Evaluating Resilience Strategies
Based on an Evolutionary Multi agent System
Kazuhiro Minami, Tomoya Tanjo, and Hiroshi
Maruyama
Institute of Statistical Mathematics, Japan
December 4, 2013
CyberneticsCom 2013
We sometimes have an unexpected event
• 3.11 earthquake and
tunami
• 9.11
• Lehman financial shock
in 2008
• 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
7/31/2012
Kazuhiro Minami
2
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)
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Kazuhiro Minami
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Resilience = Resistance + Recovery
Logstaff et al., “Building Resilient Communities,” Homeland Security Affairs, Vol VI, No.3, 2010
+
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
7/31/2012
Kazuhiro Minami
4
Goal: How to make our systems more resilient
against large unexpected events?
Financial
Crisis
Malicious
Attackers
Natural
Disasters
Civil
Infrastructure
Financial
Systems
Engineering
Systems
Society
Organizations
New
Technologies
5
Biological science might be a major source
of wisdom for resilience engineering
Redundancy
Multiple pathways
for metabolism
Diversity
Adaptability
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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 redundancy
8
Multi-agent simulations
based on a population genetics model
Colony of n agents
C: “fit” configurations
Resource
Each robot has ten binary
features (e.g., 2-leg/4-leg,
flying/non-flying, …)
E.g., <0110111011>
Constraint C
A Subset of 2(set of all 1,024
configurations)
A robot is fit if its
configuration is in C
• 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, …
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Represent a changing environment as
a sequence of dynamic constraints
fit
unfit
unfit
`
fit
fit
fit
Ct
Time t
fit
unfit
Ct+1
Time t+1
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Need to pay a cost for adaptation
Remove
Add
Resource
Unfit
System
bitstring
fit
10110010
10110011
10110011
Adaptation
Adaptation
An adaptation in our model is much faster than that in biological systems
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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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#Agents
Diversity at the beginning helps a population
survive longer
Time
Parameter
Value
Initial
population size
100
Agent bit
length
8
Constraint size
26
Constraint
transition
continu
ous
Adaptation
strategy
random
Adaptation
speed
1
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Two adaptation Strategies
1. Random strategy
(flip one bit randomly)
Constraint
10110110
2. Intelligent strategy
(flip one bit to be closer to the constraint)
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#Agents
If robots adapt intelligently,
the population grows much faster
Time
Time
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If agents share the common resource, the
sustainability of a system can be greatly improved
Sudden changes
of the constraint
Individual
resources
Sudden changes
of the constraint
Shared
resource
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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
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We consider three types of constraints
1. Disruptive changes: a new constraint Ct is generated randomly at each time t
T = t-1
T=t
T = t+1
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 = t-1
T=t
T = t+1
3. Small changes with continuous topology: Same as case 2, but all configurations in Ct are
connected
T = t-1
T=t
T = t+1
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Measure diversity considers
population abundance of each type
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
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