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Gecco 2011 - Effects of Topology on the diversity of spatially-structured evolutionary algorithms
 

Gecco 2011 - Effects of Topology on the diversity of spatially-structured evolutionary algorithms

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Gecco 2011 - Effects of Topology on the diversity of spatially-structured evolutionary algorithms Gecco 2011 - Effects of Topology on the diversity of spatially-structured evolutionary algorithms Presentation Transcript

  • Effect of Topology on Diversity ofSpatially-Structured Evolutionary AlgorithmsM. De Felice - Energy and Environment Modelling Unit@ENEA, Rome, ItalyS. Meloni - Institute for Biocomputation and Physics of ComplexSystems@University of Zaragoza, Zaragoza, SpainS. Panzieri - Dept. Informatica e Automazione@ROMA TRE University,Rome, Italy
  • OutlineWhat are Spatially-Structured EAs (SSEAs)Why studying SSEAs?ExperimentationsAnd now?
  • SSEAsEA where ‘interaction’ is graph-basedCellular Genetic Algorithms are SSEAsClassic EA SSEA } Individual 1 Individual 1 Individual 2 Individual 3 Selection Individual 2 Individual 3 ... Individual N Individual 4
  • Original Idea Panzieri et al., A Spatially Structured Genetic Algorithm over Complex Networks for Mobile Robot Localisation, IEEE Int. Conf. on Robotics and Automation (ICRA), 2007Adding a ‘structure’ seemed to improve the diversity of hypothesis
  • -2 2 2Robotic Localization-4 (a) 2 4-6 6 6 6 1 4 4 2 1 2 0 0 2-2 -2 2-4 -4 (b)-6 -6 6 6
  • Epidemic SpreadingCompartmental models [1920s] used to modelepidemic spreading with differential equations µ S I R
  • Epidemic Spreading Compartmental models [1920s] used to model epidemic spreading with differential equations µ S I REpidemic Spreading on Networks (see S.Meloniet al., traffic-driven epidemic spreading in finite-sizescale-free networks, PNAS, 2009)
  • Main Questions
  • Main Questions1. Can we model EAs as Spreading Processes?
  • Main Questions1. Can we model EAs as Spreading Processes?2. How graph topology influences diversity?
  • Main Questions1. Can we model EAs as Spreading Processes?2. How graph topology influences diversity?3. Can we use analytic tools used in Epidemic Spreading to investigate EAs dynamics?
  • SSEA as Spreading ProcessAnalogy between SI (Susceptible-Infectious) modeland EA γ S I S Non-Optimal Optimal Elitism?J.L. Payne & M.J. Eppstein, Pair Approximations ofTakeover Dynamics in Regular Population Structures, Evolutionary Computation, 2009
  • Our Algorithm 1. start with random solutions in nodes while (!terminate) for each individual i 2. select uniformly a random neighbour 3. mutate it 4. if it’s better or equal than i use it to replace i end endNo Diversity Maintenance Mechanisms!
  • Proposed problemNMAX: Combinatorial problem 8 7 6 5 fitness 4Composition of L TWOMAX functions of 3 2 1 0 0 1 2 3 4 5 6 7 8length b Ones 10010100|00011000|... |11100101 } } first TWOMAX of length b k-th TWOMAX of length b 2L optima
  • Experimentations10000 individuals (i.e. 10000 nodes)Measuring First Hitting Time (FHT), generation of fitnessconvergence (FCT) and n. of optima found (N.OPT.)[average on 100 runs]Panmictic (traditional), Random Graph (Erdös-Rényi) andLattice 1-D (2-neighbours)
  • Experimentations - 2
  • EntropiesGenotypic Entropy Phenotypic Entropy1. Random and Panmictic go All the topologies converge atquickly to the same solution the optimal fitness value2. Lattice 1D ‘converges’ toseveral optima
  • Some numbers Larger genotype leads to... ...slower convergence ...less diversity
  • Some numbers Larger genotype leads to... ...slower convergence ...less diversityWhat happens in-between?
  • Watts-Strogatz Small-World modelLandmark paper: D.J. Watts & S.H. Strogatz,Collective dynamics of ‘small-world’ networks,Nature, 1998Rewiring probability parameter r0 -> Regular Graph (lattice)1 -> Random Network
  • Rewiring and APLAverage Path Length (APL) is the averagelength of all the shortest pathsAPL measures the spreading of information ona network
  • Rewiring Factor
  • Rewiring Factor
  • Rewiring Factor - 2
  • Conclusions
  • ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamics
  • ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamicsThis is a first step...
  • ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamicsThis is a first step... ...to study how to design an ad-hoc network for a specific problem
  • ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamicsThis is a first step... ...to study how to design an ad-hoc network for a specific problem ...to apply Epidemic Spreading formalisms to SSEAs
  • Thank youDownload Networks Datawww.matteodefelice.name/research/resources/