Metaheuristics for dynamic combinatorial optimization problems.

Many real-world optimization problems are combinatorial optimization problems subject to dynamic environments. In such dynamic combinatorial optimization problems (DCOPs), the objective, decision variables and/or constraints may change over time, and so solving DCOPs is a challenging task. Metaheuristics are a good choice of tools to tackle DCOPs because many metaheuristics are inspired by natural or biological evolution processes, which are always subject to changing environments. In recent years, DCOPs have attracted a growing interest from the metaheuristics community. This paper is a tutorial on metaheuristics for DCOPs. We cover the definition of DCOPs, typical benchmark problems and their characteristics, methodologies and performance measures, real-world case study and key challenges in the area. Some future research directions are also pointed out in this paper.

[1]  Xin Yao,et al.  On the role of modularity in evolutionary dynamic optimisation , 2010, IEEE Congress on Evolutionary Computation.

[2]  Trung Thanh Nguyen,et al.  Continuous dynamic optimisation using evolutionary algorithms , 2011 .

[3]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[4]  Carlos Cruz,et al.  Optimization in dynamic environments: a survey on problems, methods and measures , 2011, Soft Comput..

[5]  A. Sima Etaner-Uyar,et al.  A new population based adaptive domination change mechanism for diploid genetic algorithms in dynamic environments , 2005, Soft Comput..

[6]  Tim Hendtlass,et al.  Solving Dynamic Single-Runway Aircraft Landing Problems With Extremal Optimisation , 2007, 2007 IEEE Symposium on Computational Intelligence in Scheduling.

[7]  Xin Yao,et al.  Robust Salting Route Optimization Using Evolutionary Algorithms , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.

[8]  David Abramson,et al.  Displacement problem and dynamically scheduling aircraft landings , 2004, J. Oper. Res. Soc..

[9]  Shengxiang Yang,et al.  Ant Colony Optimization with Immigrants Schemes in Dynamic Environments , 2010, PPSN.

[10]  Andreas König,et al.  Intrinsic Evolution of Predictable Behavior Evolvable Hardware in Dynamic Environment , 2006, 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06).

[11]  Von der Fakult.  Evolutionary Algorithms and Dynamic Optimization Problems , 2003 .

[12]  A. Sima Etaner-Uyar,et al.  A Critical Look at Dynamic Multi-dimensional Knapsack Problem Generation , 2009, EvoWorkshops.

[13]  Li Liu.  Real-time Contaminant Source Characterization in Water Distribution Systems , 2009 .

[14]  Kurt Geihs,et al.  Evolutionary Freight Transportation Planning , 2009, EvoWorkshops.

[15]  R. Dupas,et al.  A hybrid GA approach for solving the Dynamic Vehicle Routing Problem with Time Windows , 2006, 2006 2nd International Conference on Information & Communication Technologies.

[16]  Will Maden,et al.  A Road TimetableTM to aid vehicle routing and scheduling , 2006, Comput. Oper. Res..

[17]  Maarten H. van der Vlerk,et al.  A dynamic day-ahead paratransit planning problem , 2007 .

[18]  Shengxiang Yang,et al.  Memory-based immigrants for genetic algorithms in dynamic environments , 2005, GECCO '05.

[19]  Ning Wang,et al.  Adaptive Multi-topology IGP Based Traffic Engineering with Near-Optimal Network Performance , 2008, Networking.

[20]  Alan S. Perelson,et al.  The immune system, adaptation, and machine learning , 1986 .

[21]  Agostinho C. Rosa,et al.  UMDAs for dynamic optimization problems , 2008, GECCO '08.

[22]  Karsten Weicker,et al.  An Analysis of Dynamic Severity and Population Size , 2000, PPSN.

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

[24]  Juan Julián Merelo Guervós,et al.  A genetic algorithm for dynamic modelling and prediction of activity in document streams , 2007, GECCO '07.

[25]  Jürgen Branke *,et al.  Anticipation and flexibility in dynamic scheduling , 2005 .

[26]  Xin Yao,et al.  Dynamic Time-Linkage Problems Revisited , 2009, EvoWorkshops.

[27]  Thomas Jansen,et al.  Theoretical analysis of a mutation-based evolutionary algorithm for a tracking problem in the lattice , 2005, GECCO '05.

[28]  Kenneth N. Brown,et al.  Managing restaurant tables using constraints , 2007, Knowl. Based Syst..

[29]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[30]  Tom Lenaerts,et al.  Raising the Dead: Extending Evolutionary Algorithms with a Case-Based Memory , 2001, EuroGP.

[31]  Hartmut Schmeck,et al.  Designing evolutionary algorithms for dynamic optimization problems , 2003 .

