# Evolutive Two-Way Network Formation

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## WHAT IS IT?

NFGA (Network Formation Games with Accumulative-Costs) is a model designed to study the effects of accumulative costs in network formation games. The main assumption is that agents simultaneously choose who to connect with first and when agents connect to each others they have to pay no only for the directed but also for undirected connections.

This model is based on network formation games among firms in oligopolic markets. Firms essays on each round a connection with other firms. This is a two-way (non-directed) network.

## QUICK GUIDE

You should try to prove different configurations of link-costs and information costs.

Other modifications include mutation rate (usually greater than 0.01 gives trembling results), change the slide of the number of generations (for observing convergence in the algorithm), selection procedure (elitism selects best genomes, roulette selects random genomes).

## HOW IT WORKS

Social network

Agents can be connected, forming a social network. Thus, each node may link to none, one, or several nodes; this (potentially empty) set of neighbours defines the node's social neighbourhood.

The model tries to replicates theoretical results according to Goyal and Joshi (2002) but using an evolutive algorithm that takes samples of the network and then by mating and recombining, mutating and rebirth new populations evolve to achieved an optimal network architecture.

## HOW TO USE IT

First, press SETUP button and the GO button. You will see how the genetic algorithm works by randomly selecting an adjacency matrix that represent links between agents. Structure will evolve by agents modifying in their decisions of connecting people. The importance is to play atention to the final topology that emerges in the last periods of the simulation. These would be the evolving outcomes of these connection games.

## THINGS TO TRY

Try by modifying, first of all, the values of value-of-info and link-cost. If you know a little bit of genetic algorithm, try by selecting Elitism and Roulette Wheel in selection of mating peers.

## CREDITS

Juan M.C. Larrosa, Master Thesis in Scientific Computing, Universidad Nacional del Sur, 2006

Ignacio Ponzoni, Thesis Director, Universidad Nacional del Sur

Fernando Tohm_, Thesis Co-Director, Universidad Nacional del Sur.

## REFERENCES

Goyal, S and S Joshi (2002). "Networks of Collaboration in Oligopolies". http://merlin.fae.ua.es/fvega/Course/Art%EDculos%20del%20curso/Goyal-Joshi.pdf

Wilensky U (1999) NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## Comments and Questions

