Abstract
Spatially structured populations have been used in evolutionary computation for many years. Somewhat surprisingly, in the multiobjective optimization domain, very few spatial models have been proposed. In this paper, we introduce a new multiobjective evolutionary algorithm on complex networks. Here, the individuals in the evolving population are mapped onto the nodes of alternative complex networks – regular, small-world, scale-free and random. A selection regime based on a non-dominance rating and a crowding mechanism guides the evolutionary trajectory. Our model can be seen as an extension of the standard cellular evolutionary algorithm. However, the dynamical behaviour of the evolving population is constrained by the particular network architecture. An important contribution of this paper is the detailed analysis of the impact that the structural properties of the network – node degree distribution, characteristic path length and clustering coefficient – have on the behaviour of the evolutionary algorithm using benchmark bi-objective problems.
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Coello, C.C., Veldhuizen, D.V., Lamont, G.: EA for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, Chichester (2001)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland (2001)
Knowles, J.D., Corne, D.: Approximating the nondominated front using the pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000), citeseer.ist.psu.edu/knowles99approximating.html
Alba, E., Dorronsoro, B.: The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Transactions on Evolutionary Computation 9, 126–142 (2005)
Cantu-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic Publishers, Dordrecht (2000)
Van Veldhuizen, D.A., Zydallis, J.B., Lamont, G.B.: Considerations in engineering parallel multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation 7, 144–173 (2003)
Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Dorogovtsev, S., Mendes, J.: Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003)
Strogatz, S.: Exploring complex networks. Nature 410, 268–276 (2001)
Watts, D.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (1999)
Kirley, M.: Evolutionary minority games with small-world interactions. Physica A: Statistical Mechanics 365, 521–528 (2006)
Lieberman, E., Hauert, C., Nowak, M.: Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)
Giacobini, M., Tomassini, M., Tettamanzi, A.: Takeover time curves in random and small-world structured populations. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’05), pp. 1133–1340 (2005)
Giacobini, M., Tomassini, M., Tettamanzi, A., Alba, E.: Selection intensity in cellular evolutionary algorithms for regular lattices. IEEE Transactions on Evolutionary Computation 9, 489–505 (2005)
Sarma, J., De Jong, K.: An analysis of the effects of neighborhood size and shape on local selection algorithms. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN IV. LNCS, vol. 1141, pp. 236–244. Springer, Heidelberg (1996)
Laumanns, M., Rudolph, G., Schwefel, H.P.: A spatial predator-prey approach to multi-objective optimization: A preliminary study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, pp. 241–249. Springer, Heidelberg (1998)
Kirley, M.: A cellular genetic algorithm with disturbances: Optimization using dynamic spatial interactions. Journal of Heuristics 8, 321–342 (2002)
Kirley, M.: M.E.A.: A metapopulation evolutionary algorithm for multi-objective optimisation problems. In: Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, pp. 949–956 (2001)
Mehnen, J., Michelitsch, T., Schmitt, K., Kohlen, T.: pMOHypEA: Parallel evolutionary multiobjective optimization using hypergraphs. Technical Report Reihe CI-189/04, SFB 531, ISSN 1433-3325, University of Dortmund (2004)
Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–60 (1959)
Watts, D., Stogatz, S.: Collective dynamics of “small-world” networks. Nature 393, 440–441 (1998)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, G.V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
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Kirley, M., Stewart, R. (2007). Multiobjective Evolutionary Algorithms on Complex Networks. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_10
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DOI: https://doi.org/10.1007/978-3-540-70928-2_10
Publisher Name: Springer, Berlin, Heidelberg
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