Cooperative Search Based on Pheromone Communication for Vehicle Routing Problems , 1998 .

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

[32]  Paolo Toth,et al.  The Granular Tabu Search and Its Application to the Vehicle-Routing Problem , 2003, INFORMS J. Comput..

[33]  Marco Dorigo,et al.  Ant system for Job-shop Scheduling , 1994 .

[34]  James P. Kelly,et al.  A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem , 1996, Transp. Sci..

[35]  Olli Bräysy,et al.  Active guided evolution strategies for large-scale vehicle routing problems with time windows , 2005, Comput. Oper. Res..

[36]  El-Ghazali Talbi,et al.  A Taxonomy of Hybrid Metaheuristics , 2002, J. Heuristics.

[37]  Richard F. Hartl,et al.  Applying the ANT System to the Vehicle Routing Problem , 1999 .

[38]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[39]  Paolo Toth,et al.  Exact Solution of the Vehicle Routing Problem , 1998 .

[40]  Djamal Habet,et al.  Consistent Neighbourhood in a Tabu Search , 2005 .

[41]  Michel Gendreau,et al.  A guide to vehicle routing heuristics , 2002, J. Oper. Res. Soc..

[42]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[43]  Baozhen Yao,et al.  Production , Manufacturing and Logistics An improved ant colony optimization for vehicle routing problem , 2008 .

[44]  Ulrich Faigle,et al.  Some Convergence Results for Probabilistic Tabu Search , 1992, INFORMS J. Comput..

[45]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

[46]  E. Nowicki,et al.  A Fast Taboo Search Algorithm for the Job Shop Problem , 1996 .

[47]  Reginald R. Souleyrette,et al.  Implementing Vehicle Routing Models , 1990 .

[48]  L. Darrell Whitley,et al.  Problem difficulty for tabu search in job-shop scheduling , 2003, Artif. Intell..

[49]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

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

[51]  Éric D. Taillard,et al.  Parallel iterative search methods for vehicle routing problems , 1993, Networks.

[52]  Christos D. Tarantilis,et al.  BoneRoute: An Adaptive Memory-Based Method for Effective Fleet Management , 2002, Ann. Oper. Res..

[53]  Richard F. Hartl,et al.  Analyzing a Unified Ant System for the VRP and Some of Its Variants , 2003, EvoWorkshops.

[54]  Catherine Roucairol,et al.  A Parallel Tabu Search Algorithm Using Ejection Chains for the Vehicle Routing Problem , 1996 .

[55]  Yasuhiro Tsujimura,et al.  A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: hybrid genetic search strategies , 1999 .

[56]  Nicolas Zufferey,et al.  Ant Local Search and its efficient adaptation to graph colouring , 2010, J. Oper. Res. Soc..

[57]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[58]  William J. Cook,et al.  A Computational Study of the Job-Shop Scheduling Problem , 1991, INFORMS Journal on Computing.

[59]  Éric D. Taillard,et al.  Parallel Taboo Search Techniques for the Job Shop Scheduling Problem , 1994, INFORMS J. Comput..

[60]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning , 1991, Oper. Res..

[61]  Egon Balas,et al.  The Shifting Bottleneck Procedure for Job Shop Scheduling , 1988 .

[62]  Charles Fleurent,et al.  Genetic and hybrid algorithms for graph coloring , 1996, Ann. Oper. Res..

[63]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[64]  Gilbert Laporte,et al.  Classical Heuristics for the Capacitated VRP , 2002, The Vehicle Routing Problem.

[65]  Alain Hertz,et al.  A variable neighborhood search for graph coloring , 2003, Eur. J. Oper. Res..

[66]  Alain Hertz,et al.  An adaptive memory algorithm for the k-coloring problem , 2003, Discret. Appl. Math..

[67]  Christian Prins,et al.  A simple and effective evolutionary algorithm for the vehicle routing problem , 2004, Comput. Oper. Res..

[68]  R. Real,et al.  The Probabilistic Basis of Jaccard's Index of Similarity , 1996 .

[69]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..

[70]  Nicolas Zufferey,et al.  A graph coloring heuristic using partial solutions and a reactive tabu scheme , 2008, Comput. Oper. Res..

[71]  Jan Karel Lenstra,et al.  Job Shop Scheduling by Simulated Annealing , 1992, Oper. Res..

[72]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[73]  Christian Bierwirth,et al.  A search space analysis of the Job Shop Scheduling Problem , 1999, Ann. Oper. Res..

[74]  Luca Maria Gambardella,et al.  Adaptive memory programming: A unified view of metaheuristics , 1998, Eur. J. Oper. Res..

[75]  Jin-Kao Hao,et al.  Hybrid Evolutionary Algorithms for Graph Coloring , 1999, J. Comb. Optim..

[76]  Günther R. Raidl,et al.  Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification , 2005, IWINAC.