ABSTRACT
One of the most commonly-used metaphors to describe the process of heuristic search methods in solving combinatorial optimization problems is that of a fitness landscape. The landscape metaphor appears most commonly in work related to evolutionary algorithms, however, it can be used for search in general; the search space can be regarded as a spatial structure where each point (solution) has a height (objective function value) forming a landscape surface. In this scenario, the search process would be an adaptive-walk over a landscape that can range from having many peaks of high fitness flanked by cliffs falling to profound valleys of low fitness, to being smooth, with low hills and gentle valleys. Combinatorial landscapes can be seen as graphs whose vertices are the possible configurations. If two configurations can be transformed into each other by a suitable operator move, then we can trace an edge between them. The resulting graph, with an indication of the fitness at each vertex, is a representation of the given problem fitness landscape. The study of fitness landscapes consists in analyzing this graph or a relevant partition of it, with respect to the search dynamics or problem difficulty. This advanced tutorial will give an overview of the origins of the fitness landscape metaphor, and will cover alternative ways to define fitness landscapes in evolutionary computation. The two main geometries: multimodal and neutral landscapes, which correspond to two different graph partitions found in combinatorial optimization, will be considered, as well as the dynamics of metaheuristics searching on them. A short demonstration of using paradiseo software will be made to analyze the fitness landscape in practice. Furthermore, the relationship between problem hardness and fitness landscape metrics (i.e. autocorrelation, fitness distance correlation, neutral degree, etc), and the local optima network properties, studied in recent work, will be deeply analyzed. Finally, the tutorial will conclude with a brief survey of open questions and recent research directions on fitness landscapes such as multiobjective search space.
- L. Barnett. Ruggedness and neutrality - the NKp family of fitness landscapes. In C. Adami, R. K. Belew, H. Kitano, and C. Taylor, editors, ALIFE VI, Proceedings of the Sixth International Conference on Artificial Life, pages 18--27. ALIFE, The MIT Press, 1998. Google ScholarDigital Library
- Lionel Barnett. Netcrawling - optimal evolutionary search with neutral networks. In Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, pages 30--37, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 27--30 2001. IEEE Press.Google ScholarCross Ref
- U. Bastolla, M. Porto, H. E. Roman, and M. Vendruscolo. Statiscal properties of neutral evolution. Journal Molecular Evolution, 57(S):103--119, August 2003.Google Scholar
- Meriema Belaidouni and Jin-Kao Hao. An analysis of the configuration space of the maximal constraint satisfaction problem. In PPSN VI: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, pages 49--58, London, UK, 2000. Springer-Verlag. Google ScholarDigital Library
- P. Collard, M. Clergue, and M. Defoin Platel. Synthetic neutrality for artificial evolution. In Artificial Evolution: Fourth European Conference AE'99, pages 254--265. Springer-Verlag, 2000. Selected papers in Lecture Notes in Computer Sciences 1829. Google ScholarDigital Library
- J. C. Culberson. Mutation-crossover isomorphisms and the construction of discrimination function. Evolutionary Computation, 2:279--311, 1994. Google ScholarDigital Library
- J. P. K. Doye. The network topology of a potential energy landscape: a static scale-free network. Phys. Rev. Lett., 88:238701, 2002.Google ScholarCross Ref
- J. P. K. Doye and C. P. Massen. Characterizing the network topology of the energy landscapes of atomic clusters. J. Chem. Phys., 122:084105, 2005.Google ScholarCross Ref
