Inteligencia computacional y algoritmos. Inteligencia computacional y algoritmos bio-inspirados: inspirados: sistemas víricosv.

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1 Ingeniería de Organización Escuela Técnica Superior de Ingenieros. Universidad de Sevilla. Camino de los Descubrimientos s/n E-4192 Sevilla Mail: / URL: Inteligencia computacional y algoritmos bio-inspirados: inspirados: sistemas víricosv Pablo Cortés Viral systems foundations Artificial Intelligence algorithms based on trajectories Artificial Intelligence algorithms based on populations Particle swarm optimization Immune systems Multi-agent systems Reovirus Rhabdovirus Picornavirus (poliovirus) Parvovirus Adenovirus Orthomyxovirus (influenza) Herpesvirus

2 Viruses are intracellular parasites shaped by nucleic acids, such as DNA or RNA, and proteins. The protein generates a capsule, called a capsid, where the nucleic acid is located. The capsid plus the nucleic acid shape the nucleus-capsid, defining the virus. One of the main characteristics of viruses is the replication mechanism. The phage (a common type of virus) does follow lytic replication process. Coliphage structure Head Tail Baseplate DNA (inside) Tail fiber (a) bacterium (c) (e) Lytic replication virus (b) (d) (f) The virus is adhered to the border of the bacterium. Virus penetrates the border being injected inside this one, (a) and (b) The infected cell stops the production of its proteins, beginning to produce the phage proteins, starting to replicate copies of the virus nucleus-capsids, (c) and (d) After replicating a number of nucleuscapsids, the bacterium border is broken, and new viruses are released, (e) which can infect near cells, (f) (g) bacterium (i) Lysogenic replication virus (k) The virus infects the host cell, being lodged in its genome, (g) and (h) The virus remains hidden inside the cell during a while until it is activated by any cause, for example ultraviolet irradiation or X-rays, (i) The replication of cells altered, with proteins from the virus, starts Similar to a mutation process. (h) (j)

3 3. Viral System 1. Virus 5. Computationa l VS are defined by three s: a set of viruses, an organism and an interaction between them: VS = <Virus, Organism, Interaction Virus of the VS is a set consisting of single viruses: Virus = {Virus 1, Virus 2,, Virus n }. Each virus is defined in four s: Virus i = <State i, Input i, Output i, Process i State i defines the cell infected by the virus. It is typically the mathematical encoding of the solution in computational terms, which we also call genome. Input i identifies the information that the virus can collect from the organism (sensor). It represents the input s interaction with the organism. It corresponds to the neighbourhood of the cell in computational terms. Output i identifies the actions that the virus can take (actuator). It corresponds to the selection mechanism of the type of virus replication in computational terms. Process i represents the autonomous behaviour of the virus, changing the State i. It corresponds to the replication operator process in computational terms. 3. Viral System 1. Virus 2. Organism 5. Computationa l VS = <Virus, Organism, Interaction Organism of the VS is defined by two s:: Organism = < State o, Process o State o characterizes the organism state in each instant. The set of feasible solutions in a specific space R n is given by the constraints K = Each feasible solution x K is called a cell. The genome is the mathematical encoding of each cell or feasible solution. The total amount of infected cells constitutes the infected part of K for each time instant, and it is named clinical picture. The clinical picture consists of every three-tuple genome-nr-it. Genome of cell 1 (encoding of the feasible solution x 1 ) Genome of cell 2 (encoding of the feasible solution x2) Genome of cell 3 (encoding of the feasible solution x3) { x : gi ( x), i = 1,, n} NR1 NR2 NR3 It1 It2 It3 Virus 2 State Best solution (encoding of the feasible solution xn) Clinical picture NRn Itn Organism State

