Ant Colony Optimization: Overview and Recent Advances

Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the pheromone trail laying and following behavior of some ant species. Artificial ants in ACO are stochastic solution construction procedures that build candidate solutions for the problem instance under concern by exploiting (artificial) pheromone information that is adapted based on the ants’ search experience and possibly available heuristic information. Since the proposal of the Ant System, the first ACO algorithm, many significant research results have been obtained. These contributions focused on the development of high-performing algorithmic variants, the development of a generic algorithmic framework for ACO algorithms, successful applications of ACO algorithms to a wide range of computationally hard problems, and the theoretical understanding of properties of ACO algorithms. This chapter reviews these developments and gives an overview of recent research trends in ACO.

[1]  Daniel Angus,et al.  Multiple objective ant colony optimisation , 2009, Swarm Intelligence.

[2]  Michael Sampels,et al.  A MAX-MIN Ant System for the University Course Timetabling Problem , 2002, Ant Algorithms.

[3]  Andrew Lewis,et al.  A Parallel Implementation of Ant Colony Optimization , 2002, J. Parallel Distributed Comput..

[4]  Thomas Stützle,et al.  An Ant Approach to the Flow Shop Problem , 1998 .

[5]  Broderick Crawford,et al.  A hybrid Ant algorithm for the set covering problem , 2011 .

[6]  Muddassar Farooq,et al.  Routing Protocols for Next-Generation Networks Inspired by Collective Behaviors of Insect Societies: An Overview , 2008, Swarm Intelligence.

[7]  Ram V. Rachamadugu,et al.  Accurate myopic heuristics for tardiness scheduling , 1984 .

[8]  Christian Blum,et al.  New metaheuristic approaches for the edge-weighted k-cardinality tree problem , 2005, Comput. Oper. Res..

[9]  Andreas T. Ernst,et al.  Integrating ACO and Constraint Propagation , 2004, ANTS Workshop.

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

[11]  Richard F. Hartl,et al.  An ant colony optimization approach for the single machine total tardiness problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[12]  Mária Lucká,et al.  Parallel Cooperative Savings Based Ant Colony Optimization - Multiple Search and Decomposition Approaches , 2006, Parallel Process. Lett..

[13]  M. Dorigo,et al.  Ant System: An Autocatalytic Optimizing Process , 1991 .

[14]  Francisco Herrera,et al.  A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP , 2007, Eur. J. Oper. Res..

[15]  E.-G. Talbia,et al.  Parallel Ant Colonies for the quadratic assignment problem , 2001, Future Gener. Comput. Syst..

[16]  Dirk Sudholt,et al.  On the runtime analysis of the 1-ANT ACO algorithm , 2007, GECCO '07.

[17]  Marco Dorigo,et al.  Search bias in ant colony optimization: on the role of competition-balanced systems , 2005, IEEE Transactions on Evolutionary Computation.

[18]  David S. Johnson,et al.  The Traveling Salesman Problem: A Case Study in Local Optimization , 2008 .

[19]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 2005, IEEE Transactions on Neural Networks.

[20]  R. Hartl,et al.  Are COMPETants more competent for problem solving? The case of a multiple objective transportation problem. , 2001 .

[21]  Thomas Stützle,et al.  A short convergence proof for a class of ant colony optimization algorithms , 2002, IEEE Trans. Evol. Comput..

[22]  Hartmut Schmeck,et al.  Multi Colony Ant Algorithms , 2002, J. Heuristics.

[23]  Roberto Montemanni,et al.  Time dependent vehicle routing problem with a multi ant colony system , 2008, Eur. J. Oper. Res..

[24]  Christian Blum,et al.  On A Particularity In Model-based Search , 2002, GECCO.

[25]  Thomas Stützle,et al.  Local search algorithms for combinatorial problems - analysis, improvements, and new applications , 1999, DISKI.

[26]  J. Christopher Beck,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems , 2011, Lecture Notes in Computer Science.

