INNOVACIN Y COMPLEJIDAD

Carlos Eduardo MaldonadoResearch ProfessorUniversidad del RosarioINNOVATION AND COMPLEXITYINNOVATION ENTAILS COMPLEXITYComplex systems contain and lead to surprise (emergence)They are unpredictable (chaotic, catastrophic)They do not have centrality or hierarchy (local control) (self-organization)They are essentially open systems (complex networks) (NET)INNOVATION AND PROBLEM SOLVINGInnovation and problem solving: two faces of one and the same token

They root in biology, not just in cultureINNOVATION AND/AS RESEARCHBasic ResearchExperimental ResearchApplied Research

All depends on de the mode and degree of innovationIncremental InnovationRadical Innovation

Targets-based ResearchResearch grounded on habilities and skillsTwo kind of problemsDecidibleIndecidibleCannot be solved algorithmically, not even with unlimited or infinite time and space resourcesPN-PN-P CompleteN-P HardEasy/Irrevelevant ProblemsHyper-computationSimulationMetaheursticsDifficultRelevant ProblemsMODELREAL SYSTEM(REAL WORLD )COMPUTERMODELINGSIMULATIONOPTIMIZATION(COMBINATORIAL COMPLEXITY)Local Optimization (or partial)

Global OptimizationP and N-P: COMPLEXITY It is easier to find a solution than verifying it:

P: It is necessary that a problem admits a method to find a solution in a P time.

N-P: It is sufficient that a problem admits a method to verify the solution in a P time.

P, N-P and OPTIMIZATIONProblems:P = N-PP N-PP N-PP C N-PMODERN METHODS OF HEURISTICSFuzzy SystemsNeural NetworksGenetic ProgrammingAgents (multi-agents)- based SystemsTECHNIQUES FOR LOCAL OPTIMIZATION(Stochastic) Hill climbingSimulated AnnealingTaboo SearchEvolutionary AlgorithmsConstraint Handling

METHODS OF GLOBAL OPTIMIZATIONProblems of combinatorial complexityHeuristics: Algorithm that looks for good solutions at a reasonable computational cost, without though guarantee of optimality (or even feasibility). Usually works with specific problemsMetaheuristics: They are heuristics in a larger and deeper scope Bio-inspired ComputationMODELING, SIMULATION, OPTIMIZATIONData mining

OptimizationMetaheuristicsEvolutive ComputationSwarm IntelligenceArtificial LifeSciences of Complexity...Other

PredictionMulti-Agent ModelsCellular AutomataArtificial Chemistry...OtherMETAHEURISTICSSingle-Solution BasedPopulation-BasedMetaheuristics for Multiobjective OptimizationHybrid MetaheuristicsParallel Metaheuristics

Distinction between Decidable and Indecidable Problems(Computationally)

COMPLEXITY OF ALGORITHMS AND PROBLEMSDECIDIBLE PROBLEMSINDECIDIBLE PROBLEMS

Ej.: The Halting Problem (Turing)COMPLEXITY OF ALGORITHMSAn algorithm needs two important resources to solve a problem: space and timeThe time complexity of an algorithm is the number of steps required to solve a problem of size nALGORITHM AND TIMEPolynomial-time algorithmp(n) = ak . nk + + aj . nj + + al . n + ao

Exponential-time algorithmIts complexity is: O(cn), where c is a real constant superior to 1COMPLEXITY OF PROBLEMSThe complexity of a problem is equivalent to the complexity of the best algorithm solving that problemA problem is tractable (or easy) if there exists a P-time algorithm to solve itA problem is intractable (or difficult) if no P-time algorithm exists to solve the problemC/A complexity theory of problems deals with decision problems. A decision problem always has a yes or no answerOptimization MethodsExact MethodsApproximate MethodsBranch and xRestricted ProgrammingDynamic ProgrammingA*, IDA*Heuristic Algorithms and Approximate AlgorithmsMetaheuristicsSpecific heuristic problemsSingle-based solutions MetaheuristicsPopulation-based MetaheuristicsMETAHEURISTICSMetaheuristics

P Metaheuristics

Hybrid Metaheuristics

Parallel MetaheuristicsWHAT IS COMPUTABLE?That we can knowThat we can sayThat we can decide upon

That we can solveNEW PROBLEMS IN COMPUTATIONConversationsNumberingProvesFinite TimeInfinite TimeContinuous TimeDiscrete TimeNew Computational Paradigms. Changing Conceptions of What is Computable. S. Barry Cooper, B. Lwe, A. Sorbi (Eds.), Springer Verlag, 200822LOGICS AND COMPUTATIONIntuition BubblesNon-Classical Logics:Paraconsistent LogicsRelevant LogicsQuantum LogicsTime LogicsMany-Valued LogicsEpistemic LogicsFuzzy LogicsComputational ComplexityAlgorithmic ComplexityINNOVATION AND KNOWLEDGEInnovating and solving problems as a matter of pushing-back the frontiers of knowledgeMaking life every time more possibleGaining degrees of freedomPushing-back cenral controls and rigid hierarchiesTrusting in local controls and dynamic centersWorking in a small-world: complex networksINNOVATION AND AESTHETICSSpearhead science does not pretend to control or predict, any longerScience distrusts conclusive arguments and yet strives for themScience assesses harmony