Handling Time-varying Tsp Instances

Multimodal optimization algorithms are being adapted to deal with dynamic optimization, mainly due to their ability to provide a faster reaction to unexpected changes in the optimization surface. The faster reaction may be associated with the existence of two important attributes in population-based algorithms devoted to multimodal optimization: simultaneous maintenance of multiple local optima in the population; and self-regulation of the population size along the search. The optimization surface may be subject to variations motivated by one of two main reasons: modification of the objectives to be fulfilled and change in parameters of the problem. An immuneinspired algorithm specially designed to deal with combinatorial optimization is applied here to solve time-varying TSP instances, with the cost of going from one city to the other being a function of time. The proposal presents favorable results when compared to the results produced by a high-performance ant colony optimization algorithm of the literature. © 2006 IEEE.28302837George, A.J.T., Gray, D., Receptor Editing During Affinity Maturation Imm. Today, 20 (4), p. 196Zhou, A., Kang, L., Yan, Z., Solving Dynamic TSP with Evolutionary Approach in Real Time (2003) Proceedings of IEEE Congress on Evolutionary Computation, 2, pp. 951-957Berek, C., Ziegner, M., The Maturation of the Immune Response (1993) Imm. Today, 14 (8), pp. 400-402Blum, C., Dorigo, M., The Hyper-Cube Framework for Ant Colony Optimization (2004) IEEE Transactions on Systems, Man and Cybernetics Part B, 2 (34), pp. 1161-1172Blum, C., Roli, A., Dorigo, M., HC-ACO: The Hyper-Cube Frame-work for Ant Colony Optimization (2001) Proceedings of Meta-Heuristics International Conference, 2, pp. 399-403Eyckelhof, C.J., Snoek, M., Ant Systems for a Dynamic TSP: Ants Caught in a Traffic Jam (2002) Lecture Notes in Computer Science, 2463, pp. 88-99. , Proceedings of ANTS 2002, M. Dorigo, G. Di Caro, M. Samples EdsApplegate, D., Bixby, R., Chvátal, V., Cook, W., History - Solving Travelling Salesman Problem, , http://www.math.princeton.edu/tsp/histmain.html, Available on lineWhitley, D., Rana, S., Heckendorn, R.B., Island Model Genetic Algorithms and Linearly Separable Problems (1997) Lecture Notes in Computer Science, 1305, pp. 109-125. , Proceedings of the AISB Workshop on Evolutionary Computation, D. Corne and J. L. Shapiro Edsde França, F.O., Bio-Inspired Algorithms applied to Dynamic Optimization (2005) Campinas: FEEC/Unicamp, , December, Master Dissertation, School of Electrical and Computer Engineering, State University of Campinas, 139 p, In Portuguesede França, F.O., de Castro, L.N., Von Zuben, F.J., An Artificial Immune Network for Multimodal Function Optimization on Dynamic Environments (2005) Proceedings of the Genetic and Evolutionary Computation Conference, pp. 289-296de França, F.O., de Castro, L.N., Von Zuben, F.J., A Max Min Ant System Applied To The Capacitated Clustering Problem (2004) Proceedings of the IEEE International Workshop on Machine Learning for Signal Processing, 1, pp. 755-764de França, F.O., de Castro, L.N., Von Zuben, F.J., Max Min Ant System and Capacitated p-MediansExtensions and Improved Solutions (2005) Informatica, 29 (2), pp. l63-171Glover, F.W., Kochenberger, G.A., (2002) Handbook of Metaheuristics, , Kluwer Academic PublishersHeller, I., The Travelling Salesmans Problem: Part 1 - Basic Facts (1954) Research Report, , George Washington University Logistics Research Projectde Sousa, J.S., Gomes, L.C.T., Bezerra, G.B., de Castro, L.N., Von Zuben, F.J., An Immune-Evolutionary Algorithm for Multiple Rearrangements of Gene Expression Data (2004) Genetic Programming and Evolvable Machines, 5 (2), pp. 157-179L. N. de Castro and F. J. Von Zuben. aiNet: An Artificial Immune Network for Data Analysis, In Data Mining: A Heuristic Approach, H. A. Abbass, R. A. Sarker, and C. S. Newton (Eds.), Idea Group Publishing, USA, Chapter XII, 2001, pp. 231-259de Castro, L.N., Von Zuben, F.J., Learning and Optimization Using the Clonal Selection Principle (2002) IEEE Transactions on Evolutionary Computation, 3 (6), pp. 239-251de Castro, L.N., Timmis, J., An Artificial Immune Network for Multimodal Function Optimization (2002) Proceedings of the IEEE Congress on Evolutionary Computation, 1, pp. 699-674Dorigo, M., Optimization, Learning and Natural Algorithms (1992), Ph.D.Thesis, Politecnico di Milano, ItalyFarina, M., Deb, K., Amato, P., Dynamic Multiobjective Optimization Problems: Test Cases, Approximation, and Applications (2004) IEEE Transactions on Evolutionary Computation, 8 (5), pp. 425-442. , OctoberGuntsch, M., Middendorf, M., Pheromone Modification Strategies for Ant Algorithms Applied to Dynamic TSP (2001) EvoWorkshops, pp. 213-222Guntsch, M., Middendorf, M., Schmeck, H., An Ant Colony Optimization Approach to Dynamic TSP (2001) Proceedings of the Genetic and Evolutionary Computation Conference, pp. 860-867Flood, M.M., The Traveling-Salesman Problem (1956) Operations Research, 4, pp. 61-75Jerne, N.K., Towards a Network Theory of the Immune System (1974) Ann. 