[27]  Luca Maria Gambardella,et al.  A survey on metaheuristics for stochastic combinatorial optimization , 2009, Natural Computing.

[28]  Thomas Stützle,et al.  An experimental analysis of design choices of multi-objective ant colony optimization algorithms , 2012, Swarm Intelligence.

[29]  Alex Alves Freitas,et al.  Data mining with an ant colony optimization algorithm , 2002, IEEE Trans. Evol. Comput..

[30]  Holger H. Hoos,et al.  An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem , 2005, BMC Bioinformatics.

[31]  Nicolas Monmarché,et al.  On how Pachycondyla apicalis ants suggest a new search algorithm , 2000, Future Gener. Comput. Syst..

[32]  Marco Dorigo,et al.  The hyper-cube framework for ant colony optimization , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Ian C. Parmee,et al.  The Ant Colony Metaphor for Searching Continuous Design Spaces , 1995, Evolutionary Computing, AISB Workshop.

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

[35]  Walter J. Gutjahr,et al.  First steps to the runtime complexity analysis of ant colony optimization , 2008, Comput. Oper. Res..

[36]  Christian Blum,et al.  Theoretical and practical aspects of ant colony optimization , 2004 .

[37]  Thomas Stützle,et al.  PLANTS: Application of Ant Colony Optimization to Structure-Based Drug Design , 2006, ANTS Workshop.

[38]  Thomas Stützle,et al.  A Comparison Between ACO Algorithms for the Set Covering Problem , 2004, ANTS Workshop.

[39]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[40]  P. Ow,et al.  Filtered beam search in scheduling , 1988 .

[41]  Jose Miguel Puerta,et al.  Ant colony optimization for learning Bayesian networks , 2002, Int. J. Approx. Reason..

[42]  Thomas Stützle,et al.  Special issue on ant colony optimization , 2009, Swarm Intelligence.

[43]  Luca Maria Gambardella,et al.  An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem , 2000, INFORMS J. Comput..

[44]  Marco Dorigo,et al.  AntNet: Distributed Stigmergetic Control for Communications Networks , 1998, J. Artif. Intell. Res..

[45]  Krzysztof Socha,et al.  ACO for Continuous and Mixed-Variable Optimization , 2004, ANTS Workshop.

[46]  Christian Blum,et al.  Beam-ACO for Simple Assembly Line Balancing , 2008, INFORMS J. Comput..

[47]  Dirk Sudholt,et al.  Analysis of different MMAS ACO algorithms on unimodal functions and plateaus , 2009, Swarm Intelligence.

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

[49]  Thomas Stützle,et al.  Parallel Ant Colony Optimization for the Traveling Salesman Problem , 2006, ANTS Workshop.

[50]  Martin Middendorf,et al.  Pheromone Modification Strategies for Ant Algorithms Applied to Dynamic TSP , 2001, EvoWorkshops.

[51]  Patrick Albert,et al.  Integration of ACO in a Constraint Programming Language , 2008, ANTS Conference.

[52]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

[53]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[54]  Daniela Favaretto,et al.  Ant colony system for a VRP with multiple time windows and multiple visits , 2007 .

[55]  B. Bullnheimer,et al.  A NEW RANK BASED VERSION OF THE ANT SYSTEM: A COMPUTATIONAL STUDY , 1997 .

[56]  Thomas Stützle,et al.  An ant colony optimization approach to flexible protein–ligand docking , 2007, Swarm Intelligence.

[57]  Andrew B. Kahng,et al.  A new adaptive multi-start technique for combinatorial global optimizations , 1994, Oper. Res. Lett..

[58]  Yuefeng Li,et al.  Granule Based Intertransaction Association Rule Mining , 2007 .

[59]  Thomas Stützle,et al.  Special issue on Ant Algorithms , 2000 .

[60]  Luca Maria Gambardella,et al.  A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows , 1999 .

[61]  Dirk Sudholt,et al.  Running time analysis of Ant Colony Optimization for shortest path problems , 2012, J. Discrete Algorithms.