4 1. Virus 2. Organism 3. Interaction Organism of the VS is defined by two s:: Organism = < State o, Process o Process o represents the autonomous behaviour of the organism that tries to protect itself from the infection threat, consisting of antigen liberation. An antigen is any substance that elicits an immune response. The antigens generate an immune response by means of antibodies trying to fight the virus infection. The computational mission of the antigens is to liberate space in the population of infected cells (clinical picture), trying to maintain free record memory in the clinical picture to incorporate new infected cells (new feasible solutions). VS = <Virus, Organism, Interaction Interaction of the VS is conditioned by the Input and Output actions that lead to a Process of every virus and the corresponding Organism response. A Virus i process implies a resulting change in the organism, and the same applies for an Organism s process. The interaction is the union of both actions. 1. Selective infection 2. Massive infection Output ejectors: lytic replication Genome of cell 1 NR 1 Genome of cell 2 NR 2 Genome of cell 3 NR 3 Genome of cell 4 NR 4 Genome of cell 5 NR 5 Genome of cell 6 NR 6 Genome of cell i NR i -1 NR n-1 NR n NR 1, NR 6, NR i LNR Z = Bin (LNR, p r ) VIRUS PROCESS K = It 1 It 2 It 3 It 4 It 5 It 6 It i It n-1 It n Input sensors: neighbourhood V 1 (x) V i (x) V 6 (x) { x : gi ( x), i = 1,, n} ORGANISM PROCESS Virus A(x) = Ber (p an (x) INTERACTION Genome of cell 1 NR 1 Genome of cell 2 NR 2 Genome of cell 3 NR 3 Genome of cell 4 NR 4 Genome of cell 5 NR 5 Genome of cell 6 NR 6 Genome of cell i Lowest healthy cell without antigenic response (infected cell) Lowest healthy cell with antigenic response (non-infected cell) Healthy cell (non-infected cell) NR i -1 NR n-1 NR n It 1 It 2 It 3 It 4 It 5 It 6 It i It n-1 It n Initiation of lysogenic cycle

5 1. Selective infection 2. Massive infection VIRUS PROCESS Clinical picture Genome of cell 1 NR 1 It 1 Genome of cell 2 NR 2 It 2 Genome of cell 3 NR 3 It 3 Genome of cell 4 NR 4 It 4 Genome of cell 5 NR 5 It 5 Genome of cell 6 NR 6 It 6 Genome of cell i NR i It i -1 NR n-1 It n-1 NR n It n ORGANISM PROCESS Output ejectors: lytic replication Input sensors: neighbourhood Genome of cell 1 NR 1 It 1 Genome of cell 2 NR 2 It 2 Genome of cell 3 NR 3 It 3 Genome of cell 4 NR 4 It 4 Genome of cell 5 NR 5 It 5 Genome of cell 6 NR 6 It 6 Genome of cell i NR i It i -1 NR n-1 It n-1 NR n It n V 1 (x) V i (x) V 6 (x) NR 1, NR 6, NR i LNR Organism antigenic response Genome of cell 1 NR 1 It 1 Genome of cell 2 NR 2 It 2 Genome of cell 3 NR 3 It 3 Genome of cell 4 NR 4 It 4 Genome of cell 5 NR 5 It 5 Genome of cell 6 NR 6 It 6 Genome of cell i NR i It i K = { x : gi ( x), i = 1,, n} INTERACTION Genome of cell 1 Genome of cell 2 Genome of cell 3 NR 3 Genome of cell 4 Genome of cell 5 NR 5 Genome of cell 6 Genome of cell i -1 NR n It 3 It 5 It n Antigenic response in clinical picture (cells: 2, 4,n-1) p n π LNR an n π LNR ( pi V ( x) 1) ( pi V ( x) 1) + n -1 NR n-1 It n-1 NR n It n Virus Cell with antibodies Cell without antibodies 4. Study case: Steiner Study case: the Steiner Given a non-directed graph G = (N,A) with N nodes and A arcs with costs c ij (i,j) A; and a subset T N with T nodes called terminals or targets, with the rest of the nodes in N called Steiner nodes Find a network G T G joining all the terminal nodes in T at minimum cost. This network can include some of the Steiner nodes but does not have to include all the Steiner nodes : Terminal node : Steiner node : potential arc : Feasible Steiner tree

