An Investigation of Reorganization Algorithms

1
An Investigation of Reorganization Algorithms

• Master Defense
• by
• Christopher Zhong

2
Outline

• Introduction
• Background
• Reorganization Algorithm
• Problems
• Reducing Time Complexity
• Design Metrics
• Conclusions
• Question

3
Introduction

• Complex / dangerous task performed by
  computational systems
• Require at least one team of human controllers
• Multiagent systems
• Do not provide notion of controlling entity
• Organization-based approach
• Social definition a group of people who are
  coordinating together to achieve one or more
  goals
• Adaptable to dynamic environments
• Reorganization
• Algorithms for reorganization

4
Background

• Search Algorithms
• Examples BFS / DFS / A
• Organization-Based Models
• OperA (Organizations per Agent)1
• OMNI (Organizational Model for Normative
  Institutions)2
• OMACS (Organization Model for Adaptive
  Computational Systems)

• Virginia Dignum. A Model for Organizational
  Interaction Based on Agents, Founded in Logic.
  PhD thesis, Utrecht University, 2004.
• Virginia Dignum, Javier Vázquez-Salceda, and
  Frank Dignum. Omni Introducing social structure,
  norms and ontologies into agent organizations. In
  PROMAS, pages 181198, 2004.

5
Background OperA

• Multiagent systems framework
• Organizational Model
• Defines characteristics of organization
• Social Model
• Constrains the actions of agents
• Interaction Model
• Defines how agents communicate

6
Background OMNI

• Based on OperA and HarmonIA1
• Consists of Normative Dimension, Organizational
  Dimension, and Ontological Dimension

• Javier Vázquez-Salceda and Frank Dignum.
  Modelling electronic organizations. In Vladimir
  Marik, Jörg Müller, and Michal Pechoucek,
  editors, Multi-Agent Systems and Applications
  III, volume 2691 of LNAI, pages 584593.
  Springer-Verlag, 2003.

7
Background OMACS

• Consists of goals (G), roles (R), agents (A),
  capabilities (C), assignment set (?), and
  policies (P)
• ? is a tuple of agents, roles, and goals
  represented as ? a, r, g ?
• The potential() computes the score of an
  assignment ? a, r, g ?

8
Background OMACS

• oaf() function
• Computes organizational score based on current
  assignment set
• Value ranges from 0 ?
• rcf() function
• Computes the score of an agent playing a
  particular role
• Value ranges from 0 1

9
Background OMACS
10
Reorganization Algorithm

• function reorganize(oaf(), ?G, ?A)
• 1 for each goal g from ?G do
• 2 for each role r that achieves g do
• 3 maps ? ? r, g ?
• 4 end for
• 5 end for
• 6 setOfSetsOfAssignments ? P?(powerset(maps))
• 7 for each agent a from ?A do
• 8 for each set of assignments s from
  setOfSetsOfAssignments do
• 9 if a is capable of playing s then
• 10 potentialAgentAssignments ? ? a, s ?
• 11 end if
• 12 end for
• 13 end for
• 14 combinations ? combinations(P?(potentialAgent
  Assignments))
• 15 for each combination i from combinations do
• 16 for each assignment x from
  potentialAgentAssignments do
• 17 ? ? ? x.a, x.si ?
• 18 end for

• Optimal Reorganization Algorithm
• Time complexity
• Best ?(2g ? ravgg)
• Worst ?(2g ? ravgg ? a)
• Not practical for runtime

11
Problems

• oaf() and rcf() functions are black boxes to any
  general purpose reorganization algorithms
• Example oaf() for two assignments ? a, r1, g ?
  and ? a, r2, g ? can return
• 0
• 1
• gt 1

12
Reducing Time Complexity

• Extend OMACS
• Distributing the algorithm
• Assignment policies

13
Extending OMACS

• Expose internal workings of both oaf() and rcf()
  functions
• Encode relevant information into a data structure
• Provide an interface that algorithms can use

14
Distributing the Algorithm

• A distributed algorithm might lead to a better
  class of time complexity
• Simple distributed variant

15
Simple Distributed Algorithm

• Previous algorithm is broken into two parts
• Each agent computes their own potential
  assignment set and sends it to every other agent
• Computing optimal assignment set
• Time complexity
• Best ?((g ravgg) ? 2g ? ravgg / a ? ?)
• Worst ?(2g ? ravgg ? a ?)
• Improve algorithm by distributing the oaf()
  computation
• Observe the communication costs associated with
  distributed algorithms
• Communication costs depends on environment

• function reorganize(oaf(), ?G, ?A)
• 1 for each goal g from ?G do
• 2 for each role r that achieves g do
• 3 maps ? ? r, g ?
• 4 end for
• 5 end for
• 6 setOfSetsOfAssignments ? P?(powerset(maps))
• 7 for each agent a from ?A do
• 8 for each set of assignments s from
  setOfSetsOfAssignments do
• 9 if a is capable of playing s then
• 10 potentialAgentAssignments ? ? a, s ?
• 11 end if
• 12 end for
• 13 end for
• 14 combinations ? combinations(P?(potentialAgent
  Assignments))
• 15 for each combination i from combinations do
• 16 for each assignment x from
  potentialAgentAssignments do
• 17 ? ? ? x.a, x.si ?

16
Assignment Policies

• Varying effects on time complexity
• Example agents can only play one role at a
  time policy
• Agents can play 5 roles, each role achieves 3
  goals
• Without policy 25 ? 3 32,768
• With policy 5 ? 3 15
• 4 such similar agents
• Without policy 32,7684 1, 152, 921, 504, 606,
  846, 976
• With policy 154 50,625

17
Assignment Policies

• Applied at first policy reduction
• Two ways to apply the policy
• Apply after (Version 1)
• Pruning after power set function
• Apply during (Version 2)
• Replace power set function
• Compared results of test cases
• E.g. 3 goals, 2 roles, 3 agents, average 2 roles
  per goal, average 3 agents per role

• function reorganize(oaf(), ?G, ?A)
• 1 for each goal g from ?G do
• 2 for each role r that achieves g do
• 3 maps ? ? r, g ?
• 4 end for
• 5 end for
• 6 setOfSetsOfAssignments ? P?(powerset(maps))
• 7 for each agent a from ?A do
• 8 for each set of assignments s from
  setOfSetsOfAssignments do
• 9 if a is capable of playing s then
• 10 potentialAgentAssignments ? ? a, s ?
• 11 end if
• 12 end for
• 13 end for
• 14 combinations ? combinations(P?(potentialAgent
  Assignments))
• 15 for each combination i from combinations do
• 16 for each assignment x from
  potentialAgentAssignments do
• 17 ? ? ? x.a, x.si ?
• 18 end for

18
Assignment Policies
19
Design Metrics

• PRiMO (Predictable and Reliable Multiagent
  Organizations) research group
• Measure models in terms of flexibility versus
  efficiency
• Flexibility means how adaptable the model is to a
  dynamic environment
• Efficiency means how much computational power is
  required to reorganize

20
Conclusions

• Provided an optimal algorithm
• Preliminary results for further improvement of
  time complexity
• Design metrics

21
Questions