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- 1. An Analysis of a Selecto-Lamarckian Model of Multimemetic Algorithms with Dynamic Self-Organized Topology Rafael Nogueras1 Juan L.J. Laredo3 Carlos Cotta1 Carlos M. Fernandes2 Juan J. Merelo4 Agostinho C. Rosa2 1 Universidad 3 University de M´laga (Spain), 2 Technical University Lisbon (Portugal), a of Luxembourg (Luxembourg), 4 University of Granada (Spain) TPNC 2013, C´ceres, 3-5 December 2013 a R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 2. What are Memes? Memes are information pieces that constitute units of imitation. “Examples of memes are tunes, ideas, catch-phrases, clothes fashions, ways of making pots or of building arches. Just as genes propagate themselves in the gene pool by leaping from body to body via sperms or eggs, so memes propagate themselves in the meme pool by leaping from brain to brain via a process which, in the broad sense, can be called imitation.” The Selﬁsh Gene, Richard Dawkins, 1976 R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 3. What is a Memetic Algorithm? Memetic Algorithms A Memetic Algorithm is a population of agents that alternate periods of self-improvement with periods of cooperation, and competition. Pablo Moscato, 1989 Memes can be implicitly deﬁned be the choice of local-search (i.e., self-improvement) method, or can be explicitly described in the agent. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 4. Multimemetic Algoritms (and Memetic Computing) The term “multimemetic” was coined by N. Krasnogor and J. Smith (2001). In a MMA, each agent carries a solution and the meme(s) to improve it. Evolution works at these two levels, cf. Moscato (1999). Memetic Computing A paradigm that uses the notion of meme(s) as units of information encoded in computational representations for the purpose of problem solving. Ong, Lim, Chen, 2010 R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 5. Scope Some interesting issues in MMAs: Memes evolve in MMAs alongside with the solutions they attach to. It is up to the algorithm to (self-adaptively) discover good ﬁts between genotypes and memes. Memes are indirectly assessed via the eﬀect they have on genotypes. We consider an analyze an idealized model of MMAs to analyze meme propagation with dynamic self-organized spatial structures. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 6. Background Dynamic of meme propagation is more complex than genetic counterparts. Genes represent solutions objectively measurable via the ﬁtness function. Memes are indirectly evaluated by their eﬀect on solutions. A ﬁrst analysis was done by Nogueras and Cotta (2013) with panmictic and spatially-structured populations. Population structure is very important to determine the behavior of the algorithm. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 7. Dynamic Self-Organized Topology A dynamic model deﬁned by Fernandes et al. (2012) combining ideas from swarm intelligence and cellular automata is considered in this study. Model uses simple rules for movement on a large 2D-lattice, giving rise to self-organized clusters of particles. The clusters evolve and change their shape with some kind of dynamic order. We consider how memes propagate in this environment. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 8. Preliminaries Each agent is a pair g , m ∈ R2 – i.e., gene, meme . The eﬀect of a meme is captured by a function f : R2 → R, i.e., meme application g , m − − − − − → f (g , m), m −−−−− m actually represents the improvement potential of the meme. lim f n (g , m) = m if g < m n→∞ f (g , m) = g if g m The population P = [ g1 , m1 , · · · , gµ , mµ ] of the MMA is a collection of µ such agents. Agent communication is constrained by a spatial structure, characterized by a µ × µ Boolean matrix S. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 9. Model Pseudocode Algorithm 1: Selecto-Lamarckian Model for i ∈ [1 · · · µ] do Initialize gi , mi ; end while ¬ Converged (P) do i ← URand(1, µ) // Pick random location g , m ←Selection(P, S, i); g ← f (g , m) // Local improvement P ← Replace(P, S, i, g , m ); end R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 10. Concepts Let G be a grid of size r × s > µ. Each cell Guv of the grid is a tuple (ηuv , ζuv ), where: ηuv ∈ {1, · · · , µ} ∪ {•} and ζuv ∈ (D × N) ∪ {•}. ηuv indicates the index of the individual that occupies position u, v in the grid. ζuv is a mark placed by individuals which occupied that position in the past, where: f ζuv is the ﬁtness value of the individual. t ζuv is a time stamp. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 11. Individual Movement The system combine ideas from swarm intelligence and cellular automata. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 12. Individual Movement Algorithm 2: Individual Movement (i, t, G ) u, v ← ρ(i); move←true; f if exists u (i) , v (i) ∈ N u, v such that ζuv > gi then f f u , v ← arg min{ζuv | ζuv > gi }; else f if exists u (i) , v (i) ∈ N u, v such that ζuv < gi then f f u , v ← arg max{ζuv | ζuv < gi }; else if N u, v = ∅ then Pick u , v at random from N u, v ; else move ← false; end end end if move then f t ζuv ← gi ; ζuv ← t; // mark old cell ηuv = •; ηu v = i; // move to new cell end R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 13. Setting Goal Explore the dynamics of meme propagation and how it is aﬀected by factors such as the selection probability, the improvement potential of memes and the spatial structure of the population. µ = 256. pLS ∈ {1/256, 0.1, 0.5, 1.0}. Spatial structure: 1 2 3 Panmictic: full connectivity with static structure. Von Neumman neighborhood (r = 1) with static structure. Moore neighborhood (r = 1) with dynamic structure. Meme application: f (g , m) = g (g + m)/2 R. Nogueras et al. if g m if g < m MMAs with Dynamic Self-Organized Topology
- 14. Numerical Simulations Individual Distribution – Evolution Individuals start from a random distribution and quickly group in clusters during the run. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 15. Numerical Simulations Growth Curves The number of copies of the dominant meme grows until taking over the population: the panmictic model is the ﬁrst to converge. the dynamic model is closer to von Neumann model depending on the value of pS . R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 16. Numerical Simulations Qualiﬁed Run-Time Distributions – α = 1 R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 17. Numerical Simulations Qualiﬁed Run-Time Distributions – α = 1/2 R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 18. Numerical Simulations Spectral Analysis The spectrum of the average number of neighbors indicates: the intensity is proportional to f a for some a < 0. the spectrum slope is closer to pink noise. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 19. Conclusions A dynamic model provides promising results in comparison to unstructured populations and to populations arranged in static lattices. By tuning the ratio between self-organization and evolution the convergence of the algorithm can be adjusted. Future work: other topologies and movement policies, decouple movement for neighborhood and evolutionary interaction, full-ﬂedged MMA. R. Nogueras et al. MMAs with Dynamic Self-Organized Topology
- 20. Thank You! Please ﬁnd us in Facebook http://facebook.com/AnySelfProject and in Twitter @anyselfproject AnySelf Project R. Nogueras et al. MMAs with Dynamic Self-Organized Topology

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