[32]  Xin Yao,et al.  Continuous Dynamic Constrained Optimization—The Challenges , 2012, IEEE Transactions on Evolutionary Computation.

[33]  Juan Julián Merelo Guervós,et al.  Parallel Problem Solving from Nature — PPSN VII , 2002, Lecture Notes in Computer Science.

[34]  Per Kristian Lehre,et al.  Dynamic evolutionary optimisation: an analysis of frequency and magnitude of change , 2009, GECCO.

[35]  Zbigniew Michalewicz,et al.  Searching for optima in non-stationary environments , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[36]  Jürgen Branke,et al.  The Role of Representations in Dynamic Knapsack Problems , 2006, EvoWorkshops.

[37]  Xin Yao,et al.  Benchmark Generator for CEC'2009 Competition on Dynamic Optimization , 2008 .

[38]  Wiering,et al.  A Serial Population Genetic Algorithm for Dynamic Optimization Problems , 2006 .

[39]  Shengxiang Yang,et al.  An Immigrants Scheme Based on Environmental Information for Ant Colony Optimization for the Dynamic Travelling Salesman Problem , 2011, Artificial Evolution.

[40]  David W. Pearson,et al.  An Immune System-Based Genetic Algorithm to Deal with Dynamic Environments: Diversity and Memory , 2003, ICANNGA.

[41]  Susana Cecilia Esquivel,et al.  An Evolutionary Algorithm to Track Changes of Optimum Value Locations in Dynamic Environments , 2004 .

[42]  Darren M. Chitty,et al.  A Hybrid Ant Colony Optimisation Technique for Dynamic Vehicle Routing , 2004, GECCO.

[43]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[44]  Jason M. Daida,et al.  Optimal Mutation and Crossover Rates for a Genetic Algorithm Operating in a Dynamic Environment , 1998, Evolutionary Programming.

[45]  Hui Cheng,et al.  Multi-population Genetic Algorithms with Immigrants Scheme for Dynamic Shortest Path Routing Problems in Mobile Ad Hoc Networks , 2010, EvoApplications.

[46]  Lothar Thiele,et al.  Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization , 2003 .

[47]  Hitoshi Kanoh,et al.  Hybrid genetic algorithm for dynamic multi-objective route planning with predicted traffic in a real-world road network , 2008, GECCO '08.

[48]  Hui Cheng,et al.  Genetic Algorithms With Immigrants and Memory Schemes for Dynamic Shortest Path Routing Problems in Mobile Ad Hoc Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[49]  Hendrik Richter.  Behavior of Evolutionary Algorithms in Chaotically Changing Fitness Landscapes , 2004, PPSN.

[50]  Peter A. N. Bosman,et al.  Inventory management and the impact of anticipation in evolutionary stochastic online dynamic optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[51]  Anabela Simões,et al.  Improving memory’s usage in evolutionary algorithms for changing environments , 2007, 2007 IEEE Congress on Evolutionary Computation.

[52]  S. Louis,et al.  Genetic Algorithms for Open Shop Scheduling and Re-scheduling , 1996 .

[53]  Tim Hendtlass,et al.  Solving Problems with Hidden Dynamics – Comparison of Extremal Optimisation and Ant Colony System , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[54]  Shengxiang Yang,et al.  A self-organizing random immigrants genetic algorithm for dynamic optimization problems , 2007, Genetic Programming and Evolvable Machines.

[55]  Ivan Zelinka,et al.  Evolutionary Algorithms and Chaotic Systems , 2010, Evolutionary Algorithms and Chaotic Systems.

[56]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[57]  Shengxiang Yang,et al.  Memory-Based Immigrants for Ant Colony Optimization in Changing Environments , 2011, EvoApplications.

[58]  Marcus Randall.  Chapter 16 A Dynamic Optimisation Approach for Ant Colony Optimisation Using the Multidimensional Knapsack Problem , 2005, Recent Advances in Artificial Life.

[59]  Shengxiang Yang,et al.  Non-stationary problem optimization using the primal-dual genetic algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[60]  Shengxiang Yang,et al.  A comparative study of immune system based genetic algorithms in dynamic environments , 2006, GECCO.

[61]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[62]  Chun Hung Cheng,et al.  Genetic search and the dynamic layout problem , 2000, Comput. Oper. Res..

[63]  Hendrik Richter,et al.  Detecting change in dynamic fitness landscapes , 2009, 2009 IEEE Congress on Evolutionary Computation.

[64]  T. Back,et al.  On the behavior of evolutionary algorithms in dynamic environments , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[65]  Jürgen Branke,et al.  Proceedings of the Workshop on Evolutionary Algorithms for Dynamic Optimization Problems (EvoDOP-2003) held in conjunction with the Genetic and Evolutionary Computation Conference (GECCO-2003), 12 July 2003, Chicago, USA [online] , 2003 .

