Multi-agent Oriented Constraint Satisfaction

Authors: Jiming Liu, Han Jing and Y.Y. Tang

Speaker: Lin XuCSCE 976, May 1st 2002

Outline

1. Introduction2. The multi-agent model3. Approximate solution4. Empirical studies on extended

ERA methods5. Discussion6. Summary

Introduction

CSPs Related work Multi-agent system The proposed approach

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

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

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

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 searchAlso: Hill-climbing, min-conflicts, MCRW and

GSAT

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.

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

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

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

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

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

The multi-agent model

ERA fundamentals

The basic ERA algorithm

Propitiates of the basic algorithm

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

ERA fundamentals (cont’d)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, A={a1, 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}

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

EnvironmentEnvironment size:

N rows (n variable) E=<row1, row2, …, rown> Rowi=<lattice1i, lattice2i, …, lattice|Di|i> 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

Agents

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

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

System schedule

Time step =0: the system is initialized Time step time step+1:one 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

The basic ERA algorithm

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

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

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

N-queen problem

Coloring problem

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

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

Questions?If not, let’s start the

discussion