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A Dynamic Artificial Immune Algorithm Applied To Challenging Benchmarking Problems

In many real-world scenarios, in contrast to standard benchmark optimization problems, we may face some uncertainties regarding the objective function. One source of these uncertainties is a constantly changing environment in which the optima change their location over time. New heuristics or adaptations to already available algorithms must be conceived in order to deal with such problems. Among the desirable features that a search strategy should exhibit to deal with dynamic optimization are diversity maintenance, a memory of past solutions, and a multipopulation structure of candidate solutions. In this paper, an immune-inspired algorithm that presents these features, called dopt-aiNet, is properly adapted to deal with six newly proposed benchmark instances, and the obtained results are outlined according to the available specifications for the competition at the Congresson Evolutionary Computation 2009. © 2009 IEEE.423430Bazaraa, M.S., Sherali, H.D., Shetty, C.M., (2006) Nonlinear Programming: Theory and Algorithms, 2nd Ed., , Wiley-InterscienceMichalewicz, Z., Fogel, D.B., (2000) How to solve It: Modern Heuristics, , SpringerJunqueira, C., De Franca, F., Attux, R., Suyama, R., De Castro, L., Zuben, F.V., Romano, J., A proposal for blind FIR equalization of time-varying channels (2005) Machine Learning for Signal Processing 2005 IEEE Workshop on, pp. 9-14. , SeptJunqueira, C., De Franca, F.O., Attux, R., Panazio, C., De Castro, L., Zuben, F.V., Romano, J., Immune-inspired dynamic optimization for blind spatial equalization in undermodeled channels (2006) Evolutionary Computation, 2006, pp. 2896-2903. , CEC 2006. IEEE Congress onDe Franca, F., Gomes, L., De Castro, L., Zuben, F.V., Handling time-varying TSP instances (2006) Evolutionary Computation, 2006, pp. 2830-2837. , CEC 2006. IEEE Congress onBranke, J., (2001) Evolutionary Optimization in Dynamic Environments, , Norwell, MA, USA: Kluwer Academic PublishersDe Castro, L.N., Von Zuben, F.J., Learning and optimization using the clonal selection principle (2002) IEEE Transactions on Evolutionary Computation, 6 (3), pp. 239-251De França, F.O., Von Zuben, F.J., De Castro, L.N., (2005) An Artificial Immune Network for Multimodal Function Optimization on Dynamic Environments, " in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), , Washington D.C., USADe Castro, L.N., Timmis, J., An artificial immune network for multimodal optimisation (2002) 2002 Congress on Evolutionary Computation, pp. 699-704. , http://www.cs.ukc.ac.uk/pubs/2002/1374, Part of the 2002 IEEE World Congress on Computational Intelligence. Honolulu, Hawaii, USA: IEEE, May, [Online]. AvailableLi, C., Yang, S., Nguyen, T.T., Yu, E.L., Yao, X., Jin, Y., Beyer, H.-G., Suganthan, P.N., Benchmark generator for CEC'2009 competition on dynamic optimization (2008) Nanyang Technological University, Tech. Rep., , http://www3.ntu.edu.sg/home/EPNSugan/indexfiles/CEC-09-Dynamic-Opt/ CEC09-Dyn-Opt.htm, Available at, University of Leicester, University of Birmingham, , SeptemberDe Castro, L.N., Timmis, J., (2002) Artificial Immune Systems: A New Computational Intelligence Approach., , SpringerDe Castro, L.N., Von Zuben, F.J., AiNet: An artificial immune network for data analysis (2001) Data Mining: A Heuristic Approach, pp. 231-259. , H. A. Abbass, R. A. Sarker, and C. S. Newton, Eds. Idea Group PublishingBurnet, F.M., Clonal selection and after (1978) Theoretical Immunology, pp. 63-85. , G.I. Bell, A. S. Perelson, and G. H. Pimgley Jr, Eds. Marcel Dekker IncJerne, N.K., Towards a network theory of the immune system (1974) Ann. Immunol., Inst. Pasteur, 125 C, pp. 373-389Kiefer, J., Sequential minimax search for a maximum (1995) Proceedings of the American Mathematical Society, 4, pp. 502-50

A Concentration-based Artificial Immune Network For Combinatorial Optimization

