By Dr Simon Martin CHORDS Group Division of Computing Science and Mathematics School of Natural Sciences University of Stirling, Stirling FK9 4LA. [email protected] lti-agent based Cooperative Approa to Scheduling and Routing
Dec 14, 2015
ByDr Simon Martin
CHORDS GroupDivision of Computing Science and Mathematics
School of Natural Sciences University of Stirling, Stirling FK9 4LA.
A Multi-agent based Cooperative Approach to Scheduling and Routing
ContentsIntroduction – What are multi or intelligent agents?
Multi/Intelligent -agentsIEEE FIPA agent standard
MACS Agent-based platform
Case StudiesVRPPFSP
FairnessFairness in nurse rosteringFairness in requirements assignments for the next release problem
Conclusions
• Future Work
Thank you
Multi/Intelligent -agents
Agents maintain an internal representation of their environment.
They communicate by Asynchronous messaging.
They are autonomous, no one process is in overall control
They are capable of completing a task on their own or can cooperate
This means they can execute distributed algorithms where no agent is in overall control
IEEE FIPA standard
There is an IEEE standard called the Foundation for Intelligent Physical Agents (FIPA)
There are are number of Open source FIPA platforms:
FIPA-OShttp://fipa-os.sourceforge.net/index.htm
Jadex Agentshttp://www.activecomponents.org/bin/view/About/New+Home
JIAC Intellient Agentshttp://www.jiac.de/
JADEhttp://en.wikipedia.org/wiki/Java_Agent_Development_Framework
FIPA compliant Multi-Agent Platform
AMS
DF
AMS
DF
The DF (Directory Facilitator) provides a directory which announces which agents are available on the platform.
The AMS (Agent Management System) controls the platform. Is the only one who can create and destroy other agents, destroy containers and stop the platform.
Inter platform communication
Multi-Agent Cooperative System(MACS)
Meta-heuristics require careful tuning to a specific problemThey require parameter tuningBalancing intensification and diversification
Some meta-heuristics are better at some problems than others
They have different strengths and weaknesses
But what if there was a of combining these strengths and weaknesses in one system?
This might be achieved if different meta-heuristics cooperated with each other
MACS
Problem definition
Launcher Agent
Cooperating Agent
Cooperating Agent
Cooperating Agent
Cooperating Agent The Launcher Agent (LA) sends the same problem to each agent
MACS
Launcher Agent
Cooperating Agent
Cooperating Agent
Cooperating AgentAgents cooperate by passing Best edges
MACS -again ....
Problem definition
Launcher Agent
Cooperating Agent
Cooperating Agent
Cooperating Agent
Cooperating Agent Each agent sends its best overall solution to the launcher agent. The LA takes the bestAnd writes it to file
MACS – just to ram it home
Multi/Intelligent -agents
Image: Wikipedia by Utkarshraj Atmaram. http://en.wikipedia.org/wiki/Intelligent_agent#mediaviewer/File:IntelligentAgent-Learning.png
Inside a Multi/Intelligent -agent
Ontology for Scheduling and Routing
Graph
Edge
Constraints
Vertices
Cities Jobs Assignments
The Vertex objectIs the interface between theframework and specific Problem instance
Problem specific data
interface
Objects of the agent-based framework
Problem specific objects inheriting from the abstract vertex object
Subgraph
Customers & Depots
Cooperation protocol
Case Studies
Permutation Flowshop SchedulingMeta-heuristic Randomised NEHA Juan et. al
Capacitated Vehicle RoutingRandomised Clarke Wright Savings AlgorithmA Juan et. al
Fairness In Nurse RosteringVNS, Simulated Annealing and Tabu SearchMartin, Smet, Ouelhadj, Vanden Berghe, Özcan.
The platform has been applied to three case studies
Permutation Flowshop Scheduling
Permutation Flowshop SchedulingTaillard benckmark instance tai_051_50_20
Capacitated Vehicle Routing
Capacitated Vehicle Routing
Augerat Benchmark instance A-n63-k9
The Nurse Rostering problem
The Scheduling of hospital personnel is Particularly challenging because:
There are different staffing needs on different days and shifts
Staff work in shifts
Healthcare institutions work around the clockThe need for day and night shifts
The correct staff mix for each ward
Many different employment contractsPart-time Special arrangements
Fairness so that staff are happy
The standard objective function
Let C be the set of constraints. Wc is weight associated with a given constraint N
is the number of violations of that constraint.
Is the number of roster constraints
MinWS = minimise the sum of the sum of all nurses violations
Models of Fairness
Models of Fairness
New Fairness objective functions
MinMax = minimise the number of nurses × worst nurse violation
MinDev = minimise the sum of deviations from the average + the numbers of nurses × the mean roster quality
MinError = minimise the sum of the differences of max roster value – min roster value a + the mean roster quality
MinSS = minimise the sum of the squared violations associated with assigning a nurse to a given roster
Models of Fairness
Models of FairnessMeasuring fairness is done with the Jains Fairness function (Jain et al., 1984; Muhlenthaler and Wanka, 2012).
It is the sum of the squared violations in assigning a nurse to a given roster divided by the number of nurses times the squared value of assigning a nurse to a roster.
Its values range from the worse case 1/N to 1 where N is the number of nurses to 1 where the roster is completely fair.
Fairness Results
Fairness Results
Tensor Online learning
The agent system has been updated:
A new learning system has been developed based on tensors
It still uses the same conversation structure as before
Instead of sharing edges the agents now share tensors made from incumbent solutions.
Cooperation Protocol with Tensors
Tensor Online learning
Agents are 20 best incumbent solutions.
The initiator agent, for that conversation, collects all the incumbent solutions.
The initiator then builds an tensor where n is the length of problem instance and m is the number of incumbent solutions.
The tensor build from adjacent matrices of each incumbent solution.
The initiator factorises the matrix. The result is an matrix called a basic frame.
The basic frame is treated as an adjacent matrix and converted back to a list of good edges. This list is shared with all the agents.
The agents update their short-term memories.
The agents then use the list of edges in short-term memory in conjunction with their metaheuristic to build new incumbent solutions.
Conclusions
Distributed asynchronous agent platform
Modular
Ontologies
Peer to Peer
Scalable
Future Work
Fairness in requirements assignments for the next release problem
Model each customers requirements on an agent Compare multi-objective approach to single objective approach
Improve the ontology to work on more problems
Improve the tensor learning system
Papers
Simon Martin, Djamila Ouelhadj, Pieter Smet, Greet Vanden Berghe, and Ender Ozcan. Cooperative search for fair nurse rosters. Expert Systems with Applications, 40(16):6674-6683, 2013.
Simon Martin, Djamila Ouelhadj, Patrick Beullens,Ender Ozcan,Angel A. Juan,Edmund.K.Burke. A MULTI-AGENT BASED COOPERATIVE APPROACH TO SCHEDULING AND ROUTING. under review European Journal of Operational Research October 2015.
Shahriar Asta, Simon Martin, Ender Ozcan, Edmund Burke. A Multi-agent System Embedding Online Tensor Learning for flow shop Scheduling. Submitted to Information Sciences, July 2015.
Thank you