;;;;;;;;;;;; ;; This is the case for undirected graphs, genome is created by strictly upper triangular matrixes;; ;;;;;;;;;;;; ;;;;;;;;;;;; ;; Breeds ;; ;;;;;;;;;;;; ;; nodes and edges between nodes, are all turtles ;; edges are not necessarily symmetric breed [ nodes node ] breed [ edges edge ] ;;;;;;;;;;;;;;; ;; Variables ;; ;;;;;;;;;;;;;;; globals [ clock list-of-nodes ;; nodes ordered by reservation price nodes-in-round ;; nodes who have bought a product in the session avg-information-value nodos-accesibles ;; average number of nodes reachable by each buyer ;; in an infinite number of steps avg-accessibility ;; variable for drag-and-drop procedure clicked-node ;; buyer who was clicked on path my-random-seed basic-genome topology strict-upper-triang topology-random sum-fitness ranking empty-topology complete-topology density sum-links ;; genetic algorithm variables generation edge-cost fitlist edgelist best-fitness avg-fitness avg-dir avg-ind max-profits profits net-indirect-benefit net-direct-benefit global-fitness seed-genomes mix-genes chosen-size genome-size best-genome adjacency-matrix ;indirect-info transitive-matrix genome-list topology-list random-wife1 random-wife2 random-husband1 random-husband2 winner-list ] nodes-own [ ;; stores the list of nodes that this particular buyer edges to edgeees ;; these variables are used to do the layout force-x force-y genome fitness own-information direct-information indirect-info indirect-information direct-edgeing-costs indirect-edgeing-costs origin destination ] ;; The direction of the edge does matter in this model. edges-own [ origin destination ] ;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Nodes Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;;; ;; accessibility is the number of social neighbours that the node could reach in a ;; number of steps equal to "num-steps". For instance, if buyer A edges only to buyer B, ;; who edges only to buyer C, who has no social neighbours, then A's accessibility ;; in one step is 1, and in two steps is 2; B's accessibility in any number of steps is 1, ;; and C's accessibility in any number of steps is 0. ;; This is what I need for counting accumulative edgeing costs!! to-report accessibility [num-steps] set nodos-accesibles [] let step 1 let reachable-nodes edgeees let old-length 0 let new-length length reachable-nodes while [ new-length != old-length and step < num-steps] [ set old-length new-length set reachable-nodes remove-duplicates sentence reachable-nodes reduce [sentence ?1 ?2] map [ [edgeees] of ?] reachable-nodes set new-length (length reachable-nodes) set nodos-accesibles fput reachable-nodes nodos-accesibles set step (step + 1) ] set path new-length - ifelse-value (member? self reachable-nodes) [1] [0] report path end to-report accessibility-by-node [tag-node num-steps] let step 1 let node-zero node tag-node let reachable-nodes [edgeees] of node-zero let old-length 0 let new-length length reachable-nodes while [ new-length != old-length and step < num-steps] [ set old-length new-length set reachable-nodes remove-duplicates sentence reachable-nodes reduce [sentence ?1 ?2] map [ [edgeees] of node ?] reachable-nodes set new-length (length reachable-nodes) set step (step + 1) ] set path new-length - ifelse-value (member? self reachable-nodes) [1] [0] report path end ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;; to startup ask patches [set pcolor white - .15] end to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) __clear-all-and-reset-ticks ; random-seed random-normal 4 1 set topology-list [] set density 0 ct ask patches [set pcolor black - .15] set-default-shape edges "line" set avg-fitness 0 set best-fitness 0 repeat generations * .02 [ create-initial-genetic-info sort-global-fitness build-ga-network item 0 topology-list set best-fitness item compute-factorial num-nodes item 0 topology-list plot-density ] end to make-nodes set-default-shape nodes "circle" let colornode 0 ;; create nodes and provide them with initial endowment of information create-ordered-nodes num-nodes [ set size .6 if B&W [ set color colornode ] if information-endowment = "deterministic" [set own-information value-of-info] if information-endowment = "random" [set own-information random-normal value-of-info 1] set edgeees [] ;; empty list ;; nodes are automatically created with evenly spaced headings, ;; so if they just move forward they will form a circle fd max-pxcor - 2 if colornode > 9 [set colornode 0] set colornode colornode + .5 ] if information-endowment = "heterogeneous" [ let lista-valores (list 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35) ask nodes [set own-information item who lista-valores set label (word