biologically-inspired computing lecture 21 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing

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1 lecture 21 -nspred

2 Sectons I485/H400 course outlook Assgnments: 35% Students wll complete 4/5 assgnments based on algorthms presented n class Lab meets n I1 (West) 109 on Lab Wednesdays Lab 0 : January 14 th (completed) Introducton to Python (No Assgnment) Lab 1 : January 28 th Measurng Informaton (Assgnment 1) Graded Lab 2 : February 11 th L-Systems (Assgnment 2) Graded Lab 3: March 25 th Cellular Automata & Boolean Networks (Assgnment 3) Graded Lab 4: Aprl 8 th Genetc Algorthms (Assgnment 4) Due: Aprl 22 nd Lab 5: Aprl 22 nd Ant Clusterng Algorthm (Assgnment 5) Due May 4 th

3 Readngs untl now Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computng: Basc Concepts, Algorthms, and Applcatons. Chapman & Hall. Chapters 1,2,3,7,8 Chapter 5, all sectons Secton 7.7, 8.3.1,8.3.6, Lecture notes Chapter 1: What s Lfe? Chapter 2: The Logcal Mechansms of Lfe Chapter 3: Formalzng and Modelng the World Chapter 4: Self-Organzaton and Emergent Complex Behavor Chapter 5: Realty s Stranger than Fcton posted

4 fnal proect schedule ALIFE 15 Proects Due by May 6 th n Oncourse ALIFE 15 (14) Actual conference due date: pages (LNCS proceedngs format) D= Prelmnary deas overdue! Indvdual or group Wth very defnte tasks assgned per member of group

5 based on dead body cleanng ant clusterng algorthm (ACA) Very smple rules for colony clean up Pck dead ant. f a dead ant s found pck t up (wth probablty nversely proportonal to the quantty of dead ants n vcnty) and wander. Drop dead ant. If dead ants are found, drop ant (wth probablty proportonal to the quantty of dead ants n vcnty) and wander. Data vector: X x 1 x 2 x 3 x n-1 x n x 1 x 2 x 3 x n-1 x n Lumer, E. D. and Faeta, B Dversty and adaptaton n populatons of clusterng ants. In From Anmals To Anmats 3, pp x 1 x 2 x 3 x n-1 x n Cluster data (N samples) accordng to ant clean up rules

6 for multvarate data ant clusterng algorthm (ACA) Group n-dmensonal data samples n 2-dmensonal grd Data vector: X 1 x 1,1 x 1,2 x 1,3 x 1,n-1 x 1,n Dstance between two data samples (n orgnal space): ) D( x ) (,x = x, k x, k Data vector: X 2 e.g. Eucldean k = 1 x 2,1 x 2,2 x 2,3 x 2,n-1 x 2,n Ants see data ponts n a certan neghborhood n 2 s 2 : area of neghborhood (sde s, radus 1)

7 usng thresholds Clusterng rules Pck data sample If there are few smlar Drop data sample. If there are many smlar Reduces dmensonalty No a pror number of clusters Overshoots number of clusters p f d ( x ) ant clusterng algorthm (ACA) Probablty of pckng up p p ( x ) = k Probablty of droppng ( ) ( ) 1 2 = s x Negh 0 ( s s) 1 ( x ) k1 + f ( x, x ) ( x ) 2 f x f f x < k2 ( x ) = 1 otherwse Neghborhood Smlarty or densty measure p D 1 α f otherwse Dscrmnaton factor Improved wth d = k Threshold 2 f + 2 ( x ) f ( x ) f > 0 Dfferent movng speeds, Shortterm memory, Behavoral swtches Coolng cycle for thresholds, progressve vson, pheromone renforcement 2

8 The workngs ant clusterng algorthm (ACA) 1. Proect hgh-dmensonal data tems onto 2-dmensonal grd randomly 2. Dstrbute N ants randomly on grd 3. repeat For every ant n colony Compute neghborhood densty f(x ) If ant s unloaded and ts cell s occuped wth data tem x then pck up x wth probablty p p (x ) Else f ant s loaded wth x and ts cell s empty drop x wth probablty p d (x ) Move randomly to neghbor cell wth no ant 4. Untl maxmum teratons

