Multi-agent Oriented Constraint Satisfaction

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Multi-agent Oriented Constraint Satisfaction

• Authors Jiming Liu, Han Jing and Y.Y. Tang
• Speaker Lin Xu
• CSCE 976, May 1st 2002

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Outline

1. Introduction
2. The multi-agent model
3. Approximate solution
4. Empirical studies on extended ERA methods
5. Discussion
6. Summary

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Introduction

• CSPs
• Related work
• Multi-agent system
• The proposed approach

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CSPs

• A CSP consists of
• A finite set of variables
• A domain set, containing a finite and discrete
  domain for each variable
• A constraint set, each constraint is a set of
  tuples indicating the mutually consistent values
  of the variables
• The solution, S, for a CSP is an assignment to
  all variables such that the assignment satisfies
  all given constraint
• Example n-queen, coloring problem

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Related work

• General methods for solving CSP
• generate-test (GT)
• generates each possible combination of the
  variables systematically and then checks whether
  it is a solution
• Backtracking (BT)
• assignment values to variables sequentially
  and then checks constraints for each variable
  assignment
• In this respect, BT is more efficient than GT

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Improvement for BT

• Avoid thrashing
• Consistency techniques (Arc consistency and
  k-consistency)
• Avoid both thrashing and redundant-work
• Dependency-directed backtracking scheme
• Increasing the efficiency
• Search Order
• BT is still unable to solve nontrivial
  large-scale CSPs in a reasonable runtime

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Improvement for GT

• Stochastic and heuristic algorithms
• most popular ideas is to perform local
  search
• Three key elements in local search
• Configuration
• Evaluation value
• Neighbor
• Local search uses repair or hill climbing
• To avoid local optima, random-walk and tabu
  search
• Also Hill-climbing, min-conflicts, MCRW and GSAT

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Min-conflicts heuristics Minton

• Selects a new value that minimizes the number
  of outstanding constraint violation after each
  step
• The multi-agent approach utilized the idea of
  inconsistency reduction on a complete initial
  assignment
• The approach differs from the min-conflicts
  approach in a number of ways.

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Other methods

• Other methods for solving CSPs Neural Network
  and Genetic Algorithms
• all methods, techniques have their advantages and
  disadvantages
• BT small size problem, stable and complete
• Local search large scale problem, incomplete

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Multi-agent systems

• Computational systems in which several agents
  interact or work together in order to achieve
  goals
• Agent may be homogeneous or heterogeneous
• Agent may have the common goals or distinct goals

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Distributed constraint satisfaction

• Distributed CSP is a CSP in which variables and
  constraints are semantically partitioned into
  sub-problems, each of which is solved by an agent
  
• The agents have to comply with certain
  constraints among them
• Find a solution requires that all agents find the
  values for their variables that satisfy not only
  their own constraints but also interagent
  constraints
• Yokoo et al. developed algorithm
• asynchronous backtracking
• asynchronous weak-commitment search
• multi-agent real-time-A algorithm

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Swarm-like systems

• Swarm is a formulation for simulating distributed
  multi-agent systems, which involves three key
  environment
• Living environment
• Agents with reactive rules
• Schedule serving
• Liu developed
• an evolutionary autonomous agent system
• An energy-based artificial-life model for solving
  n-queen

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The proposed approach

• Environment, Reactive rules, and agents (ERA)
• Intended to provided an alternative, multi-agent
  formulation that can solve general CSPs and to
  find approximate solution without too much cost
• This system self-organizes itself
• The main difference between ERA and local search
  the evaluation value

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The multi-agent model

• ERA fundamentals
• The basic ERA algorithm
• Propitiates of the basic algorithm

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ERA fundamentals

• The notions of agent and multi-agent system can
  be defined as
• An agent is a virtual entity
• Be able to live and act in the environment
• Be able to sense its local environment
• Be driven by certain objectives
• Have some reactive behaviors

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ERA fundamentals (contd)

• A multi-agent system is a system that contains
• An environment E is a space in which the agent
  live
• A set of reactive rules, R, governing the
  interaction between the agents and their
  environment, they are the laws of the agent
  universe
• A set of agents, Aa1, a2, a3,, an
• Goal examine how exact or approximate solutions
  to CSPs can self-organized by a multi-agent
  system, consisting of E, R, A

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Overview of the multi-agent formulation

• Environment records the number of constraint
  violations of the current state
• Agent represents a variable and the position of
  agent corresponds the value
• Objective is the move to a position whose
  constraint violation number is 0
• Solution state is when every agent finds its
  zero-position

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Environment

• Environment
• size
• N rows (n variable) Eltrow1, row2, , rowngt
• Rowiltlattice1i, lattice2i, , latticeDiigt
• E is an array of size ? Dk.e(I,j)
• Values
• Domain value e(i,j).value records the ith value
  of domain Dj
• Attack ((x1, y1), (x2, y2))
• Violation number e(I, j).violation
• Zero-position

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Agents

• Agents trying to find better positions that can
  lead them to a solution based on certain reactive
  moving behaviors

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Local reactive behaviors

• To find a solution state, the agents will select
  and execute some predefined local reactive
  behaviors
• Least-move
• Better-move
• Random-move

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System schedule

• Time step 0 the system is initialized
• Time step ? time step1one unit increment of the
  system clock, all agent have a chance to decide
  their moves
• End all agents are at zero-positions or its
  clock exceeds a time threshold

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The basic ERA algorithm
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Properties of the basic ERA algorithm

• Termination
• Correctness
• Complexity
• Space complexity is O(?Di)
• Time complexity of the initialization is O(?Di)
• Time complexity of each step is O(n?Di) in the
  worst case

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Approximate solution

• Each state represents an approximate solution
• The system always evolves toward a better state
  in which more constraints are satisfied
• After a few step, the assignments of most
  variables will satisfy constraints

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Empirical studies on extended ERA methods with
behavior prioritization and different selection
probabilities

• Presents several empirical results on solving
  different n-queen and coloring problem
• Discusses how to apply and implement this
  approach by choosing the probabilities of
  least-move and random-move
• Examines the effectiveness of prioritizing agent
  behaviors in order to efficiently derive an
  approximate solution

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N-queen problem
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Coloring problem
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Discussion

• Comparison with min-conflicts heuristics
• Comparison with Yokoo et al.s distributed
  constraint satisfaction
• Remarks on partial constraint satisfaction
• Remarks on agent information and communication
  for conflict-check
• Remarks on sequential-iteration implementation

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Summary

• Described a multi-agent oriented approach to
  solving CSP ERA
• Introduced three reactive behaviors better-move,
  least-move and random-move
• Presented several empirical studies
• Compared the ERA with some of the existing
  heuristic

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Questions?If not, lets start the discussion