Effect of Topology on Diversity ofSpatially-Structured Evolutionary            AlgorithmsM. De Felice - Energy and Environ...
OutlineWhat are Spatially-Structured EAs (SSEAs)Why studying SSEAs?ExperimentationsAnd now?
SSEAsEA where ‘interaction’ is graph-basedCellular Genetic Algorithms are SSEAsClassic EA                   SSEA          ...
Original Idea         Panzieri et al., A Spatially Structured Genetic Algorithm over         Complex Networks for Mobile R...
-2                             2                           2Robotic Localization-4             (a)                       2...
Epidemic SpreadingCompartmental models [1920s] used to modelepidemic spreading with differential equations                ...
Epidemic Spreading Compartmental models [1920s] used to model epidemic spreading with differential equations              ...
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 analy...
SSEA as Spreading        ProcessAnalogy between SI (Susceptible-Infectious) modeland EA                                   ...
Our Algorithm                     1. start with random solutions                     in nodes                     while (!...
Proposed problemNMAX: Combinatorial problem                              8                                                ...
Experimentations10000 individuals (i.e. 10000 nodes)Measuring First Hitting Time (FHT), generation of fitnessconvergence (F...
Experimentations - 2
EntropiesGenotypic Entropy                       Phenotypic Entropy1. Random and Panmictic go     All the topologies conve...
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...
Rewiring and APLAverage Path Length (APL) is the averagelength of all the shortest pathsAPL measures the spreading of info...
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 h...
ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamicsThis is a first step...  ...to study h...
Thank youDownload Networks Datawww.matteodefelice.name/research/resources/
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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

    1. 1. 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
    2. 2. OutlineWhat are Spatially-Structured EAs (SSEAs)Why studying SSEAs?ExperimentationsAnd now?
    3. 3. 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
    4. 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
    5. 5. -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
    6. 6. Epidemic SpreadingCompartmental models [1920s] used to modelepidemic spreading with differential equations µ S I R
    7. 7. 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)
    8. 8. Main Questions
    9. 9. Main Questions1. Can we model EAs as Spreading Processes?
    10. 10. Main Questions1. Can we model EAs as Spreading Processes?2. How graph topology influences diversity?
    11. 11. 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?
    12. 12. 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
    13. 13. 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!
    14. 14. 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
    15. 15. 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)
    16. 16. Experimentations - 2
    17. 17. 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
    18. 18. Some numbers Larger genotype leads to... ...slower convergence ...less diversity
    19. 19. Some numbers Larger genotype leads to... ...slower convergence ...less diversityWhat happens in-between?
    20. 20. 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
    21. 21. Rewiring and APLAverage Path Length (APL) is the averagelength of all the shortest pathsAPL measures the spreading of information ona network
    22. 22. Rewiring Factor
    23. 23. Rewiring Factor
    24. 24. Rewiring Factor - 2
    25. 25. Conclusions
    26. 26. ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamics
    27. 27. ConclusionsWe investigated the relationship betweennetwork topology and SSEA dynamicsThis is a first step...
    28. 28. 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
    29. 29. 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
    30. 30. Thank youDownload Networks Datawww.matteodefelice.name/research/resources/
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