Multi-objective and Multi-mode Assignment and Scheduling Problem

for large volume Surveillance

Olfa Dridi Saoussen Krichen Adel Guitouni

Salamanca, Spain, 19-30 September

OutlineScheduling Theory1.

Areas of Application2.

Problem Description3.

Literature Review4.

Proposed Model5.

Multi-criteria Genetic approach 6.

A bi-level ASP7.

Integration in Inform Lab8.

Conclusion9.

1. Scheduling Theory• The project scheduling and resource management

dates from five hundred years: The Egyptian pyramids, the Great wall of China, the temples of Maya by using rudimental tools.

• Scheduling theory was emerged as an active research area in the early 1950s.

• In the 1980s, different directions were pursued in academy and industry. Since then, the field has attracted a lot of researcher’s attention and has become an important branch of operations research.

• Project Scheduling and resource management solutions are in demand throughout the world as a fundamental tools for the survival and success of the compagnies.

This is what can happen without effective resources management

2. Areas of Application• Production scheduling• Large volume surveillance problem• Robotic cell scheduling• Computer processor scheduling• Timetabling• Crew scheduling• Railway scheduling• Air traffic control

• The large volume surveillance problem is a complex decision problem characterized by the employment of mobile and fixed assets to a large geographic area in order to accomplish the maximum number of surveillance tasks.

• Example of surveillance problem:

- fishing boat in distress

- search of illegal immigrants

- piracy situations

3. Problem Description

System constraints

What is the ‘best’ and feasible resources assignment and task scheduling to achieve mission goals?

A set of heterogeneous and distributed resources

+A set of surveillance tasks

Problem

3.1. Research Problematic

3.2. Motivations

Surveillance TasksDistributed resources

There are few works related model the resource management for large volume surveillance as Multi-Objective and Multi-Mode Assignment and Scheduling problem.

4. Literature Review

Assignment and Scheduling

problem

Single modeMulti-mode

Without preemption

With preemption

Multi-Objectif Mono-Objectif

Nonrenewableresources

Renewable resources

• Multi-Mode• Each task can be

accomplished by one out of a set of different modes.

• executing time, cost and amount of resources depend on the adopted mode.

• Single Mode Each task has

only one execution mode, this means that the duration and the requirements for resources are constant.

• Multi-ObjectiveWe consider more than one objective to optimize.

we search not only the best optimal solution but the pareto optimal solutions.

xx

xx x

x

x

x

xx

x

xx

x

obj 1

obj2

• Single Objective We consider only one objective to

optimize. The main and the most used objective in literature is the minimization of the makespan which represents the total duration of the project.

objmin

• Renewable resourcesA known amount of resources available with its full capacity during the planning horizon. Example: machines, equipments, manpower.

• Nonrenewable resources

They are limited in amount and are not recoverable.

Example: financial budget

• Without Preemption

A Task cannot be interrupted once it has been started.

• With Preemption

A Task can be interrupted after each integer unit of its processing time.

Exact

Branch & Bound

Dynamic programming

Heuristics

Genetic Algorith

m

Ant Colony

Tabou search

Simulated

Annealing

…

Resolution approaches

e.g.:Sprecher et al. (1997) Heilmann (2003) Zhu et al. (2006)

e.g.: Li et al. (2008)e.g.: Mendes et al. (2009)Lova et al. (2009) e.g.: Loukil et al.(2005)e.g.: Lee et Lee (2003)

Ben Abdelaziz et al. (2007)Lo et al. (2008)

e.g.: Belfares et al. (2007)

Example of resolution approaches

Resource Assignment and Scheduling

problemMulti-mode

without Preemption

Multi-Objectif

Renewable resources

5. Proposed Model

Mode 1Mode 2

Mathematical Formulation

max

1 1,...,1 1 1

max ( )i

k k

T M Rt

i N im ijmt k j

Z t d x

max

21 1 1 1

i

k

T MN Rt

j ijmi t k j

Z c x

max

31 1 1 1 1 1

1 i i

k k

T M MN R Rt

ij ijm ijmi t k j k j

Z P x qN

Min makespan

Min Cost

Max probability of sucess

Objectives functions

System constraints

max1 1

, 1,..., , 1,...,i

k k

MNt tijm ijm j

i k

x q R j R t T

maxmax max

1 1 1 11

, 1,...,p k

k k ki

tTT M R T pjmt t

ijm pjm pmt k j tpt k

xtx Max tx d i N

m

1 1

11, 1,...,i

k

M R tijmk j

k

x i Nm

max

max11, 1,..., , 1,..., , 1,...,

k

T tijmtx i N j R k T

max0,1 , 1,..., , 1,..., , 1,..., , 1,...,k

tijm ix i N j R k M t T

The Multi-objective and Multi-mode Assignment and Scheduling Problem

NP-Hard• Genetic Algorithms have been implemented for

providing high-quality solutions to a wide variety of challenging scheduling problems.