own-information "c " ) set label-color black set plabel-color red] ] end to create-initial-genetic-info ct set fitlist [] make-nodes create-genome warshall ;; aca se forman adjacency y transitive indirect-information-matrix update-transitive-matrix calculate-profits ; show (word basic-genome " bg") let genome-reduction (list reduce [sentence ?1 ?2] basic-genome) set genome-reduction reduce [sentence ?1 ?2] genome-reduction set genome-reduction fput genome-reduction fitlist let incoming reduce [sentence ?1 ?2] genome-reduction ;;show incoming set topology-list lput incoming topology-list end to create-genetic-info ct set genome-list [] set fitlist [] make-nodes theory-driven update-genome ;; here is where seed-genomes become nodes' genome again warshall indirect-information-matrix update-transitive-matrix calculate-profits ; show (word seed-genomes " sg") let genome-reduction (list reduce [sentence ?1 ?2] seed-genomes) set genome-reduction reduce [sentence ?1 ?2] seed-genomes set genome-reduction fput seed-genomes fitlist let incoming reduce [sentence ?1 ?2] genome-reduction set topology-list lput incoming topology-list end ;;;;;;;;;;;;;;;;;;;;;; ;;; Main Procedure ;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;; to go set generation (generation + 1) if (generation > generations ) [export stop] do-best-of-age-plot plot-density mate-recombine mutate rebirth end ;;;;;;;;;;;;;;;;;;;;;;; ;;; edge Operations ;;; ;;;;;;;;;;;;;;;;;;;;;;; to build-ga-network [adjacency] ;; Nodes randomly are provided with their connection's structure. This is a node procedure. no-display ;show adjacency ask nodes [set genome n-values num-nodes [0]] ;; Ahora, copia esos datos y se lo inserta en los genomas de los nodos respectivos (la diagonal principal nunca es usada) let y 0 let f 0 while [y < (num-nodes - 1)] ;; recorro todos los nodos menos el _ltimo [let g y + 1 while [g < num-nodes] ;; de cada nodo, tengo que llegar al final del genome [ask node y [set genome replace-item g genome item f adjacency] set g g + 1 set f f + 1] set y y + 1 ] ;; se completa la diagonal inferior para todos los nodos, simetrica a la superior let i 0 let j 0 while [i < num-nodes ][set j 0 while [j < num-nodes ][ if (item j [genome] of node i = 1) [ask node j [set genome replace-item i genome 1] ] set j j + 1] set i i + 1] ; let a 0 ;while [a < num-nodes] ; [ask node a [show genome] ; set a a + 1 ] set j 0 set i 0 ;; agregu_ un contador i porque me parece que cuenta a cada nodo su conexi_n pero no recorre todos los nodos. while [i < num-nodes ] [set j 0 while [j < num-nodes ] [if (item j [genome] of node i = 1) [make-edge node i node j ] set j j + 1] set i i + 1 ] plot-accessibility display end to calculate-profits ;; Nodes procedure ask nodes [ set direct-edgeing-costs 0 set direct-information own-information set indirect-information 0 set indirect-edgeing-costs 0 set net-direct-benefit 0 set net-indirect-benefit 0 set profits 0 set edge-cost own-information / ratio-info-edge set genome (replace-item who genome 0)] ;; iterate over the nodes and ask them for their "direct" costs and information benefits let j 0 let k 0 while [j < num-nodes] [set k 0 while [k < num-nodes] [ask node j [if (item k genome = 1) [ifelse decay [set direct-information direct-information + (rate-of-decay * [own-information] of node k)] [set direct-information direct-information + [own-information] of node k] set direct-edgeing-costs direct-edgeing-costs + (edge-cost / 2) ]] set k k + 1] set j j + 1] set j 0 while [j < num-nodes] [set k 0 while [k < num-nodes] [ask node j [ifelse (item k indirect-info > 0) [ifelse decay [set indirect-information indirect-information + ([direct-information] of node k * (rate-of-decay ^ item k indirect-info))] [set indirect-information indirect-information + [direct-information] of node k] set indirect-edgeing-costs indirect-edgeing-costs + (item k indirect-info * ( edge-cost / 2 ))] [set indirect-information indirect-information set indirect-edgeing-costs indirect-edgeing-costs]] set k k + 1] set j j + 1] ask nodes [ if edge-Cost-Structure = "direct cost direct info" [set indirect-information 0 set indirect-edgeing-costs 0] if edge-Cost-Structure = "direct cost indirect info" [set indirect-edgeing-costs 0] if edge-Cost-Structure = "indirect cost direct info" [set indirect-information 0] if edge-Cost-Structure = "indirect cost indirect info" [] ] ;; viene del primer ask nodes ;; obtain now the total costs of individuals set net-direct-benefit sum [direct-information] of nodes - sum [direct-edgeing-costs] of nodes set net-indirect-benefit sum [indirect-information] of nodes - sum [indirect-edgeing-costs] of nodes set profits precision (net-indirect-benefit + net-direct-benefit) 3 set avg-ind smoothness * avg-ind + (1 - smoothness) * net-indirect-benefit set avg-dir smoothness * avg-dir + (1 - smoothness) * net-direct-benefit let max-links num-nodes * (num-nodes - 1) set density sum-links / max-links set fitlist lput profits fitlist plot-direct-profits plot-indirect-profits end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; edge procedures ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; The algorithm for the following procedure has been borrowed from the ;; model "Giant Component", in the "Models library". ;; The copyright for this procedure is included at the bottom of this file ;; makes a edge from edgeer to edgeee to make-edge [edgeer edgeee] if member? edgeee [edgeees] of edgeer [ user-message (word "There is already a edge from " edgeer " to " edgeee) stop ] create-edges 1 [ set origin edgeer set destination edgeee if show-network-evolution [ set color [color] of edgeer reposition-edge] ;set direct-edgeing-costs direct-edgeing-costs + edge-cost ] ;; add edgeee to the edgeer's list of edgeees ; set [edgeees] of edgeer fput edgeee [edgeees] of edgeer ask edgeer [ set edgeees fput edgeee edgeees ] end to delete-edge [edgeer edgeee] ifelse (member? edgeee [edgeees] of edgeer) [ ask edges [die] ] [ user-message (word "There is no edge from " edgeer " to " edgeee) stop ] create-edges 1 [ set origin edgeer set destination edgeee if show-network-evolution [ set color [color] of edgeer reposition-edge] ] ;; add edgeee to the edgeer's list of edgeees ; set [edgeees] of edgeer fput edgeee [edgeees] of edgeer ask edgeer [ set edgeees fput edgeee edgeees ] end ;; The algorithm for the following procedure has been borrowed from the ;; model "Giant Component", in the "Models library". ;; The copyright for this procedure is included at the bottom of this file ;; repositions and resizes the edge according to the position of the ;; nodes to reposition-edge ;; edge procedure setxy ([xcor] of origin) ([ycor] of origin) set size distance-nowrap destination ;; watch out for special case where origin and destination are ;; at the same place if size != 0 [ ;; position edge at midpoint between origin and destination set heading towards-nowrap destination jump size / 2 ] end ;;;;;;;;;;;;;;;; ;;; Plotting ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;; to plot-accessibility let steps accessibility-steps let accessibility-by-node-list [] if accessibility-steps = "Infinity" [set steps num-nodes] ;; you cannot sort agents because that creates a list that is not processable as is. let accessibility-list [accessibility steps] of nodes let max-accessibility max accessibility-list set-current-plot "Accessibility Distribution" set-plot-x-range 0 (max-accessibility + 1) ;; + 1 to make room for the width of the last bar histogram accessibility-list ;set accessibility-by-node-list values-from nodes [accessibility-by-node i steps] end to plot-direct-profits auto-plot-on set-current-plot "Direct Benefits" set-current-plot-pen "net-direct-benefits" plot net-direct-benefit set-current-plot-pen "avg-dir" plot avg-dir end to plot-indirect-profits auto-plot-on set-current-plot "Indirect Benefits" set-current-plot-pen "net-indirect-benefits" plot net-indirect-benefit set-current-plot-pen "avg-ind" plot avg-ind end to do-best-of-age-plot set-current-plot "Best-Average-Profit" set-current-plot-pen "Moving-Average" plot avg-fitness set-current-plot-pen "Best" plot best-fitness end to plot-density auto-plot-on set-current-plot "Network Density" set-current-plot-pen "density" plot density end ;;;;;;;;;;;;;; ;;; Layout ;;; ;;;;;;;;;;;;;; ;; The algorithm for the following procedure has been borrowed from the ;; model "Giant Component", in the "Models library". ;; The copyright for this procedure is included at the bottom of this file to layout no-display ;; these values are arbitrarily chosen to give a good layout ;; for typical model settings let spring-constant 0.2 let natural-length 9.0 let repulsion-constant 1.0 ;; reset force-x and force-y ask nodes [ set force-x 0 set force-y 0 ] ;; add the forces due to the springs without-interruption ;; process edges one at a time, not concurrently [ ask edges [ let spring-force (spring-constant * (size - natural-length)) ;; take care of zero sized spring ifelse size = 0 [ set spring-force spring-constant * natural-length ;; we know force but dont know the direction in which to apply it ;; make an arbitrary choice of direction ( postive and negative x direction) ask origin [set force-x force-x + spring-force] ask destination [set force-x force-x - spring-force] ] [ ask origin [ set force-x force-x + spring-force * sin towards-nowrap [destination] of myself set