Evaluating Resilience Strategies Based on an Evolutionary Multi agent System

Kazuhiro Minami, Tomoya Tanjo, and Hiroshi Maruyama

Institute of Statistical Mathematics, Japan

December 4, 2013CyberneticsCom 2013

We sometimes have an unexpected event

• 9.11• Lehman financial shock

in 2008

• 3.11 earthquake and tunami

7/31/2012 Kazuhiro Minami 2

• We cannot completely prevent such disasters• Instead, we should aim to design a system that contains a damage

and is readily recoverable to an acceptable level

Resilience: Definition

“Capacity of a (social-ecological) system to absorb a spectrum of shocks or perturbations and to sustain and develop its fundamental function, structure, identity, and feedbacks as a result of recovery or reorganization in a new context.”

-- by Buzz Holling (1973)

7/31/2012 3Kazuhiro Minami

Resilience = Resistance + Recovery

Taoi-cho, Miyagi Pref.http://www.bousaihaku.com/cgi-bin/hp/index2.cgi?ac1=B742&ac2=&ac3=1574&Page=hpd2_view http://fullload.jp/blog/2011/04/post-265.php

+

Logstaff et al., “Building Resilient Communities,” Homeland Security Affairs, Vol VI, No.3, 2010

7/31/2012 Kazuhiro Minami 4

Goal: How to make our systems more resilient against large unexpected events?

5Financial Systems

Civil Infrastructure

Engineering Systems

Society

Organizations

Natural Disasters

Financial Crisis

New Technologies

Malicious Attackers

Biological science might be a major source of wisdom for resilience engineering

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Redundancy

Diversity Adaptability

Multiple pathwaysfor metabolism

Redundancy and diversity are heavily used techniques in Computer Science

• Maintain a backup system in a cloud service– Financial companies was able to continue their services

after 9.11 event– Many web sites maintain multiple copies of the server

• Software diversity makes it difficult for hackers to compromise multiple servers of the same service– Change compiler options or use different algorithms

• Ethernet uses a randomization technique to avoid message collision

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However, applying those techniques to real-world systems is NOT so trivial

• Cost for replication would be high in NON-ICT systems

• Replication sometimes decreases the quality of service– Inconsistency of data– Timely monitoring of a system is more difficult; thus

need to sacrifice the adaptability of a system• Toyota’s supply chain system put precedence

on adaptability over redundancy8

Multi-agent simulationsbased on a population genetics model

Colony of n agents Each robot has ten binary features (e.g., 2-leg/4-leg, flying/non-flying, …)E.g., <0110111011>

C: “fit” configurationsResource

• Resource Reserve R– Fit robots contribute to build up R – A robot consumes one unit for reconfiguring its one feature

• The colony is resilient if robots can survive a series of changing constraints C1, C2, …, Ct, …

Constraint CA Subset of 2(set of all 1,024

configurations)

A robot is fit if its configuration is in C

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Represent a changing environment as a sequence of dynamic constraints

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Ct

`

Ct+1

Time t Time t+1

fit

fit

fit fit

fit

unfit

unfit

unfit

Need to pay a cost for adaptation

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Resource

Adaptation10110010 10110011 10110011System

bitstring

Unfit fit

Remove Add

An adaptation in our model is much faster than that in biological systems

Adaptation

A robot could produce a clone or die

• Make a clone– when the amount of the resource is doubled

• Die – when the resource is used up

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Metrics of resilience in our model

• Redundancy– How much resource does a robot maintain?

• Diversity – Diversity index

• Adaptability– How many bits a robot can flip at a time?

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Multi-agent Simulations• Define initial parameters

– Population size– Bit length of a robot– Size and type of constraints– Initial amount of each robot’s resource– Initial diversity index– Adaptation strategy

• Random or intelligent• #flips at a time

• Run the system at 100 time steps• Examine how a population size, the diversity index vary

over time

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Diversity at the beginning helps a population survive longer

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Parameter Value

Initial population size

100

Agent bit length

8

Constraint size 26

Constraint transition

continuous

Adaptation strategy

random

Adaptation speed

1

Time

#Age

nts

Two adaptation Strategies

1. Random strategy (flip one bit randomly)

2. Intelligent strategy (flip one bit to be closer to the constraint)

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10110110

Constraint

If robots adapt intelligently, the population grows much faster

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Time

#Age

nts

Time

If agents share the common resource, the sustainability of a system can be greatly improved

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Sharedresource

Individualresources

Sudden changes of the constraint

Sudden changes of the constraint

Summary• Explore design space parameterized by three

resilience properties based on an evolutionary multi-agent system– Redundancy– Diversity– Adaptability

• Obtain quantitative initial results regarding design strategies for building resilient systems

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Future work: Further possibilities for adaptation strategies

• Local vs Global– Local: Each robot makes its own decision independently

from others– Global: There is a global coordination. Every robot must

follow the order– Mixed

• Complete vs Incomplete knowledge on C– Complete knowledge: max 10 steps to become fit again– Incomplete knowledge: probabilistic (max 1023 steps if

the landscape is stable)

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Backup

We consider three types of constraints

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1. Disruptive changes: a new constraint Ct is generated randomly at each time t

2. Small changes: a new constraint Ct is generated from Ct-1 by adding a neighbor configuration into Ct-1 or removing a configuration in Ct-1

T = tT = t-1 T = t+1

T = tT = t-1 T = t+1

3. Small changes with continuous topology: Same as case 2, but all configurations in Ct are connected

T = tT = t-1 T = t+1

Measure diversity considers population abundance of each type

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where N is the size of a population and pi is the size of an individual i

Example 1: if N=5, Pr(`1101’) = 5, then D = 52/52 = 1

Example 2: if N=5, size(`1101’) = 3, and size(`1111’) = 2, then D = 52/32+22 = 25/13 = 1.92