Download COMPLEXITY - Carlos Eduardo Maldonado

INNOVATION AND COMPLEXITY
Carlos Eduardo Maldonado
Research Professor
Universidad del Rosario
INNOVATION ENTAILS COMPLEXITY
 Complex 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 Research
 Incremental
 Experimental
Innovation
 Radical Innovation
Research
 Applied Research
Targets-based
 All depends on de
the mode and degree
of innovation
Research
Research grounded
on habilities and skills
Two kind of problems
Decidible
Difficult
P
N-P
Relevant
Easy/Irrevelevant Problems
Problems
N-P Complete
Indecidible
Cannot be solved
algorithmically, not
even with unlimited or
infinite time and space
resources
N-P Hard •Simulation
•Metaheurístics
Hypercomputation
MODEL
MODELING
REAL SYSTEM
(REAL WORLD )
SIMULATION
COMPUTER
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 OPTIMIZATION
Problems:
P = N-P
P ≠ N-P
P ≤ N-P
P C N-P
MODERN METHODS OF HEURISTICS
Fuzzy Systems
Neural Networks
Genetic Programming
Agents (multi-agents)- based
Systems
TECHNIQUES FOR LOCAL
OPTIMIZATION
(Stochastic) Hill climbing
Simulated Annealing
Taboo Search
Evolutionary Algorithms
Constraint 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
Prediction
Metaheuristics
•Multi-Agent Models
•Cellular Automata
•Artificial Chemistry
•.
•.
•.
•Other
•Evolutive
Computation
•Swarm
Intelligence
•Artificial Life
•Sciences of
Complexity
.
.
.
•Other
METAHEURISTICS
 Single-Solution Based
 Population-Based
 Metaheuristics for Multiobjective Optimization
 Hybrid Metaheuristics
 Parallel 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 TIME
 Polynomial-time algorithm
p(n) = ak . nk + … + aj . nj + … + al . n + ao
 Exponential-time algorithm
Its complexity is: O(cn), where c is a real constant
superior to 1
COMPLEXITY OF PROBLEMS
 The 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 Ptime 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 Methods
Exact Methods
Approximate Methods
Branch and x
Heuristic Algorithms and
Restricted Programming
Approximate Algorithms
Dynamic Programming
Metaheuristics
Specific heuristic
A*, IDA*
problems
Single-based solutions
Metaheuristics
Population-based
Metaheuristics
METAHEURISTICS
 Metaheuristics
 P Metaheuristics
 Hybrid Metaheuristics
 Parallel Metaheuristics
WHAT IS COMPUTABLE?
 That we can know
 That we can say
 That we can decide upon
 That we can solve
NEW PROBLEMS IN COMPUTATION
 Conversations
 Numbering
 Proves
 Finite Time
 Infinite Time
 Continuous Time
 Discrete Time
New Computational Paradigms. Changing
Conceptions ofWhat is Computable. S.
Barry Cooper, B. Löwe, A. Sorbi (Eds.),
Springer Verlag, 2008
LOGICS AND COMPUTATION
 Intuition Bubbles
 Computational
 Non-Classical Logics:
Complexity
 Algorithmic
Complexity
Paraconsistent Logics
Relevant Logics
Quantum Logics
Time Logics
Many-Valued Logics
Epistemic Logics
Fuzzy Logics
INNOVATION AND KNOWLEDGE
 Innovating and solving problems as a matter of
pushing-back the frontiers of knowledge
 Making life every time more possible
 Gaining degrees of freedom
 Pushing-back cenral controls and rigid hierarchies
 Trusting in local controls and dynamic centers
 Working 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