force-y force-y + spring-force * cos towards-nowrap [destination] of myself ] ask destination [ set force-x force-x + spring-force * sin towards-nowrap [origin] of myself set force-y force-y + spring-force * cos towards-nowrap [origin] of myself ] ] ] ] ;; add a force of repulsion between nodes, ;; inversely proportional to square of distance without-interruption ;; process nodes one at a time, not concurrently [ ;; exempt edgeless nodes from the force let connected-nodes nodes with [not empty? edgeees] ask connected-nodes [ ask connected-nodes with [self != myself] [ let angle 0 let force 0 ifelse xcor = [xcor] of myself and ycor = [ycor] of myself ;; the two nodes are exactly on top of each other. theoretically ;; this shouldn't occur, but in practice, it might because the world ;; is bounded and nodes can get forced into the corners. not clear ;; how to handle this, so just apply a small arbitrary force in a ;; random direction. [ set angle random-float 360 ;; arbitrary set force repulsion-constant ;; arbitrary ] ;; normal case where nodes aren't on top of each other [ set angle towards-nowrap myself set force repulsion-constant / ((distance-nowrap myself) ^ 2) ] set force-x force-x - force * sin angle set force-y force-y - force * cos angle ] ] ] ;; actually move the nodes ask nodes [ ;; the current layout scheme has an issue where ;; sometimes heavily connected nodes are thrown back and forth. ;; to prevent that we cap the movement of nodes ifelse force-x > 1 [ set force-x 1 ] [ if force-x < -1 [set force-x -1] ] ifelse force-y > 1 [ set force-y 1 ] [ if force-y < -1 [set force-y -1] ] move (xcor + force-x) (ycor + force-y) ] ;; reposition all the edges ask edges [ reposition-edge ] ;; update the display, for smooth animation display end ;; move, but take care not to wrap around edge of world to move [x y] ;; buyer procedure ifelse x > max-pxcor [ set x max-pxcor ] [ if x < min-pxcor [ set x min-pxcor ] ] ifelse y > max-pycor [ set y max-pycor ] [ if y < (min-pycor + 1) [ set y (min-pycor + 1) ] ] setxy x y end to drag-and-drop-nodes ifelse mouse-down? [ ifelse is-agent? clicked-node [ ask clicked-node [ setxy mouse-xcor mouse-ycor ] ] [ ;; no buyer had been clicked ;; if there are nodes at the current mouse location, then pick one if any? nodes-at mouse-xcor mouse-ycor [ set clicked-node one-of nodes-at mouse-xcor mouse-ycor ] ] ask edges [ reposition-edge ] ] [ ;; mouse not down set clicked-node nobody ] end ;; The algorithm for the following procedure has been borrowed from the ;; model "Preferential Attachment", in the "Models library". ;; The copyright for this procedure is included at the bottom of this file ;; resize-nodes, change back and forth from size based on degree to a size of 1 to resize-nodes ifelse ( not (any? nodes with [size > 1]) ) [ ask nodes [ set size sqrt length edgeees] ] [ ask nodes [ set size 1 ] ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Genetic Algorithms Procedures ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to-report compute-factorial [x] let n 1 let factorial 0 repeat (x - 1) [set factorial factorial + n set n n + 1 ] report factorial end to create-genome ;; here is where I must create a random binary string for each node and it must have a zero in ;; position corresponding to the node because there's no loop condition (no self-connection). ask nodes [ set genome [] set genome n-values num-nodes [0]] ;; crea el genoma basico de grafo no dirigido (matriz triangular superior) set basic-genome [] set basic-genome n-values compute-factorial num-nodes [random 2] ;; Ahora, copia esos datos y se lo inserta en los genomas de los nodos respectivos (la diagonal principal nunca es usada) let y 0 let g 1 while [y < (num-nodes - 1)] ;; recorro todos los nodos menos el _ltimo [set g y + 1 while [g < num-nodes] ;; de cada nodo, tengo que llegar al final del genome [ask node y [set genome replace-item g genome item y basic-genome] set g g + 1 ] set y y + 1 ] ;; se completa la diagonal inferior para todos los nodos, simetrica a la superior let i 0 let j 0 while [i < num-nodes ][set j 0 while [j < num-nodes ][ if [item j genome] of node i = 1 [ask node j [set genome replace-item i genome 1] ] set j j + 1] set i i + 1] ;show basic-genome ;let a 0 ;while [a < num-nodes] ; [ask node a [show genome] ; set a a + 1 ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to warshall set sum-links 0 ;; It creates the reachability-matrix by adding individual's node genome set adjacency-matrix [] set transitive-matrix [] ;; this is the adjancency matrix let p 0 while [p < num-nodes] [set adjacency-matrix lput [genome] of node p adjacency-matrix set sum-links sum-links + sum [genome] of node p set p p + 