[66]  Peter A. N. Bosman,et al.  Learning, anticipation and time-deception in evolutionary online dynamic optimization , 2005, GECCO '05.

[67]  Tom Holvoet,et al.  The DynCOAA algorithm for dynamic constraint optimization problems , 2006, AAMAS '06.

[68]  Michael Guntsch,et al.  Applying Population Based ACO to Dynamic Optimization Problems , 2002, Ant Algorithms.

[69]  Hitoshi Kanoh,et al.  Dynamic route planning for car navigation systems using virus genetic algorithms , 2007, Int. J. Knowl. Based Intell. Eng. Syst..

[70]  B. Fernandez,et al.  Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems , 2008 .

[71]  Sanja Petrovic,et al.  SURVEY OF DYNAMIC SCHEDULING IN MANUFACTURING SYSTEMS , 2006 .

[72]  Shengxiang Yang,et al.  Evolutionary dynamic optimization: A survey of the state of the art , 2012, Swarm Evol. Comput..

[73]  Peter Ross,et al.  An Immune System Approach to Scheduling in Changing Environments , 1999, GECCO.

[74]  Anabela Simões,et al.  Improving prediction in evolutionary algorithms for dynamic environments , 2009, GECCO.

[75]  Gary G. Yen,et al.  Dynamic Evolutionary Algorithm With Variable Relocation , 2009, IEEE Transactions on Evolutionary Computation.

[76]  Shengxiang Yang,et al.  Ant Colony Optimization Algorithms with Immigrants Schemes for the Dynamic Travelling Salesman Problem , 2013 .

[77]  Shengxiang Yang,et al.  An Analysis of the XOR Dynamic Problem Generator Based on the Dynamical System , 2010, PPSN.

[78]  Xin Yao,et al.  Dual population-based incremental learning for problem optimization in dynamic environments , 2003 .

[79]  Kok Cheong Wong,et al.  A New Diploid Scheme and Dominance Change Mechanism for Non-Stationary Function Optimization , 1995, ICGA.

[80]  Xin Yao,et al.  Attributes of Dynamic Combinatorial Optimisation , 2008, SEAL.

[81]  Peter A. N. Bosman,et al.  Learning and anticipation in online dynamic optimization with evolutionary algorithms: the stochastic case , 2007, GECCO '07.

[82]  Arvind S. Mohais,et al.  DynDE: a differential evolution for dynamic optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[83]  Ketan Kotecha,et al.  Multi objective genetic algorithm based adaptive QoS routing in MANET , 2007, 2007 IEEE Congress on Evolutionary Computation.

[84]  A. Sima Etaner-Uyar,et al.  Towards an analysis of dynamic environments , 2005, GECCO '05.

[85]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[86]  Xin Yao,et al.  Benchmarking and solving dynamic constrained problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[87]  David E. Goldberg,et al.  Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy , 1987, ICGA.

[88]  M. Chowdhury,et al.  Benchmarks for testing evolutionary algorithms , 1998 .

[89]  Xin Yao,et al.  Capacitated arc routing problem in uncertain environments , 2010, IEEE Congress on Evolutionary Computation.

[90]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[91]  Shengxiang Yang,et al.  Associative Memory Scheme for Genetic Algorithms in Dynamic Environments , 2006, EvoWorkshops.

[92]  Shengxiang Yang,et al.  On the Design of Diploid Genetic Algorithms for Problem Optimization in Dynamic Environments , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[93]  Karsten Weicker,et al.  Performance Measures for Dynamic Environments , 2002, PPSN.

[94]  Edmund K. Burke,et al.  On-line decision support for take-off runway scheduling with uncertain taxi times at London Heathrow airport , 2008, J. Sched..

[95]  Changhe Li,et al.  A Generalized Approach to Construct Benchmark Problems for Dynamic Optimization , 2008, SEAL.

[96]  Ronald W. Morrison,et al.  Designing Evolutionary Algorithms for Dynamic Environments , 2004, Natural Computing Series.

[97]  Stefan Droste,et al.  Analysis of the (1+1) EA for a dynamically changing ONEMAX-variant , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[98]  Anabela Simões,et al.  Evolutionary Algorithms for Dynamic Environments: Prediction Using Linear Regression and Markov Chains , 2008, PPSN.

[99]  Gerardo Rubino,et al.  A GRASP Algorithm Using RNN for Solving Dynamics in a P2P Live Video Streaming Network , 2008, 2008 Eighth International Conference on Hybrid Intelligent Systems.

[100]  William Rand,et al.  Measurements for understanding the behavior of the genetic algorithm in dynamic environments: a case study using the Shaky Ladder Hyperplane-Defined Functions , 2005, GECCO '05.

