Upload
nichelle-brown
View
32
Download
4
Embed Size (px)
DESCRIPTION
Analysis of a Benchmark Generator for the Reactive Scheduling Problem. Amedeo Cesta 1 , Nicola Policella 2 , a nd Riccardo Rasconi 1 1 ISTC-cnr, Institute for Cognitive Science and Technology 2 ESA/ESOC, European Space Agency. Introduction. - PowerPoint PPT Presentation
Citation preview
Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & RasconiScheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Analysis of a Benchmark Generator for theReactive Scheduling Problem
Amedeo Cesta1, Nicola Policella2, and Riccardo Rasconi1
1ISTC-cnr, Institute for Cognitive Science and Technology2ESA/ESOC, European Space Agency
2Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Introduction
• Q8: Should the competition include benchmarks for dynamic scheduling problems, such as on-line scheduling and scheduling execution monitoring?
– Reactive Scheduling Test-sets Generator (this talk)
• Our goal is to produce a General Framework for Project Scheduling Problems
3Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Project Scheduling
• We focus our attention on Project Scheduling
• Scheduling is primarily concerned with figuring out WHEN tasks/activities should be executed so that the final solution guarantees “good performance”– Management of space missions– Transportation scheduling– Production chains in a factory
• Different techniques have been studied by many scientific communities, such as the Artificial Intelligence, Management Science and Operations Research
4Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Project Scheduling Problems [RCPSP/max]
t
r1
t
r2
resources
c2=3
c1=2resource
constraints
Project Activity Network
temporal constraints
[2, 5]
4 18
4
5
1
1 51 0
612
0
max separation
5Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Schedule’s life is short!
• Unfortunately the synthesis of initially feasible solutions is hardly ever sufficient!
– In real working environments, unforeseen events tend to quickly invalidate the schedules predictive assumptions
• Approaching a scheduling problem requires the coupling of – a predictive scheduling engine, able to propose a possible
solution in a compact representation, and – a reactive scheduling engine, able to manage the current
solution and to adjust the schedule at execution time
6Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Broadening Project Scheduling Definition
• A broader definition of project scheduling problem, consists in the following two components:
– the static sub-problem (or Predictive Scheduling): given a set of activities (or tasks) and a set of constraints (time and/or resource), it consists in computing a feasible assignment of start and end times for each activity.
– the dynamic sub-problem (or Reactive Scheduling): it consists in monitoring the actual execution of the schedule and repairing the current solution (or producing brand new solutions), every time it is necessary.
predictive scheduling solvers have been thoroughly evaluated through the production of several benchmark data sets and metrics
the aspect related to reactive scheduling has not yet received the same level of attention
HERE we define a benchmark generator!
7Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Empirical Framework
TestsetsGenerator
TestsetsGenerator
ProjectScheduling
ProblemPredictiveScheduler
PredictiveScheduler
ReactiveScheduler
ReactiveSchedulerInitial
Schedule
Set of Exogenous
Events
FinalSolution
------------------------------------- 2 {eventDelay a6 7 2} {eventDuration a2 5 4}-------------------------------------
8Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Project Scheduling with Uncertainty
Resource availability
temporal uncertainty
resource uncertainty
causal uncertainty
Activities last longer than expected or they can be postponed
A new precedence relation between a pair of activities requires a revision ofprevious choices
Difference between nominal (left) and actual (right) resource availability.
Reduction of resource availability blocks the execution of some activities an their consequent delay
9Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
• Activity delay
ai
taware
∆st
This element specifies the instant where the specific event is supposed to happen.
10Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
• Activity duration
ai
taware
∆dur
11Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
• Change of resource availability
taware
∆cap
stev etev
rj
12Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
• Change of activities set
ak
taware
ak
taware
r1
r2
estk letk
durk
μa= add
reqk= {1,2}
13Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
• Insertion/removal constraint
aprec
taware
asucc
[dmin, dmax]
μc= add
14Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Benchmark ingredients
1. Activity delay,
2. Activity duration
3. Change of resource availability,
4. Change of activities set,
5. Insertion/removal constraint
temporal
causal
resource
15Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Instant Modifier
• To formally model an execution event we introduce the concept of Instant Modifier:
– An Instant Modifier is an operator defined by a set of modifications Z and a time of execution tE, and whose application on the problem P produces a change of the problem at time tE.
– Given a problem P the reactive scheduling problem is:
16Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Testsets generator
• INPUT:– The scheduling problem– Number of events to generate– Probability of occurrence for each single type of event– The minimum and maximum magnitude of each type of
event.
• OUTPUT:– Set of exogenous events SPACED in time
• Definition of consistent taware,
------------------------------------- 2 {eventDelay a6 7 2} {eventDuration a2 5 4}-------------------------------------
17Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Timing the Exogenous Events consistently
• taware values determine the instants where each specific event is supposed to happen.– How to find consistent values for all possible executions?
• FIRST STEP: we add a set of simplifying assumptions on the events that have to be generated:– activities cannot be anticipated,– activity durations can only increase– there are only reduction of resource availability
• SECOND STEP: we used a relaxed version of the scheduling problem in which resource constraints are not taken into account.– This relaxed problem consists in a Simple Temporal Problem (STP)– This allows to compute the lower and the upper bound for the
start and the end time of each activity
18Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Timing the Exogenous Events consistently
The assumptions guarantee the monotonic increase condition in the case of constrainedness.
Limitation: it is not possible to model situations like activity anticipations or processing time reductions which entail constraints retractions.
19Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Producing consistent taware values
• in the case of a delay of activity ai (edelay),
taware<= lb(sti)
• in the case of change of duration of the activity ai (edur),
taware<= lb(eti)
• in the case of adding/removing activity ak (eact),
taware<= lb(stk) if ak is removedtaware<= estk otherwise;
• in the case of adding/removing a constraint between aprec and asucc (econstr),
taware<= lb(stprec) if the constraint is removed
taware<= min(lb(stprec), lb(stsucc)) otherwise.
20Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Further constraints
• the width of the delay on activity ai (edelay),
∆st <= ub(sti) - lb(sti)
• the change of activity duration (edur),
∆dur <= ub(eti) - lb(sti) - pi
• the change of resource availability (eres),
0 <= ∆cap <= capj
21Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Tuning the Instances Difficulty
• It is fundamental to control the difficulty related to each generated event
• Use well known metrics to measure the structural properties of a problem before and after the insertion on an event
t
e1 e2
e3 e4
22Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Possible metrics
• Temporal Metrics
• Resource Metrics
(Schwindt 1998)
(Cesta et al. 1998)
(Mastor 1970)
23Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Example
• 8 activities • 2 resources both with capacity 2• oddly numbered activities
require one instance of r1 while evenly numbered activities require one instance of r2
• all the oddly numbered activities have a start-time of at least 3
• D= {4, 7, 4, 7, 3, 5, 3, 5}
2 resources both with capacity 2
------------------------------------- 2 {eventDelay a6 7 2} {eventDuration a2 5 4}-------------------------------------
24Analysis of a Benchmark Generator for the Reactive Scheduling Problem – Cesta, Policella, & Rasconi
Scheduling a Scheduling Competition - ICAPS07 workshop, September 22, 2007
Conclusions
• The benchmark generator represents a fundamental means to foster:– Significant experimental analysis– Scheduling competition
• Benchmarks consist of a set of modification events– Type of modifications that can affect a schedule– To simulate the environmental uncertainty events are time
spaced– It is worth to asses the difficulty of the instances
• Next step consists in the introduction of a “General Scheduling Execution framework”– Different combinations of proactive and reactive scheduling
techniques can be evaluated