Diversity maintenance is an important aspect in population-based metaheuristics for optimization, as it tends to allow a better exploration of the search space, thus reducing the susceptibility to local optima in multimodal optimization problems. In this context, metaheuristics based on the Artificial Immune System (AIS) framework, especially those inspired by the Immune Network theory, are known to be capable of stimulating the generation of diverse sets of solutions for a given problem, even though generally implementing very simple mechanisms to control the dynamics of the network. To increase such diversity maintenance capability even further, a new immune-inspired algorithm was recently proposed, which adopted a novel concentration-based model of immune network. This new algorithm, named cob-aiNet (Concentration-based Artificial Immune Network), was originally developed to solve real-parameter single-objective optimization problems, and it was later extended (with cob-aiNet[MO]) to deal with real-parameter multi-objective optimization. Given that both cob-aiNet and cob-aiNet[MO] obtained competitive results when compared to state-of-the-art algorithms for continuous optimization and also presented significantly improved diversity maintenance mechanisms, in this work the same concentration-based paradigm was further explored, in an extension of such algorithms to deal with single-objective combinatorial optimization problems. This new algorithm, named cob-aiNet[C], was evaluated here in a series of experiments based on four Traveling Salesman Problems (TSPs), in which it was verified not only the diversity maintenance capabilities of the algorithm, but also its overall optimization performance. © 2011 IEEE.12421249De Castro, L.N., (2006) Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications, Ser. Chapman & Hall/CRC Computer & Information Science Series, , Chapman & Hall/CRCDe Castro, L.N., Timmis, J., (2002) Artificial Immune Systems: A New Computational Intelligence Approach, , Springer VerlagJerne, N.K., Towards a network theory of the immune system (1974) Annales d'immunologie, 125 (1-2), pp. 373-389De França, F.O., Coelho, G.P., Castro, P.A.D., Von Zuben, F.J., Conceptual and practical aspects of the aiNet family of algorithms (2010) International Journal of Natural Computing Research, 1 (1), pp. 1-35De França, F.O., Coelho, G.P., Von Zuben, F.J., On the diversity mechanisms of opt-aiNet: A comparative study with fitness sharing (2010) Proc. of the 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 3523-3530Coelho, G.P., Von Zuben, F.J., A concentration-based artificial immune network for continuous optimization (2010) Proc. of the 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 108-115Coelho, G.P., Von Zuben, F.J., A concentration-based artificial immune network for multi-objective optimization (2011) Proc. of the 6th. International Conference on Evolutionary Multi-Criterion Optimization (EMO), Ser. Lecture Notes in Computer Science, 6576, pp. 343-357. , Springer Berlin/HeidelbergApplegate, D.L., Bixby, R.E., Chvátal, V., (2006) The Traveling Salesman Problem: A Computational Study, Ser. Princeton Series in Applied Mathematics, , W. J. Cook, Princeton University PressLawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B., (1985) The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, , ser. Wiley-Interscience series in discrete mathematics and optimization. WileyTSPLIB - A Traveling Salesman Problem Library, , http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95Burnet, F.M., Clonal selection and after (1978) Theoretical Immunology, pp. 63-85. , G. I. Bell, A. S. Perelson, and G. H. Pimgley Jr, Eds. Marcel Dekker IncBersini, H., Revisiting Idiotypic Immune Networks (2003) Lecture Notes in Computer Science, (2801), pp. 164-174. , Advances in Artificial LifeBersini, H., Self-assertion vs self-recognition: A tribute to Francisco Varela (2002) Proc. of the 1st International Conference on Artificial Immune Systems (ICARIS), pp. 107-112Lin, S., Kernighan, B.W., An effective heuristic algorithm for the traveling-salesman problem (1973) Operations Research, 21 (2), pp. 498-516De Franca, F.O., Gomes, L.C.T., De Castro, L.N., Von Zuben, F.J., Handling time-varying TSP instances (2006) 2006 IEEE Congress on Evolutionary Computation, CEC 2006, pp. 2830-2837. , 1688664, 2006 IEEE Congress on Evolutionary Computation, CEC 2006Prokopec, A., Marin, G., Adaptive mutation operator cycling (2009) Proc. of the 2nd Intl. Conference on the Applications of Digital Information and Web Technologies (ICADIWT), pp. 661-66