Multi-agent Oriented Constraint Satisfaction Authors: Jiming Liu, Han Jing and Y.Y. Tang Speaker: Lin Xu CSCE 976, May 1st 2002

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

Environment size: N rows (n variable) E= Rowi= E is an array of size  |D k |.e(I,j) Values Domain value: e(i,j).value records the i th value of domain D j 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