[62]  Luca Maria Gambardella,et al.  AntHocNet: an adaptive nature-inspired algorithm for routing in mobile ad hoc networks , 2005, Eur. Trans. Telecommun..

[63]  R. Burkard,et al.  The Travelling Salesman Problem on Permuted , 1999 .

[64]  Shigeyoshi Tsutsui,et al.  Ant Colony Optimisation for Continuous Domains with Aggregation Pheromones Metaphor , 2004 .

[65]  Thomas Stützle,et al.  On the Design of ACO for the Biobjective Quadratic Assignment Problem , 2004, ANTS Workshop.

[66]  W. Gutjahr,et al.  Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement , 2008 .

[67]  Thomas Stützle,et al.  Ant Colony Optimization: models and applications , 2002 .

[68]  Christine Solnon,et al.  A study of ACO capabilities for solving the maximum clique problem , 2006, J. Heuristics.

[69]  Martin Middendorf,et al.  A Population Based Approach for ACO , 2002, EvoWorkshops.

[70]  Luca Maria Gambardella,et al.  Using Ant Agents to Combine Reactive and Proactive Strategies for Routing in Mobile Ad-hoc Networks , 2005, Int. J. Comput. Intell. Appl..

[71]  Shigeyoshi Tsutsui.  cAS: Ant Colony Optimization with Cunning Ants , 2006, PPSN.

[72]  Holger H. Hoos,et al.  Improving the Ant System: A Detailed Report on the MAX-MIN Ant System , 1996 .

[73]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

[74]  Shigeyoshi Tsutsui.  Ant Colony Optimization with Cunning Ants , 2007 .

[75]  M. Dorigo,et al.  1 Positive Feedback as a Search Strategy , 1991 .

[76]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

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

[78]  Martin Middendorf,et al.  Modeling the Dynamics of Ant Colony Optimization , 2002, Evolutionary Computation.

[79]  Richard Bellman,et al.  Mathematical Aspects Of Scheduling And Applications , 1982 .

[80]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[81]  Frank Neumann,et al.  Theoretical analysis of two ACO approaches for the traveling salesman problem , 2011, Swarm Intelligence.

[82]  W. Gutjahr.  On the Finite-Time Dynamics of Ant Colony Optimization , 2006 .

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

[84]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[85]  Mihalis Yannakakis,et al.  2. Computational complexity , 2003 .

[86]  Thomas Stützle,et al.  A SHORT CONVERGENCE PROOF FOR A CLASS OF ACO ALGORITHMS , 2002 .

[87]  Marco Dorigo,et al.  Mobile agents for adaptive routing , 1998, Proceedings of the Thirty-First Hawaii International Conference on System Sciences.

[88]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[89]  Dimitri P. Bertsekas,et al.  Network optimization : continuous and discrete models , 1998 .

[90]  Adnan Acan.  An External Memory Implementation in Ant Colony Optimization , 2004, ANTS Workshop.

[91]  J. Deneubourg,et al.  The self-organizing exploratory pattern of the argentine ant , 1990, Journal of Insect Behavior.

[92]  Richard F. Hartl,et al.  D-Ants: Savings Based Ants divide and conquer the vehicle routing problem , 2004, Comput. Oper. Res..

[93]  Luca Maria Gambardella,et al.  An Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem , 2002, PPSN.

[94]  Francisco Herrera,et al.  A New ACO Model Integrating Evolutionary Computation Concepts: The Best-Worst Ant System , 2000 .

[95]  Thomas Stützle,et al.  A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem , 2007, Eur. J. Oper. Res..

[96]  Corso Elvezia,et al.  Ant colonies for the traveling salesman problem , 1997 .

[97]  Michael Sampels,et al.  Ant Algorithms for the University Course Timetabling Problem with Regard to the State-of-the-Art , 2003, EvoWorkshops.

[98]  Thomas Stützle,et al.  An incremental ant colony algorithm with local search for continuous optimization , 2011, GECCO '11.

