Carlos Eduardo MaldonadoResearch Professor

Universidad del Rosario

INNOVATION AND COMPLEXITY

INNOVATION 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 SOLVING

Innovation and problem solving: two faces of one and the same token

They root in biology, not just in culture

INNOVATION AND/AS RESEARCH

Basic ResearchExperimental

ResearchApplied Research

All depends on de the mode and degree of innovation

Incremental Innovation

Radical Innovation

Targets-based Research

Research grounded on habilities and skills

Two kind of problemsDecidible Indecidible

Cannot be solved

algorithmically, not even with

unlimited or infinite time

and space resources

P N-P

N-P Complete

N-P Hard

Easy/Irrevelevant Problems

Hyper-computation

•Simulation•Metaheurístics

DifficultRelevant Problems

MODEL

REAL SYSTEM(REAL

WORLD )COMPUTER

MODELING SIMULATION

OPTIMIZATION(COMBINATORIAL COMPLEXITY)

Local Optimization (or partial)

Global Optimization

P 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-P

MODERN METHODS OF HEURISTICS

Fuzzy SystemsNeural NetworksGenetic ProgrammingAgents (multi-agents)- based Systems

TECHNIQUES FOR LOCAL OPTIMIZATION

(Stochastic) Hill climbingSimulated AnnealingTaboo SearchEvolutionary AlgorithmsConstraint Handling

METHODS OF GLOBAL OPTIMIZATION

Problems of combinatorial complexity

Heuristics: Algorithm that looks for good solutions at a reasonable computational cost, without though guarantee of optimality (or even feasibility). Usually works with specific problems

Metaheuristics: They are heuristics in a larger and deeper scope

Bio-inspired Computation

MODELING, SIMULATION, OPTIMIZATION

Data mining

•Optimization Metaheuristics

•Evolutive Computation•Swarm Intelligence•Artificial Life•Sciences of Complexity...•Other

Prediction

•Multi-Agent Models•Cellular Automata•Artificial Chemistry•.•.•.•Other

METAHEURISTICSSingle-Solution BasedPopulation-BasedMetaheuristics for Multiobjective Optimization

Hybrid MetaheuristicsParallel Metaheuristics

Distinction between Decidable and Indecidable Problems

(Computationally)

COMPLEXITY OF ALGORITHMS AND PROBLEMS

DECIDIBLE PROBLEMS

INDECIDIBLE PROBLEMS

Ej.: The Halting Problem (Turing)

COMPLEXITY OF ALGORITHMS

An algorithm needs two important resources to solve a problem: space and time

The time complexity of an algorithm is the number of steps required to solve a problem of size n

ALGORITHM 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 1

COMPLEXITY OF PROBLEMSThe complexity of a problem is

equivalent to the complexity of the best algorithm solving that problem

A problem is tractable (or easy) if there exists a P-time algorithm to solve it

A problem is intractable (or difficult) if no P-time algorithm exists to solve the problem

C/A complexity theory of problems deals with decision problems. A decision problem always has a yes or no answer

Optimization MethodsExact Methods Approximate

MethodsBranch and xRestricted ProgrammingDynamic ProgrammingA*, IDA*

Heuristic Algorithms and Approximate Algorithms

Metaheuristics Specific heuristic problems

Single-based solutions Metaheuristics

Population-based Metaheuristics

METAHEURISTICSMetaheuristics

P Metaheuristics

Hybrid Metaheuristics

Parallel Metaheuristics

WHAT IS COMPUTABLE?

That we can knowThat we can sayThat we can decide upon

That we can solve

NEW PROBLEMS IN COMPUTATIONConversationsNumberingProvesFinite TimeInfinite TimeContinuous TimeDiscrete Time New Computational

Paradigms. Changing Conceptions of What is Computable. S. Barry Cooper, B. Löwe, A. Sorbi (Eds.), Springer Verlag, 2008

LOGICS AND COMPUTATIONIntuition

BubblesNon-Classical

Logics:Paraconsistent

LogicsRelevant LogicsQuantum LogicsTime LogicsMany-Valued

LogicsEpistemic LogicsFuzzy Logics

Computational Complexity

Algorithmic Complexity

INNOVATION AND KNOWLEDGE

Innovating and solving problems as a matter of pushing-back the frontiers of knowledge

Making 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 networks

INNOVATION AND AESTHETICS

Spearhead science does not pretend to control or predict, any longer

Science distrusts conclusive arguments and yet strives for them

Science assesses harmony