9 by brood sortng Same prncple as Clusterng Rules Pck data sample of type t If there are few of type t Drop data sample of type t. If there are many of type t p p d p ( x t) = k sortng wth ants 1 k + f 1 t ( x ) Probablty of pckng up tem of type t ( x t) = k 2 ft + ( x ) f ( x ) t 2 2 f t ( x ) Probablty of droppng tem of type t 1 2 = s x Neght 0 ( s s) D 1 ( x, x ) otherwse α Neghborhood densty of type t f f > 0

10 based on ant algorthm sortng swarm-robots Holland O. & Melhush C. (1999) Stgmergy, Self-organsaton, and Sortng n Collectve Robotcs Journal of Adaptve Behavour. 5(2). Brstol Robotcs Laboratory. See Also: J. L. Deneubourg, S. Goss, N. Franks, A. Sendova-Franks, C. Detran, L. Chreten. The Dynamcs of Collectve Sortng Robot-Lke Ants and Ant-Lke Robots. From Anmals to Anmats: Proc. of the 1st Int. Conf. on Smulaton of Adaptve Behavour (1990).

11 ant colony optmzaton Path optmzaton Stgmergy foragng, routng, and optmzaton Renforcement: Shortest path contans probablstcally more pheromone Frst ants to get to food source are those usng the shortest path, so pheromone remans stronger n the whole path, whch makes them choose the path more often when gong back Dependence on dynamc parameters (self-organzaton) Pheromone evaporaton, number of ants, length of paths If shortest path s ntroduced much later, t wll not be chosen unless pheromone evaporates very quckly Pheromone release s proportonal to food source qualty Explotaton of better sources Ants wander off path wth a certan probablty Random behavor necessary for exploraton of space Dstrbuted search Populaton of foragng ants Collectve Path Optmzaton (global coordnaton) A sngle ant (one soluton) cannot solve t, path optmzaton s a property of the collectve

12 robustness pheromone evaporaton E. Bonabeau

13 basc defntons graphs Drected graph connected undrected graph dsconnected w( e) R weghted G = ( V, E) Vertces Edges Path: Sequence of vertex, edge, vertex, edge. v Adacency Matrx v w( e, ) = 0.6

14 fndng the shortest path ant colony optmzaton (ACO) Start wth a weghted graph where edge weghts are dstances d(e). A soluton s a path from vertex s to vertex d Length of path p s e p d ( e) Pheromone level on edge e, : τ, Pheromone evaporates τ, (t+1) = (1-ρ) τ, (t) Populaton of artfcal ants Ant z traverses a edge (or path) at each teraton t Releases pheromone every tme t traverses an edge: Δτ Chooses next path to traverse after reachng vertex v : p z, = ( ) a ( ) b τ, d, ( ) a τ ( d ) [ ] b, k, k k N Desrablty or vsblty v N v

15 ant colony optmzaton Travelng-sales ants d = dstance between cty and cty τ = vrtual pheromone on edge(,) m agents, each buldng a tour At each step of a tour, the probablty to go from cty to cty s proportonal to (τ ) a (d ) -b After buldng a tour of length L, each agent renforces the edges s has used by an amount proportonal to 1/L The vrtual pheromone evaporates: τ (1 ρ) τ E. Bonabeau

16 For the travelng salesman problem ant colony optmzaton (ACO) Pheromone release proportonal to qualty of soluton τ z, = C z L Length of path completed by ant z p z, = ( ) a ( ) b τ, d, ( ) a τ ( d ) [ ] b, k, k k N

17 Multple solutons travelng sales ants Dorgo M. & L.M. Gambardella (1997). Ant Colones for the Travelng Salesman Problem. BoSystems, 43:73-81.

18 readngs Next lectures Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computng: Basc Concepts, Algorthms, and Applcatons. Chapman & Hall. Chapter 5, all sectons Secton 7.7, 8.3.1,8.3.6, Lecture notes Chapter 1: What s Lfe? Chapter 2: The logcal Mechansms of Lfe Chapter 3: Formalzng and Modelng the World Chapter 4: Self-Organzaton and Emergent Complex Behavor Chapter 5: Realty s Stranger than Fcton posted Optonal materals Scentfc Amercan: Specal Issue on the evoluton of Evoluton, January 2009.