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 9.11 Lehman financial shock in earthquake and tunami 7/31/2012Kazuhiro Minami2 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) 7/31/20123Kazuhiro Minami

Resilience = Resistance + Recovery Taoi-cho, Miyagi Pref Logstaff et al., “Building Resilient Communities,” Homeland Security Affairs, Vol VI, No.3, /31/2012Kazuhiro Minami4

Goal: How to make our systems more resilient against large unexpected events? 5 Financial 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 6 Redundancy Diversity Adaptability Multiple pathways for 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 7

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 Each robot has ten binary features (e.g., 2-leg/4-leg, flying/non-flying, …) E.g., C: “fit” configurations Resource 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 C 1, C 2, …, C t, … Constraint C A Subset of 2 (set of all 1,024 configurations) A robot is fit if its configuration is in C 9

Represent a changing environment as a sequence of dynamic constraints 10 CtCt ` ` C t+1 Time tTime t+1 fit unfit

Need to pay a cost for adaptation 11 Resource Adaptation System 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 12

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? 13

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 14

Diversity at the beginning helps a population survive longer 15 ParameterValue Initial population size 100 Agent bit length 8 Constraint size26 Constraint transition continu ous Adaptation strategy random Adaptation speed 1 Time #Agents

Two adaptation Strategies 1. Random strategy (flip one bit randomly) 2. Intelligent strategy (flip one bit to be closer to the constraint) Constraint

If robots adapt intelligently, the population grows much faster 17 Time #Agents Time

If agents share the common resource, the sustainability of a system can be greatly improved 18 Shared resource Individual resources 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 19

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) 20

21 Backup

We consider three types of constraints Disruptive changes: a new constraint C t is generated randomly at each time t 2. Small changes: a new constraint C t is generated from C t-1 by adding a neighbor configuration into C t-1 or removing a configuration in C t-1 T = tT = t-1T = t+1 T = tT = t-1T = t+1 3. Small changes with continuous topology: Same as case 2, but all configurations in C t are connected T = tT = t-1T = t+1

Measure diversity considers population abundance of each type 23 where N is the size of a population and p i is the size of an individual i Example 1: if N=5, Pr(`1101’) = 5, then D = 5 2 /5 2 = 1 Example 2: if N=5, size(`1101’) = 3, and size(`1111’) = 2, then D = 5 2 / = 25/13 = 1.92