- Ricardo Garcia-Pelayo and Peter F. Stadler. Correlation length, isotropy, and meta-stable states. Physica D, 107:240--254, 1997. Santa Fe Institute Preprint 96-05-034. Google ScholarDigital Library
- Josselin Garnier and Leila Kallel. Efficiency of local search with multiple local optima. SIAM Journal on Discrete Mathematics, 15(1):122--141, 2002. Google ScholarDigital Library
- P. Gitchoff and G. Wagner. Recombination induced hypergraphs: A new approach to mutation-recombination isomorphism, 1996.Google Scholar
- David E. Goldberg and Philip Segrest. Finite markov chain analysis of genetic algorithms. In ICGA, pages 1--8, 1987. Google ScholarDigital Library
- M. Huynen. Exploring phenotype space through neutral evolution. Journal Molecular Evolution, 43:165--169, 1996.Google ScholarCross Ref
- E. Izquierdo-Torres. The role of nearly neutral mutations in the evolution of dynamical neural networks. In J. Pollack and al, editors, Ninth International Conference of the Simulation and Synthesis of Living Systems (Alife 9), pages 322--327. MIT Press, 2004.Google Scholar
- T. Jones. Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico, Albuquerque, 1995.Google Scholar
- S. A. Kauffman. The Origins of Order. Oxford University Press, New York, 1993.Google Scholar
- M. Kimura. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge, UK, 1983.Google ScholarCross Ref
- J. Lobo, J. H. Miller, and W. Fontana. Neutrality in technology landscape, 2004.Google Scholar
- M. Newman and R. Engelhardt. Effect of neutral selection on the evolution of molecular species. In Proc. R. Soc. London B., volume 256, pages 1333--1338, 1998.Google Scholar
- Erik Van Nimwegen, James P. Crutchfield, and Martijn Huynen. Metastable evolutionary dynamics: Crossing fitness barriers or escaping via neutral paths. Technical Report 99-07-041, SanteFe institute, 1999.Google Scholar
- Marmion, M.-É., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S., 2011. NILS: a neutrality-based iterated local search and its application to flowshop scheduling. In: Proceedings of the 12th European Conference of Evolutionary Computation in Combinatorial Optimization. Vol. 6622 of EvoCOP 2011. LNCS, Springer, pp. 191-- 202. Google ScholarDigital Library
- Marmion, M.-É., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S., 2011. On the neutrality of flowshop scheduling fitness landscapes. In: Proceedings of the 5th Learning and Intelligent OptimizatioN Conference. Vol. 6683 of LION 2011. LNCS, Springer, pp. 238--252. Google ScholarDigital Library
- Gabriela Ochoa, Marco Tomassini, Sébastien Verel, and Christian Darabos. A Study of NK Landscapes' Basins and Local Optima Networks. In Proceedings of the 10th annual conference on Genetic and evolutionary computation Genetic And Evolutionary Computation Conference, pages 555--562, Atlanta États-Unis d'Amérique, 07 2008. ACM New York, NY, USA. best paper nomination. Google ScholarDigital Library
- M. Defoin Platel. Homologie en Programmation Génétique - Application à la résolution d'un problème inverse. PhD thesis, Université Nice Sophia Antipolis, France, 2004.Google Scholar
- Eduardo Rodriguez-Tello, Jin-Kao Hao, and Jose Torres-Jimenez. A new evaluation function for the minla problem. In Proceedings of the MIC 2005, pages 796--801, Vienna Austria, 2005.Google Scholar
- Helge Rosé, Werner Ebeling, and Torsten Asselmeyer. The density of states - a measure of the difficulty of optimisation problems. In Parallel Problem Solving from Nature, pages 208--217, 1996. Google ScholarDigital Library
- P. Schuster, W. Fontana, P. F. Stadler, and I. L. Hofacker. From sequences to shapes and back: a case study in RNA secondary structures. In Proc. R. Soc. London B., volume 255, pages 279--284, 1994.Google Scholar
- Peter F. Stadler. Landscapes and their correlation functions. J.\ Math.\ Chem., 20:1--45, 1996.Google Scholar
- Peter F. Stadler and W. Schnabl. The landscape of the traveling salesmen problem. Phys. Letters, A(161):337--344, 1992.Google ScholarCross Ref
- Peter F. Stadler and Gunter P. Wagner. Algebraic theory of recombination spaces. Evolutionary Computation, 5(3):241--275, 1997. Google ScholarDigital Library
