autopilot 2001

AutoPilot 2001

Jerrold F. Stach, Ph.D.

Eun Kyo Park, Ph.D.

School of Interdisciplinary Computing and Engineering

University of Missouri – Kansas City

Perception by Fuzzy Membership Function

Multi-attribute Decision Making for Agent Mobility

September 20, 2001

AutoPilot Framework

Sensing

Perception

Reasoning

Behavior

Meta data

•Years 1,2 concentrated on the theoretical basis of mobility and construction of baseline simulator. •Network load leveling was demonstrated as a second order effect of individual agent mobility

decisions.•Year 3 concentrated on quantification of perception using characteristic functions and subjective time.

Autonomous, Rational Agent

September 20, 2001

Sensory Functions

Sensing

Objective Time

Distance

Population Density

Trader Place and Local Service Place Inquiries

•Current Time•Distance in Hops•Queue Length•Arrival Rate•Service Rate

Service Planner at SPprovides instantaneouslocal measures.Trader Place provides measures of remote SPs since last update.

September 20, 2001

Perception In Subjective Time

Perception

•Congestion •Acceptance with Goodness of Fit•Acceptance with Certainty•Difference•Reliability/Mortality

September 20, 2001

Reasoning

Reasoning

•Next Migration•Next Computation•Death (Subjective Time)

- indicates future work

- indicates intermediate progress

September 20, 2001

Behavior

Behavior

Non-Deterministic Choice– stay or go– next location– next computation– self replicate– genetic mutate(signature splice)

•Request Transport



September 20, 2001

Meta Data

Meta data


•Life History (experiences)•Algebraic Signature (Genotype)•Phenotype•Intermediate Data e.g. progress toward goal, beliefs etc.•Join locations


September 20, 2001

2000 Results

Single attribute functions were given for – Distance

(Objective time based on hops and payload)– Cost of Service– Accuracy (quality) of Service

Mobility was solved using a graph theoretic solution which is optimal but has exponential running time

Service Places were weighted in a task graph using a multi-attribute normalization

September 20, 2001

Mapping of Subjective Time to Scalar Time for Linear Attributes such as Cost and Accuracy was Given:

1. Compute the Origin and Limit of Scalar Time Bounds of current network diameter

2. For each attribute:I. compute the slope of the attribute scale

II. obtain the time correspondent

III. compute the mass of the attribute using its weight*Time Correspondent value

3. Create a Time Vector of the attributes

September 20, 2001

Linear and Scalar attributes cont.

4. Compute the mass of the time vector as a multi-body system:

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September 20, 2001

2000 Observations

Many environmental (sensed) attributes do not scale linearly– congestion– quality– reliability– acceptance

AutoPilots must be able to reason over attributes with various CDFs in subjective time

September 20, 2001

2001 Observation

Many non-linear, environmental attributes exhibit characteristic CDFs over a universe of discourse

– congestion (exponential)

– strength of yes/no (parabola)

– magnitude of difference (logarithmic)

– reliability/mortality (bath tub)

September 20, 2001

2001 Research Goals

Develop a set of relevant perception functions producing Percepts by Fuzzy Membership Functions | 0≤i≤ for Service Place and Service attributes Develop a method to interpret the Percepts for individual attributes

Prove the multi-mass function developed in 2000 is pareto-optimal

Prototype and validate the Percepts

September 20, 2001

The notion of membership

For a “fuzzy” set A→[0,1], A is calledthe membership function and A(u) for u U is called the degree of membership of u in the fuzzy set.

The degree of membership is not intended to convey a likelihood or probability that u has some particular attribute.

September 20, 2001

2001 Research Tasks

Design ways to get “reasonable” membership functions

Functions should have good correspondence to the subjective notions they represent

Functions should be based in theory, i.e. a characteristic function over the universe values of the attribute.

September 20, 2001

The Notion of Perception

An Agent’s life is finite in the system

An Agent carries a Phenotype and Genotype (task signature) yielding an expectation of the duration of work

An Agent must therefore “sense” its own mortality with regard to achieving its goal, i.e. reason in subjective time.

September 20, 2001

Example - Perceiving Congestion

Perception

Safe Region

Unsafe Region

Waiting Time as a Function of Service Place Utilization

The vertical line can be moved to the left according to the agent’s subjective model of time. “Congested”nodes need not be considered in the mobility decision.

Theoretical Basis

Characterizing the World

September 20, 2001

Trader Place is a Sensor with Memory

At each update interval the following is reported from each Service Place to its Trader Place– Service Place Name < name >

– Node Queue Length Lq

– Agent Service Rate μ– Agent Arrival Rate λ

A Service Place can inquire to the Trader Place <?World> and receive response < {[SP1, Lq,μ,λ],s1,s2,...,sk}, ..., {[SPn, Lq,μ,λ ],s1,s2,...,sm} >

September 20, 2001

Observation

Trader Place update intervals are relatively long compared to agent arrival rates and service rates

Each Trader Place Update is a snapshot of one state of the Universe at a near past instant of measurement

Trader Advertisements are “recent history”, not current state.

September 20, 2001

Agent Sensory Functions

An Agent can enquire to the Service Place <?D,Service_Place_Name> with response <Service_Place_Name,h> where d is in hops.

An Agent can enquire to the situated Service Place <?Environment> with response <Lq,μ,λ> for current local information

An Agent can Inquire to the Service Place <?service_name> and receive reply < [SP1, Lq,μ,λ] ... [SPn, Lq,μ,λ] > where SPn is a Service_Place_Name.

September 20, 2001

Argument for Exponential Streams In The Agent Population

At any observation SP staten can only transition to staten+1 (birth) or staten-1 (death), independent of arrival rate or time. This is the memoryless property of an exponential stream.

Exponential distribution is the limiting distribution of the normalized statistic of random samples drawn from continuous populations

Exponential distribution provides the least information where information content has entropy. It is the most random law and is a conservative approach to modeling the agent population as a dynamic entity as we move to an A-Life model of the AutoPilot agency.

September 20, 2001

Service Place Population Characterization

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September 20, 2001

Service Place State Characterization

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September 20, 2001

Service Place Effectiveness

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September 20, 2001

Service Place Effectiveness continued

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Theoretical Basis

The Notion of Fuzzy Sets and Membership

September 20, 2001

The notion of a fuzzy set

A “crisp” set is defined

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A “fuzzy” subset of a set U is a function

1,0U

On the Powerset P(U) of all subsets of U are the familiar functions of union, intersection and complement.

autopilot 2001

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