[101]  Jason M. Daida,et al.  (1+1) genetic algorithm fitness dynamics in a changing environment , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[102]  Karsten Weicker,et al.  Analysis of local operators applied to discrete tracking problems , 2005, Soft Comput..

[103]  Hui Cheng,et al.  Genetic algorithms with immigrants schemes for dynamic multicast problems in mobile ad hoc networks , 2010, Eng. Appl. Artif. Intell..

[104]  Stephen F. Smith,et al.  Airlift mission monitoring and dynamic rescheduling , 2008, Eng. Appl. Artif. Intell..

[105]  Chelsea C. White,et al.  State space reduction for nonstationary stochastic shortest path problems with real-time traffic information , 2005, IEEE Transactions on Intelligent Transportation Systems.

[106]  Donald E. Waagen,et al.  Proceedings of the 7th International Conference on Evolutionary Programming VII , 1998 .

[107]  Xiaohong Jiang,et al.  Ant-based survivable routing in dynamic WDM networks with shared backup paths , 2006, The Journal of Supercomputing.

[108]  Hajime Kita,et al.  Adaptation to Changing Environments by Means of the Memory Based Thermodynamical Genetic Algorithm , 1997, ICGA.

[109]  Shengxiang Yang,et al.  Genetic Algorithms with Memory- and Elitism-Based Immigrants in Dynamic Environments , 2008, Evolutionary Computation.

[110]  Shengxiang Yang,et al.  Constructing dynamic test environments for genetic algorithms based on problem difficulty , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[111]  Kalyanmoy Deb,et al.  Dynamic Multi-objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-thermal Power Scheduling , 2007, EMO.

[112]  C. J. Eyckelhof,et al.  Ant Systems for a Dynamic TSP - Ants Caught in a Traffic Jam , 2002 .

[113]  Ponnuthurai N. Suganthan,et al.  Evolutionary programming with ensemble of explicit memories for dynamic optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[114]  Karsten Weicker,et al.  Evolutionary algorithms and dynamic optimization problems , 2003 .

[115]  Shengxiang Yang,et al.  Evolutionary Computation in Dynamic and Uncertain Environments , 2007, Studies in Computational Intelligence.

[116]  Shengxiang Yang,et al.  A memetic ant colony optimization algorithm for the dynamic travelling salesman problem , 2011, Soft Comput..

[117]  Xin Yao,et al.  Dynamic combinatorial optimisation problems: an analysis of the subset sum problem , 2011, Soft Comput..

[118]  Thomas Stützle,et al.  Ant Colony Optimization Theory , 2004 .

[119]  S. Salhi,et al.  A survey of effective heuristics and their application to a variety of knapsack problems , 2007 .

[120]  Xin Yao,et al.  A Hybrid Ant Colony Optimization Algorithm for the Extended Capacitated Arc Routing Problem , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[121]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[122]  Xin Yao,et al.  Solving dynamic constrained optimisation problems using repair methods , 2010 .

[123]  Hui Cheng,et al.  Genetic algorithms with elitism-based immigrants for dynamic load balanced clustering problem in mobile ad hoc networks , 2011, 2011 IEEE Symposium on Computational Intelligence in Dynamic and Uncertain Environments (CIDUE).

[124]  Xin Yao,et al.  Population-Based Incremental Learning With Associative Memory for Dynamic Environments , 2008, IEEE Transactions on Evolutionary Computation.

[125]  Ming Yang,et al.  A New Approach to Solving Dynamic Traveling Salesman Problems , 2006, SEAL.

[126]  David Z. Zhang,et al.  Agent-based model for optimising supply-chain configurations , 2008 .

[127]  G. F. Page,et al.  Designing Evolutionary Algorithms for Dynamic Environments, by Ronald W. Morrison, Springer, 2004, ISBN 3-540-21231-0. , 2006 .

[128]  Tim Hendtlass,et al.  Ant Colony Optimisation Applied to a Dynamically Changing Problem , 2002, IEA/AIE.

[129]  Emma Hart,et al.  A Comparison of Dominance Mechanisms and Simple Mutation on Non-stationary Problems , 1998, PPSN.

[130]  Jacek M. Zurada,et al.  Swarm and Evolutionary Computation , 2012, Lecture Notes in Computer Science.

[131]  Hendrik Richter,et al.  Evolutionary Optimization and Dynamic Fitness Landscapes , 2010, Evolutionary Algorithms and Chaotic Systems.

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

[133]  Xin Yao,et al.  Experimental study on population-based incremental learning algorithms for dynamic optimization problems , 2005, Soft Comput..

[134]  Peter A. N. Bosman.  Learning and Anticipation in Online Dynamic Optimization , 2007, Evolutionary Computation in Dynamic and Uncertain Environments.