- Terry Stewart. Extrema selection: Accelerated evolution on neutral networks. In Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, pages 25--29, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 27--30 May 2001. IEEE Press.Google Scholar
- Marco Tomassini, Sébastien Verel, and Gabriela Ochoa. Complex-network analysis of combinatorial spaces: The NK landscape case. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 78(6):066114, 12 2008. 89.75.Hc; 89.75.Fb; 75.10.Nr.Google Scholar
- Vesselin K. Vassilev and Julian F. Miller. The advantages of landscape neutrality in digital circuit evolution. In ICES, pages 252--263, 2000. Google ScholarDigital Library
- Sebastien Verel, Philippe Collard, and Manuel Clergue. Measuring the evolvability landscape to study neutrality. In M. Keijzer and et al., editors, Poster at Genetic and Evolutionary Computation -- GECCO-2006, pages 613--614, Seatle, 8--12 July 2006. ACM Press. Google ScholarDigital Library
- Sébastien Verel, Gabriela Ochoa, and Marco Tomassini. The Connectivity of NK Landscapes' Basins: A Network Analysis. In Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems Artificial Life XI, pages 648--655, Winchester France, 08 2008. MIT Press, Cambridge, MA. tea team.Google Scholar
- F. Chicano, F. Daolio, G. Ochoa, S. Verel, M. Tomassini, and E. Alba. Local optima networks, landscape autocorrelation and heuristic search performance. In Proceedings of Parallel Problem Solving from Nature - PPSN XII, volume 7492 of Lecture Notes in Computer Science, pages 337--347. Springer, 2012. Google ScholarDigital Library
- E. D. Weinberger. Correlated and uncorrelatated fitness landscapes and how to tell the difference. In Biological Cybernetics, pages 63:325--336, 1990.Google Scholar
- F. Daolio, M. Tomassini, S. Verel, and G. Ochoa. Communities of minima in local optima networks of combinatorial spaces. Physica A: Statistical Mechanics and its Applications, 390(9):1684--1694, 2011.Google ScholarCross Ref
- G. Ochoa, S. Verel, and M. Tomassini. First-improvement vs. best-improvement local optima networks of nk landscapes. In Proceedings of Parallel Problem Solving from Nature - PPSN XI, volume 6238 of Lecture Notes in Computer Science, pages 104--113. Springer, 2010. Google ScholarDigital Library
- L. Vanneschi, M. Tomassini, P. Collard, and S. Verel. Negative slope coefficient. a measure to characterize genetic programming fitness landscapes. In P. Collet et al., editor, Proceedings of the 9th European Conference on Genetic Programming, volume 3905 of Lecture Notes in Computer Science, pages 178--189. Springer, Berlin, Heidelberg, New York, 2006. Google ScholarDigital Library
- S. Verel, F. Daolio, G. Ochoa, and M. Tomassini. Local optima networks with escape edges. In Proceedings of the International Conference on Artificial Evolution, EA-2011, volume 7401 of Lecture Notes in Computer Science, pages 49--60. Springer, 2012. Google ScholarDigital Library
- S. Verel, G. Ochoa, and M. Tomassini. Local optima networks of NK landscapes with neutrality. IEEE Transactions on Evolutionary Computation, 15(6):783--797, 2011.Google ScholarCross Ref
- Katherine M. Malan and Andries P. Engelbrecht. A survey of techniques for characterising fitness landscapes and some possible ways forward. Information Sciences, (0):--, 2013. Google ScholarDigital Library
- Guanzhou Lu, Jinlong Li, and Xin Yao. Fitness-probability cloud and a measure of problem hardness for evolutionary algorithms. In Proceedings of the 11th European conference on Evolutionary computation in combinatorial optimization, EvoCOP'11, pages 108--117, Berlin, Heidelberg, 2011. Springer-Verlag. Google ScholarDigital Library
- S. Wright. The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In Proceedings of the Sixth International Congress of Genetics 1, pages 356--366, 1932.Google Scholar
Index Terms
- Fitness landscapes and graphs: multimodularity, ruggedness and neutrality
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