6 Adapting VS to the Steiner Organism State is given by the feasibility region: ( δ( )) 1,,, (( \ ) ) x, ( i,j) A x K:X W W N W T NW T 1 ; integer ij Organism process: antigenic response from cells Virus state is the three-tuple: Genome: a bit string with the Steiner nodes that are in the tree number of replicated nucleus-capsids (lytic replication) Number of hidden generations (lysogenic replication) Output ejector: type of replication Input sensor: neighbourhood constant and N-T sized Virus process: new cells infected (mapping the feasibility region) 5. Computation al Trials: OR-Library J.E. Beasley Imperial College (series C, D & E) Series C: 5 nodes, arcs varying from 625 to 12,5, and terminals from 5 to 25 Series D: 1, nodes, arcs varying from 1,25 to 25,, and terminals from 5 to 5 Series E: 2,5 nodes, arcs varying from 3,125 to 62,5, and terminals from 5 to 1,25 Comparison to: Tabu Search: Gendreau, M., Larochelle, J.-F., Sansò, B. A tabu search heuristic for the Steiner tree. Networks 1999; 34 (2): Genetic Algorithms: Esbensen, H. Computing near-optimal solutions to the Steiner in a graph using genetic algorithm. Networks 1995; 26, Genetic Algorithms: Voss, S. and Gutenschwager, K. A chunking based genetic algorithm for the Steiner tree in graphs. In Pardalos, P.M., Du, D., (Eds.) Network Design: Connectivity and Facilities Location, DIMAC series in Discrete Mathematics and Theoretical Computer Science 4, AMS, Providence, p Steiner s categories: Steiner group 1: % terminals < 15% (shortest path approaches provide good solutions) Steiner group 2: % terminals between 15% and 3% (more difficult cases) Steiner group 3: %terminals 3% (MST approaches provide good solutions)

7 5. Computation al Calibration of parameters: Experimental design based on a fractional factorial design at two levels A number of factors k in a full factorial design, 2 k runs must be computed Fractional factorial designs for 2-level experiments includes the desirable properties of being both balanced and orthogonal The two-level parameters of the VS : ITER: number of iterations. 5, (+) / 1, (-) POB: clinical picture. 1 (+) / 5 (-) PLITI: probability for the lytic cycle..7 (+) /.3 (-) LNR: Limit of iterations for the lytic cycle (number of replications inside the cell to be broken). 2 (+) / 1 (-) LIT: Limit of iterations for the lysogenic cycle. 2 (+) / 1 (-) PZ: Probability of replicating z nucleus-capsids..7 (+) /.3 (-) We used series C for the calibration. 5. Computation al Stein-C: group 1 Adjusted R-squared = Standard error = E-3 Stein-C: group 2 Adjusted R-squared =.9317 Standard error = E-3 Stein-C: group 3 Adjusted R-squared = Standard error = E-3 arameter Coefficient t-ratio P[ T t] Coefficient t-ratio P[ T t] Coefficient t-ratio P[ T t] TER OB LITI NR IT Z TER_POB TER_PLI TER_LNR TER_LIT TER_PZ OB_PLIT OB_LNR OB_LIT OB_PZ LITI_LN LITI_LI LITI_PZ NR_LIT NR_PZ IT_PZ E E E E E E E E E E E E E E E E E E E E E-4 Least squares regression analysis for Stein-C set of s E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Adequate parameters selection Group 1 Group 2 Group 3 Parameters 1 st set 2 nd set 1 st set 2 nd set 1 st set 2 nd set ITER 5, (+) 1, (-) 5, (+) 5, (+) 1, (-) 5, (+) POB 1 (+) 5 (-) 1 (+) 5 (-) 5 (-) 5 (-) PLITI.7 (+).7 (+).7 (+).7 (+).7 (+).7 (+) LNR 15 (~) 15 (~) 15 (~) 15 (~) 1 (-) 1 (-) LIT 1 (-) 1 (-) 2 (+) 1 (-) 1 (-) 1 (-) Pz.5 (~).5 (~).5 (~).5 (~).5 (~).5 (~)