[99]  Luca Maria Gambardella,et al.  Principles and applications of swarm intelligence for adaptive routing in telecommunications networks , 2010, Swarm Intelligence.

[100]  Marco Dorigo,et al.  Ant colony optimization and its application to adaptive routing in telecommunication networks , 2004 .

[101]  Mauro Birattari,et al.  Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands , 2005, J. Math. Model. Algorithms.

[102]  Thomas Stützle,et al.  Iterated Ants: An Experimental Study for the Quadratic Assignment Problem , 2006, ANTS Workshop.

[103]  Ying Zhang,et al.  Improvements on Ant Routing for Sensor Networks , 2004, ANTS Workshop.

[104]  Christian Blum,et al.  An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training , 2007, Neural Computing and Applications.

[105]  Roberto Montemanni,et al.  Ant colony optimization for real-world vehicle routing problems , 2007, Swarm Intelligence.

[106]  Hartmut Schmeck,et al.  Ant colony optimization for resource-constrained project scheduling , 2000, IEEE Trans. Evol. Comput..

[107]  Thomas Sttitzle.  Parallelization Strategies for Ant Colony Optimization , 2006 .

[108]  Marco Dorigo,et al.  Ant colony optimization theory: A survey , 2005, Theor. Comput. Sci..

[109]  R. Montemanni,et al.  Ant colony optimization for real-world vehicle routing problems From theory to applications , .

[110]  Gabriele Kotsis,et al.  Parallelization strategies for the ant system , 1998 .

[111]  Manuel López-Ibáñez,et al.  Beam-ACO for the travelling salesman problem with time windows , 2010, Comput. Oper. Res..

[112]  Daniel Merkle,et al.  Ant Colony Optimization with Global Pheromone Evaluation for Scheduling a Single Machine , 2004, Applied Intelligence.

[113]  Thomas Stützle,et al.  Parallelization Strategies for Ant Colony Optimization , 1998, PPSN.

[114]  Thomas Stützle,et al.  Ant Colony Optimization and Swarm Intelligence: 5th International Workshop, ANTS 2006, Brussels, Belgium, September 4-7, 2006, Proceedings (Lecture Notes in Computer Science) , 2006 .

[115]  Toshihide Ibaraki,et al.  A 3-flip neighborhood local search for the set covering problem , 2006, Eur. J. Oper. Res..

[116]  R. Steele.  Optimization , 2005 .

[117]  Frank Neumann,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Runtime Analysis of a Simple Ant Colony Optimization Algorithm Runtime Analysis of a Simple Ant Colony Optimization Algorithm , 2022 .

[118]  Marco Dorigo,et al.  Ant Colony Optimization and Stochastic Gradient Descent , 2002, Artificial Life.

[119]  J. Dréo,et al.  Continuous interacting ant colony algorithm based on dense heterarchy , 2004, Future Gener. Comput. Syst..

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

[121]  Adnan Acan.  An External Partial Permutations Memory for Ant Colony Optimization , 2005, EvoCOP.

[122]  Z. Michalewicz,et al.  A new version of ant system for subset problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[123]  Christian Blum,et al.  Ant colony optimization for multicasting in static wireless ad-hoc networks , 2009, Swarm Intelligence.

[124]  Luca Maria Gambardella,et al.  MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows , 1999 .

[125]  Shigeyoshi Tsutsui.  An Enhanced Aggregation Pheromone System for Real-Parameter Optimization in the ACO Metaphor , 2006, ANTS Workshop.

[126]  Thomas Stützle,et al.  Ant Colony Optimization and Swarm Intelligence: 4th International Workshop , ANTS 2004. Proceedings , 2004 .

[127]  Frank Neumann,et al.  Ant Colony Optimization and the minimum spanning tree problem , 2010, Theor. Comput. Sci..

[128]  Luca Maria Gambardella,et al.  Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem , 1995, ICML.