1] ;diag-zero adjacency-matrix ;;; Warshall's algorithm ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; let i 0 let j 0 let k 0 ;; Get a copy of the transitive closure matrix set transitive-matrix adjacency-matrix let track 1 while [i < num-nodes] [ set j 0 while [j < num-nodes] [if (item j item i transitive-matrix = 1) [set k 0 set track 1 while [k < num-nodes] [ if (item j item k transitive-matrix = 1) [set transitive-matrix (replace-item i transitive-matrix ( replace-item k (item i transitive-matrix) track ))] set track track + 1 set k k + 1]] set j j + 1] set i i + 1] ;show (word transitive-matrix "a") ;; Finally we got the transitive closure matrix for the original adjacency-matrix end to indirect-information-matrix let prev-indirect-info n-values num-nodes [n-values num-nodes [0]] ;; a matrix of num-nodes of zeroes is created ask nodes [set indirect-info []] let r 0 let s 0 while [r < num-nodes] [set s 0 while [s < num-nodes] [ set prev-indirect-info (replace-item r prev-indirect-info (replace-item s (item r prev-indirect-info) (item s item r transitive-matrix - item s item r adjacency-matrix))) ;; acabo de agregar valor absoluto set s s + 1] set r r + 1] let i 0 while [i < num-nodes] [ ask node i [set indirect-info item i prev-indirect-info] set i i + 1 ] end to update-transitive-matrix ;; Back transformation, return reachability-matrix to reachability-matrix in the original ;; format of genome set transitive-matrix [] let p 0 while [p < num-nodes] [ set transitive-matrix lput [indirect-info] of node p transitive-matrix set p p + 1 ] ;show (word transitive-matrix "b") end to sort-global-fitness set topology-list remove-duplicates topology-list set topology-list sort-by [ item compute-factorial num-nodes ?1 > item compute-factorial num-nodes ?2] topology-list end to mate-recombine ;let scd compute-factorial num-nodes / 2 set best-fitness item compute-factorial num-nodes item 0 topology-list set avg-fitness smoothness * avg-fitness + (1 - smoothness) * best-fitness ;; Ac_ tengo que elegir entre cual configuraci_n, provista por genome, me da mayor pago, provista por fitness, y seleccionar la mejor. ;; tengo entonces que ver como formo la matriz de adyacencia de la que deriva la formaci_n original y la nueva que se utilizar_ ;; con el algoritmo gen_tico. if Selection = "Elitism" [elitism set seed-genomes item 0 winner-list] if Selection = "Roulette" [wheel-roulette let chosen-generation item random-float length ranking ranking let chosen-topology position chosen-generation ranking set seed-genomes item chosen-topology topology-list ] if Selection = "Tournament" [tournament set seed-genomes item 0 winner-list] ; will only allow mating between chosen ones of previous generation (not their offspring) make-mix-genes ;recombine genomes of those who mate let o 0 while [o < (compute-factorial num-nodes)] [ set seed-genomes (replace-item o mix-genes item o seed-genomes) set o o + 1 ] end to wheel-roulette let i 0 set sum-fitness 0 set ranking [] while [i < min (list (generations * .01) length topology-list) ] [ set sum-fitness sum-fitness + item compute-factorial num-nodes item i topology-list set i i + 1 ] set i 0 while [i < min (list (generations * .01) length topology-list) ] [ set ranking lput ((item compute-factorial num-nodes item i topology-list) / sum-fitness) ranking set i i + 1 ] end to tournament let draftlist topology-list set winner-list [] set draftlist shuffle topology-list set winner-list n-of (1 + random(length draftlist / 2)) draftlist set winner-list sort-by [ item (compute-factorial num-nodes) ?1 > item (compute-factorial num-nodes) ?2] winner-list end to elitism let draftlist topology-list set winner-list [] set winner-list sublist draftlist 0 (1 + random (length draftlist - 1)) end to driven-theory set empty-topology n-values compute-factorial num-nodes [0] set complete-topology n-values compute-factorial num-nodes [1] ;set complete-topology diag-zero complete-topology end to make-mix-genes ;; trabajan con seed-genomes, toman un _tem al azar y crean el marido. Igualan a la esposa con el marido ;; si el item 0 de seed-genomes = item 1 de seed-genomes no pasa nada, pero si no son iguales entonces ;; igualo ambos let k 0 let i random compute-factorial ( num-nodes - 1) let v compute-factorial num-nodes - i set mix-genes [] let husband [] let wife [] let chosen random-float 1 let swap false while [k < i][ ifelse chosen < .5 [ set swap true if Selection = "Elitism" [ set husband lput item k seed-genomes husband] if Selection = "Roulette" [ set husband lput item k seed-genomes husband] if Selection = "Tournament" [ set husband lput item k item 0 winner-list husband] ] [ if Selection = "Elitism" [set wife lput