Complex consisting of interconnected or interdependent parts Why Define

Complex consisting of interconnected or

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Complex: consisting of interconnected or interdependent parts Why Define Complexity? To estimate how long a particular system will take to solve a problem To estimate difficulty in engineering complex systems To understand the limits of prediction, approximation, and simulation To answer fundamental scientific questions Complexity vs. Complicated Complexity is difficult to describe If we say something is complex in ‘everyday’ language we mean something that is difficult or impossible to understand with simple logic (i.e., long term weather patterns) A car is not complex, just complicated. Cars do exhibit “unwanted functionality” Complicated Systems: Often difficult to describe, but succumb to divide-and-conquer approaches. Complicated is easier to cope with than complex – Seth Bullock Numerous techniques to resolve complicated systems
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As a last resort, use brute force/trial and error But, complicated systems are often complex: Software does suffer from “emergent” bugs!! Explanation vs Prediction Low-level behavior is unpredictable (gas molecules bouncing around, pigs pigging about) We can explain how more gas increases temperature (ideal gas law) but not easy to explain how more pigs brings about an abrupt phase transition in pig violence For simple (linear) systems: a small change to a system’s components → a small change at the system level For complex (non-linear) systems: a small change to a system’s components → large/small/no change at the system level Considering complex adaptive systems, we are interested in: how interactions give rise to patterns of behavior understanding the ways of describing complex systems how complex systems form through pattern formation and evolution how complex systems adapt to their changing environment How to measure a system’s complexity? By its unpredictability? By how difficult it is to describe? No single model adequate to describe system---the more models that are required, the more complex the system. (Lee Segel) By measuring how long before it halts, if ever? By how long until it repeats itself? Entropy? Multiple levels of organization? Number of interdependencies?
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Evolutionary Computation Evolutionary Computation is a variety of computational systems that use ideas inspired from natural evolution. Evolution has optimized biological processes, so adopting the evolutionary paradigm to computation may help us find optimal solutions to some problems. Largely, stochastic search procedures in large search spaces based on selection. Some varieties: Genetic Algorithms Swarm Intelligence Self-organizing Maps Cultural Algorithms Natural Selection Population of individuals with individual characteristics Limited number of resources Competition for resources results in struggle for existence Success depends on fitness -- Fitness of an individual: how well-adapted an individual is to their environment.
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  • Spring '15
  • StephenKaisler

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