[129]  L Manuel,et al.  The Automatic Design of Multi-Objective Ant Colony Optimization Algorithms , 2012 .

[130]  Marco Dorigo,et al.  An Investigation of some Properties of an "Ant Algorithm" , 1992, PPSN.

[131]  W. Gutjahr.  S-ACO: An Ant-Based Approach to Combinatorial Optimization Under Uncertainty , 2004, ANTS Workshop.

[132]  Kwang Mong Sim,et al.  Ant colony optimization for routing and load-balancing: survey and new directions , 2003, IEEE Trans. Syst. Man Cybern. Part A.

[133]  Michael Sampels,et al.  Ant colony optimization for FOP shop scheduling: a case study on different pheromone representations , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[134]  Thomas Stützle,et al.  Estimation-based ant colony optimization and local search for the probabilistic traveling salesman problem , 2009, Swarm Intelligence.

[135]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .

[136]  Daniel Merkle,et al.  Bi-Criterion Optimization with Multi Colony Ant Algorithms , 2001, EMO.

[137]  Christine Solnon,et al.  Combining two pheromone structures for solving the car sequencing problem with Ant Colony Optimization , 2008, Eur. J. Oper. Res..

[138]  Antonella Carbonaro,et al.  An ANTS heuristic for the frequency assignment problem , 2000, Future Gener. Comput. Syst..

[139]  Vittorio Maniezzo,et al.  Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem , 1999, INFORMS J. Comput..

[140]  Andrew McCallum,et al.  Dynamic conditional random fields: factorized probabilistic models for labeling and segmenting sequence data , 2004, J. Mach. Learn. Res..

[141]  Gianni A. Di Caro,et al.  AntNet: A Mobile Agents Approach to Adaptive Routing , 1999 .

[142]  Thomas Stützle,et al.  Guest editorial: special section on ant colony optimization , 2002, IEEE Trans. Evol. Comput..

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

[144]  Wolfgang Domschke,et al.  Operations Research Proceedings 1999 , 2000 .

[145]  Walter J. Gutjahr,et al.  Mathematical runtime analysis of ACO algorithms: survey on an emerging issue , 2007, Swarm Intelligence.

[146]  J. Deneubourg,et al.  Self-organized shortcuts in the Argentine ant , 1989, Naturwissenschaften.

[147]  Thomas Stützle,et al.  Special Section on Ant Colony Optimization , 2002 .

[148]  Thomas Stützle,et al.  Iterated Greedy Algorithms for a Real-World Cyclic Train Scheduling Problem , 2008, Hybrid Metaheuristics.

[149]  Mauro Birattari,et al.  Applications Metaheuristics for the Vehicle Routing Problem with Stochastic Demands , 2004, PPSN.

[150]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[151]  Zhang Chun-fang,et al.  Adaptive Parallel Ant Colony Algorithm , 2006 .

[152]  Andreas T. Ernst,et al.  Beam-ACO Based on Stochastic Sampling for Makespan Optimization Concerning the TSP with Time Windows , 2009, EvoCOP.

[153]  Guenther Fuellerer,et al.  Ant colony optimization for the two-dimensional loading vehicle routing problem , 2009, Comput. Oper. Res..

[154]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[155]  Panos M. Pardalos,et al.  High Performance Algorithms and Software in Nonlinear Optimization , 2011 .

[156]  William M. Springer.  Review of the traveling salesman problem: a computational study by Applegate, Bixby, Chvátal, and Cook (Princeton University Press) , 2009, SIGA.

[157]  Michael Jünger,et al.  Provably good solutions for the traveling salesman problem , 1994, Math. Methods Oper. Res..

[158]  Alex Alves Freitas,et al.  cAnt-Miner: An Ant Colony Classification Algorithm to Cope with Continuous Attributes , 2008, ANTS Conference.

[159]  Christian Blum,et al.  Beam-ACO - hybridizing ant colony optimization with beam search: an application to open shop scheduling , 2005, Comput. Oper. Res..