8 5. Computation al Steiner series C Problem Optimum GA-E GA-V MPH P-Tabu F-Tabu VS C1 85,%,%,%,%,%,% C ,67%,83%,%,%,%,% C3 754,13%,13%,%,%,%,% C4 179,11%,4%,9%,%,%,% C5 1579,%,%,%,%,%,% C6 55,73% 1,9%,%,%,%,% C7 12 1,76% 2,75%,%,%,%,% C8 59,63%,51%,%,%,%,% C9 77 1,5% 1,3%,99%,14%,14%,% C1 193,26%,27%,9%,%,%,% C ,88% 1,88%,%,%,%,% C ,3%,43%,%,%,%,% C ,1% 1,32%,78%,%,%,% C14 323,87%,68% 1,24%,31%,31%,% C15 556,25%,22%,18%,%,%,% C16 11,%,%,%,%,%,% C17 18,%,%,%,%,%,% C18 113,71%,71% 5,31%,88%,%,% C19 146,41%,82% 4,79%,68%,%,% C2 267,%,%,37%,%,%,% Best approach Steiner series D Problem Optimum GA-E GA-V MPH P-Tabu F-Tabu VS D1 16,57%,88%,%,%,%,% D2 22,%,73%,%,%,%,% D3 1565,92% 1,25%,77%,26%,6%,% D4 1935,52%,63%,16%,%,%,% D5 325,12%,19%,6%,%,%,% D6 67,%,%,%,%,%,% D7 13 1,94% 3,62%,%,%,%,% D ,55% 2,28% 1,59%,47%,37%,47% D9 1448,5% 1,15%,83%,41%,21%,69% D1 211,13%,44%,38%,%,%,% D ,7% 1,84%,%,%,%,% D12 42,%,%,%,%,%,% D13 5,56% 1,48% 2,%,%,%,% D14 667,3%,75%,75%,15%,15%,15% D ,16%,39%,36%,%,%,% D16 13,%,%,%,%,%,% D17 23,%,%,%,%,%,% D ,26% 1,43% 6,28% 1,35%,9%,9% D ,3% 1,2% 5,81%,65%,32%,65% D2 537,15%,16%,19%,%,%,37% Best approach Steiner series E Problem Optimum GA-E MPH P-Tabu F-Tabu VS E1 111,%,%,%,%,% E2 214,93%,%,%,%,% E3 413,% 1,7%,42%,32%,24% E4 511,2%,18%,%,%,% E5 8128,%,2%,%,%,% E6 73,%,%,%,%,% E7 145,% 2,7% 2,7%,%,% E8 264,23% 1,63%,49%,42% 1,14% E9 364,19% 1,17%,42%,14%,47% E1 56,%,21%,4%,4%,14% E11 34,%,%,%,%,% E ,49% 1,49% 1,49% 1,49%,% E13 128,7% 1,88%,78%,63% 1,33% E ,23% 1,4%,29%,23%,64% E ,%,22%,11%,11%,% E16 15,%,%,%,%,% E17 25,%,%,%,%,% E ,37% 7,62% 2,66% 1,6% 2,66% E ,26% 4,35% 1,19% 1,19% 1,18% E2 1342,%,67%,%,%,15% Best approach Computational Time analysis Set of Problems Group Best Case Worst Case Stein-C Stein-C Stein-C Stein-D Stein-D 2 1,471 4,329 Stein-D Stein-E Stein-E 2 4,692 19,892 Stein-E , Computation al OR-Library Group 1 Group 2 Group 3 Trials C{1,2,6,7,11,12,16,17} D{1,2,6,7,11,12,16,17} E{1,2,6,7,11,12,16,17} C{8,9,13,14,18,19} D{8,13,14,18,19} E{8,13,14,18,19} C{3,4,5,1,15,2} D{3,4,5,9,1,15,2} E{3,4,5,9,1,15,2} Average value MPH GA-V GA-E P-Tabu F-Tabu VS-s Standard Deviation MPH GA-V GA-E P-Tabu F-Tabu VS-s Maximum error MPH : GA-V: GA-E : P-Tabu: F-Tabu : VS-s:.15%.88%.6%.15%.6%.%.5% 1.8%.78%.5%.3%.% 2.7% 3.62% 2.7% 2.7% 1.49%.% MPH : GA-V: GA-E : P-Tabu: F-Tabu : VS-s: MPH GA-V GA-E P-Tabu F-Tabu VS-s MPH : GA-V: GA-E : P-Tabu: F-Tabu : VS-s: 2.88% 1.13%.95%.63%.39%.57% 2.32%.49%.73%.66%.46%.72% 7.62% 2.28% 3.37% 2.66% 1.6% 2.66% MPH : GA-V: GA-E : P-Tabu: F-Tabu : VS-s: MPH GA-V GA-E P-Tabu F-Tabu VS-s MPH : GA-V: GA-E : P-Tabu: F-Tabu : VS-s:.35%.37%.17%.8%.4%.1%.35%.39%.23%.15%.9%.19% 1.17% 1.25%.92%.42%.32%.69% Difficulties for Steiner group 2: % terminals between 15% and 3% VS massive infection Problem Optimum % terminals MPH GA-Voss GA-Esb P-Tabu F-Tabu VS-select VS-massive C %.%.51%.63%.%.%.%.39% C %.99% 1.3% 1.5%.14%.14%.%.% C %.78% 1.32% 1.1%.%.%.%.% C % 1.24%.68%.87%.31%.31%.%.% C % 5.31%.71%.71%.88%.%.%.% C % 4.79%.82%.41%.68%.%.%.% D % 1.59% 2.28% 1.55%.47%.37%.47%.47% D % 2.% 1.48%.56%.%.%.%.2% D %.75%.75%.3%.15%.15%.15%.% D % 6.28% 1.43% 1.26% 1.35%.9%.9%.% D % 5.81% 1.2% 1.3%.65%.32%.65%.% E % 1.63% --.23%.49%.42% 1.14% 1.78% E % 1.88% --.7%.78%.63% 1.33%.55% E % 1.4% --.23%.29%.23%.64%.29% E % 7.62% % 2.66% 1.6% 2.66%.35% E % 4.35% % 1.19% 1.19% 1.18%.% MPH GA-Voss GA-Esb P-Tabu F-Tabu VS-select VS-massive Average 2.88% 1.13%.95%.63%.39%.57%.25% Stand. Deviation 2.32%.49%.73%.66%.46%.72%.44% Max. Error 7.62% 2.28% 3.37% 2.66% 1.6% 2.66% 1.78% Optimums Best approach