• In this work, we investigate the ability of a genetic algorithm to effectively solve the Assignment and Scheduling Problem

1 , 1 2 2 1 3

mod

,..., ,..., , ,...,N N N N N

period prioritye

chromosome gene gene gene gene gene gene

6. A Multi-criteria Genetic Approach

Selection: elitism method

Crossover: random key

Mutation

Chromosome representation

Each solution chromosome is made of 3n genes ( n: number of tasks)

Genetic operators

• Consists of retaining the best individuals from the current population into the next generation based on their fitness value. This selection method is called elitist or elitism.

• It forms a succesful selection strategy used to ensure that the best solutions are preserved in the next generation and allows to converge towards the pareto frontier.

Selection Operator

• Two individuals are randomly selected from the current population to act as parents.

• For each gene a random number between [0,1] is generated. If the generated number is smaller than a threshold value, the gene of the first parent is copied into the offstring chromosome. Otherwise, the gene of the second parent is used.

• The threshold value is an input data and is called Crossover Probability.

Crossover Operator

• Randomly applied to explore other areas in the solution space and avoid the convergence caused by selection and crossover operators.

• The probability of the mutation Mr is inversely propotional to the population size.

• After the crossover has occurred, an individual can be selected from the current population for mutation. It consists to switch the mode associated to the selected task i based on its neighborhood set Hi of the resources’ combination.

Mutation Operator

Generate the initial populationinitialize the parameters

At iteration g

Select two chromosomes parents

Apply crossover operator

Evaluation of the new population (fitness)

Activate/Deactivate mutation

Stopping criterion

Stop

New population

noyes

Generate offstring chromosome

The Algorithm

The experimental results

• Cardinality of the approximation set

• Diversity of the approximation set

• Diversity of the pareto approximation front

1 1

1 1, log

log( )iN M ik ik

s i ii ki size size

n nD H avec H

N M pop pop

,

**

max ( ) ( )100, {1,2,3}known

i

x y P i iZ

i i

Z x Z yCov i

Z Z

sN

Wilcoxon signed –rank test

: 95.5%At confidence level

: 0.05level

• As we address simultaneously assignment and scheduling problem

• While the proposed approach is effective for medium assignment and scheduling problem,

• The proposed model becomes computationally intractable for large sized problem when adding some realistic assumptions.

• Hence, we propose a rigorous bi-level decomposition model that reduces the computational effort of the problem

• We decompose the original problem into an upper and a lower level.

7. The bi-level ASP

Objectif Minimize the makespan

Constraints Task

precedence constraints time window priority localization

Objectif Minimize the total cost

Constraints Resources

Availability fuel constraints/autonomy

Upper level: Scheduling

Lower level: Assignment Problem

InformLab simulator

Distributed Dynamic Information Fusion (DIF)

Distributed Dynamic Resource Management (DRM)

Goals SituationEvidence

Decision

8. The Integration to InformLab

• Cooperative Search need to be detected:

‘fish boat in distress’

• Non-Cooperative Search attemps to avoid detection:

‘illegal immigrants’

Integration process Scheduler code

Input dataModePlan

ModePlan Schedules

C/C++Data File

JavaNativeInterface (JNI)Dynamic library

InformLab Testbed

JavaScheduler classPlansExtractor classScheduleConverter class

Scheduler Interface

Schedules (Java object)ModePlan objects

ProxySchedules

Editor

Viewer

XML files

XML vignette

• we proposed a new formulation for the resource allocation and tasks scheduling for large volume surveillance problem.

• A Multi-criteria GA it was developed to solve the problem formulation

• The approach was tested using InformLab Multi-agent simulator

• We will propose an alternative model based on the bi-level formulation

9. Conclusion