[160]  Walter J. Gutjahr,et al.  ACO algorithms with guaranteed convergence to the optimal solution , 2002, Inf. Process. Lett..

[161]  Monique Snoeck,et al.  Classification With Ant Colony Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[162]  Dirk Sudholt,et al.  Runtime analysis of the 1-ANT ant colony optimizer , 2011, Theor. Comput. Sci..

[163]  Marco Dorigo,et al.  Ant colony optimization for continuous domains , 2008, Eur. J. Oper. Res..

[164]  Christine Solnon,et al.  Ant Colony Optimization for Multi-Objective Optimization Problems , 2007, 19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007).

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

[166]  Christian Blum,et al.  An ant colony optimization algorithm for DNA sequencing by hybridization , 2008, Comput. Oper. Res..

[167]  Francisco Herrera,et al.  Analysis of the Best-Worst Ant System and Its Variants on the QAP , 2002, Ant Algorithms.

[168]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[169]  Chandrasekharan Rajendran,et al.  Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs , 2004, Eur. J. Oper. Res..

[170]  Richard K. Moore,et al.  From theory to applications , 1986 .

[171]  Matthijs den Besten,et al.  Ant Colony Optimization for the Total Weighted Tardiness Problem , 2000, PPSN.

[172]  Léon J. M. Rothkrantz,et al.  Ant-Based Load Balancing in Telecommunications Networks , 1996, Adapt. Behav..

[173]  Erick Cantú-Paz,et al.  Efficient and Accurate Parallel Genetic Algorithms , 2000, Genetic Algorithms and Evolutionary Computation.

[174]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[175]  Roberto Montemanni,et al.  Coupling ant colony systems with strong local searches , 2012, Eur. J. Oper. Res..

[176]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[177]  Sally C. Brailsford,et al.  Combined Discrete-event Simulation and Ant Colony Optimisation Approach for Selecting Optimal Screening Policies for Diabetic Retinopathy , 2006, Comput. Manag. Sci..

[178]  Mauro Birattari,et al.  Toward the Formal Foundation of Ant Programming , 2002, Ant Algorithms.

[179]  Thomas Stützle,et al.  Ant Algorithms , 2000, Lecture Notes in Computer Science.

[180]  Roberto Montemanni,et al.  Ant Colony System for a Dynamic Vehicle Routing Problem , 2005, J. Comb. Optim..

[181]  Mauro Birattari,et al.  Model-Based Search for Combinatorial Optimization: A Critical Survey , 2004, Ann. Oper. Res..

[182]  C. J. Eyckelhof,et al.  Ant Systems for a Dynamic TSP , 2002, Ant Algorithms.

[183]  Andrea Roli,et al.  Two-Level ACO for Haplotype Inference Under Pure Parsimony , 2008, ANTS Conference.

[184]  J. Deneubourg,et al.  Modulation of trail laying in the antLasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source , 1993, Journal of Insect Behavior.

[185]  Yuri Kochetov,et al.  Behavior of the Ant Colony Algorithm for the Set Covering Problem , 2000 .

[186]  Marco Dorigo,et al.  The ant colony optimization meta-heuristic , 1999 .

[187]  Marco Dorigo,et al.  Ant Colonies for Adaptive Routing in Packet-Switched Communications Networks , 1998, PPSN.

[188]  Luca Maria Gambardella,et al.  Solving symmetric and asymmetric TSPs by ant colonies , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[189]  Zhi-Gang Ren,et al.  New ideas for applying ant colony optimization to the set covering problem , 2010, Comput. Ind. Eng..

[190]  T. Stützle,et al.  MAX-MIN Ant System and local search for the traveling salesman problem , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[191]  Thomas Stützle,et al.  An analysis of communication policies for homogeneous multi-colony ACO algorithms , 2010, Inf. Sci..

[192]  Walter J. Gutjahr,et al.  A Graph-based Ant System and its convergence , 2000, Future Gener. Comput. Syst..

[193]  Junie McCree.  The travelling salesman , 1913 .