9 A new approach is presented based on a virus infection Perspective from the opposite side to Artificial Immune systems Very promising approach outperforming very good approaches such as Gendreau et al TS, Voss et al GA or Esbenssen GA. Further research: We are testing VS in other NP-Hard s in production (scheduling) context. We are analysing other virus behaviour different from phages to analyse alternative replication cycles and alternative antigenic responses from organisms Library of different viruses (Ebola, AIDS, Smallpox, etc.) Parallel programming computation (population of computers). A virus in each computer = Trajectories + Population MAS perspective: virus agent, communication between virus, virus collaborative infection, alien nation P. Cortés, J.M. García, J. Muñuzuri & L. Onieva (28). Viral Systems: a new optimisation approach. Computers & Operations Research, 35 (9), P. Cortés, J. M. García, L. Onieva, J. Muñuzuri & J. Guadix (28). Viral Systems to solve optimization s: an immune-inspired computational intelligence approach. Lecture Notes in Computer Science. Special issue: Artificial Immune Systems Vol. 5132, pp P. Cortés, J.M. García, J. Muñuzuri & J. Guadix. A Viral System massive infection algorithm to solve the Steiner tree in graphs with medium terminal density. International Journal of Bio- Inspired Computation. In press.

10 Ingeniería de Organización Escuela Técnica Superior de Ingenieros. Universidad de Sevilla. Camino de los Descubrimientos s/n E-4192 Sevilla Mail: / URL: Inteligencia computacional y algoritmos bio-inspirados: inspirados: sistemas víricosv Pablo Cortés