item k seed-genomes wife] if Selection = "Roulette" [set wife lput item k seed-genomes wife] if Selection = "Tournament" [set wife lput item k item 0 winner-list wife] ] ;assigns random genome to husband set k k + 1 ] ;; consultar este procedimiento con Ignacio: el esposo es mitad del item k de seed-genomes en elitism...? while [k < v][ ifelse swap = true [ ;set wife lput item k item random generation topology-list wife if Selection = "Elitism" [set wife lput item k item random length winner-list winner-list wife] if Selection = "Roulette" [set wife lput item k item random length topology-list topology-list wife] if Selection = "Tournament" [set wife lput item k item 0 winner-list wife] ] [ if Selection = "Elitism" [set husband lput item k item random length winner-list winner-list husband] if Selection = "Roulette" [set husband lput item k item random length topology-list topology-list husband] if Selection = "Tournament" [set husband lput item k item 0 winner-list husband] ] ;other half goes to wife set k k + 1 ] while [k < compute-factorial num-nodes][ ;ifelse chosen < .5 [ set swap true ifelse swap = true [ if Selection = "Elitism" [ set husband lput item k seed-genomes husband] if Selection = "Roulette" [ set husband lput item k seed-genomes husband] if Selection = "Tournament" [ set husband lput item k item 0 winner-list husband] ] [ if Selection = "Elitism" [set wife lput item k seed-genomes wife] if Selection = "Roulette" [set wife lput item k seed-genomes wife] if Selection = "Tournament" [set wife lput item k item 0 winner-list wife] ] ;assigns random genome to husband set k k + 1 ] let wh [] set wh lput wife wh set wh lput husband wh let mix-previous reduce [sentence ?1 ?2] wh set mix-genes reduce [sentence ?1 ?2] mix-previous end to mutate ;; Here is where a mask covering the zeroes in diagonal must be added. let genome-m 0 while [genome-m < length seed-genomes] [ ; scan all genes if (random-float 1000 < mutation-rate * 1000) ; change bit if mutation rate threshold is met [ let switch item genome-m seed-genomes ifelse (switch = 1) [ set seed-genomes (replace-item genome-m seed-genomes 0 ) ] [ set seed-genomes (replace-item genome-m seed-genomes 1 ) ] ] set genome-m genome-m + 1 ; moves to next genome ] ;set seed-genomes diag-zero seed-genomes end to rebirth ask patches [set pcolor black - .15] set-default-shape edges "line" create-genetic-info sort-global-fitness if length topology-list > 50 [set topology-list butlast topology-list] set topology-list remove-duplicates topology-list build-ga-network item 0 topology-list end to update-genome ask nodes [set genome n-values num-nodes [0] ] ; show seed-genomes ;; Ahora, copia esos datos y se lo inserta en los genomas de los nodos respectivos (la diagonal principal nunca es usada) let j 0 let q 0 while [j < (num-nodes - 1)][ let i j + 1 while [i < num-nodes] [ask node j [set genome (replace-item i genome item q seed-genomes)] set q q + 1 set i i + 1 ] set j j + 1] ;; se completa la diagonal inferior para todos los nodos, simetrica a la superior let i 0 set j 0 while [i < num-nodes ][set j 0 while [j < num-nodes ][ if [item j genome] of node i = 1 [ask node j [set genome replace-item i genome 1] ] set j j + 1] set i i + 1] ;let a 0 ;while [a < num-nodes] ; [ask node a [show genome] ; set a a + 1 ] ; end to theory-driven if theory-driven? [driven-theory let chosen random-float 1 ifelse chosen < .5 [ set seed-genomes empty-topology] [set seed-genomes complete-topology ] set theory-driven? false] end ;to-report diag-zero [matrix] ;;; zero diagonal mask ;;; esta mal, hace cualquier cosa... ; ;let s matrix ; ;let p length s ; ;show s ; let i 1 ; let j num-nodes ; while [j < (num-nodes * num-nodes)] ; [ set matrix replace-item (i + j) matrix 0 ; set i i + 1 ; set j j + num-nodes ; ] ; set matrix replace-item 0 matrix 0 ; set matrix replace-item (num-nodes * num-nodes - 1) matrix 0 ; ;show s ; report matrix ;end ;;;;;;;;;;;;;;;;;;;;; ;;; Export Outcomes ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;; to export let i 0 file-delete "GA_1.txt" file-open "GA_1.txt" while [i < num-nodes][ ask node i [print (word "node " i " " genome)] set i i + 1 ] export-output "GA_1.txt" file-close export-view (word edge-Cost-Structure "-" generations "-" "-" ".png") export-plot "Accessibility Distribution" "Access.csv" end

There is only one version of this model, created almost 8 years ago by Juan MC Larrosa.

## Attached files

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Evolutive Two-Way Network Formation.png | preview | Preview for 'Evolutive Two-Way Network Formation' | over 7 years ago, by Juan MC Larrosa | Download |

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