Post on 18-Jan-2016
transcript
Franciszek Seredynski, Damian KurdejPolish Academy of Sciences andPolish-Japanese Institute of Information Technology
AAPPLYINGPPLYING L LEARNINGEARNING C CLASSIFIERLASSIFIER SSYSTEMSYSTEMS for for MULTIPROCESSOR SCHEDULING MULTIPROCESSOR SCHEDULING PROBLEMPROBLEM
Motivations
• New scheduling algorithms are proposed near every day• In the light of
– NP-hard compliteness of the scheduling problem, and– No free lunch theorem concerning metaheuristics
this situation may last forever, at least till the moment of appearing quantum computers
• Can we use the knowledge gained from the experience with already known scheduling algorithms (hypeheuristics approach) ?
• We will use GA-based Learning classifier systems (LCS) to extract some knowledge and use it in the scheduling process
Multiprocessor Scheduling Problem The idea of LCS The concept of LCS-based scheduling Experimental results Conclusions
4
Multiprocessor system: undirected, unweighted graph Gs=(Vs,Es), called a system graph.
Parallel program: weighted, directed, acyclic graph GP=<VP,EP>, called a precedence task graph or a program graph.
The purpose of the scheduling is to distribute the tasks among the processors in such a way that the precedence constraints are preserved and the response time T (the total execution time) is minimized.
T = f (allocation, scheduling_policy = const)
Examples of a precedence task graph (a) and a system graph (b).
t1t1
t3t3t2
t2
5 3
1
2
3
5
5
t4t4
P1P1
P3P3 P4
P4
P2P2
a) b)
MUTIPROCESSOR SCHEDULING MUTIPROCESSOR SCHEDULING PROBLEMPROBLEM
Problem formulation • Given a set of program graph instances • Given a multiprocessor system• Given a number of scheduling algorithms (heuristics)
solving instances of the scheduling problem with some efficiency
• Is it possible to train LCS system to match a given instance of the scheduling problem with the best for it scheduling algorithm (to minimize the total exectution time) from a set of scheduling algorithms ?
Idea of GA-based Learning Classifier System (LCS)
Learning Classifier System
Evaluation system
Decision system
System for discovery
of new rules
Environment
Idea of Learning Classifier System (LCS)
Learning Classifier System
System for
discovery
of new rules
Decision systemEvaluation
system
Environment
Environment state or messagee.g.10100
Idea of Learning Classifier System (LCS)
Learning Classifier System
System for
discovery
of new rules
Decision systemEvaluation
system
Environment
actione.g. Turn right
Environment statee.g.10100
Idea of Learning Classifier System (LCS)
Learning Classifier System
System for
discovery
of new rules
Decision systemEvaluation
system
Environment
rewarde.g. 120
actione.g. Turn right
Environment statee.g.10100
Classifier (rule) in classical LCS
• The structure of a classifier– Condtition part C
– Action A
– Strength S
• Strength S– Used when a classifier is selected from a set of
classifiers to perform an action– Used when GA creates new rules
#011: 01 : 43C
A
S
Classifier in XCS
• C: condition part• a: action• p: expected reward• e: prediction error• f: fitness• exp: experience of classifier• ts: remembers recent time when GA was applied to this
classifier • as: expected population size [A], in which appears
classifier• num: numerosity of classifier
010##0#####:0 1000 2,504 0,77 499 19924 146,76 109
C
a
p
ε
f ts
exp as
num
XCSEnvironment
Detector
0011
Population [P]
C : a : p: e: f#011:01:43:.01:99#0##:11:11:.13:9001#:01:27:.05:52#0#1:11:18:.24:311##:00:32:.02:921#01:10:24:.17:15
...
Match set [M]
C : a : p: e: f#011:01:43:.01:99#0##:11:11:.13:9001#:01:27:.05:52#0#1:11:18:.24:3
Action set [A]
C : a : p: e: f#011:01:43:.01:99001#:01:27:.05:52
Action set [A]-1
C : a : p: e: f11##:00:32:.02:92
Efector
01
cover
1.
2.
3.
4.
5.
6.
Prediction array PA
00-
01 37.49
1112,75
10-
Enforcement
GA Subsumption
7.
8.9.
ρ
σa
Features of XCS
• Creates population of classifiers• Processes messages received from
environment• Applies GA to evolve classifiers• Sends action to environment• Learns, generalizes and modifies the set
of classifiers
Our problem • Given 200 program graph instances created on the
base of the 15-tree graph: training set• Each instance is a tree with different random task
and communication weights• Two processor system is considered• Given 5 scheduling heuristics• We want to train LCS system to select in the best
way the scheduling heuristic to solve given set of instance of the scheduling problem to provide the best possible solutions ?
Set of list algorithms
• ISH (Insert Scheduling Heuristic)• MCP (Modified Critical Path)• STF (Shortest Time First)• LTF (Longest Time First)• own list algorithm: priority of a task
depends on a size of the subgraph• We know how works each algorithm
(response time) on the set of scheduling instances
XCS-based scheduling system
1. XCS receives information about an instance of the scheduling problem
Program graph
+System graph
XCS
1.
XCS-based scheduling system
1. XCS receives information about an instance of the scheduling problem
2. XCS selects the best available heuristic
Program graph
+System graph
XCS
schedulingalgorithm
1.
2.
XCS-based scheduling system
1. XCS receives information about an instance of the scheduling problem
2. XCS selects the best heuristic from the set of available heuristics
3. Program graph and a system graph become input data of scheduling algorithm
Program graph+System graph
XCS
schedulingalgorithm
1.
2.3.
XCS-based scheduling system
1. XCS receives information about an instance of the scheduling problem
2. XCS selects the best heuristic from the set of available heuristics
3. Program graph and a system graph become input data of scheduling algorithm
4. Scheduling algorithm delivers a solution
Program graph+System graph
XCS
schedulingalgorithm
Gantt diagram
1.
2.3.
4.
Program graph signature: the basic information concerning program graph
• LCS receives from environment a signature of program graph • The signature codes some static properties of program graph
– comm/comp – the averaged communication to computation time for a program graph (3 bits)
– information about distribution of tasks with a given computational requirements (12 bits)
– information about distribution of communication time requirements to communicate between tasks (12 bits)
– Information about critical path based on evaluation of comp/comm (16bits)
• The length of the signature: 43 bits
Distribution of tasks with a given computational requirements/distribution of communication time requirements
Coding information concerning critical path based on evaluation of comp/comm
• Computing ratios on critical path:ratios[0] = 1/4, ratios[1] = 5/3, ratios[2] = 1/3
• Normalization:ratios[0] = 3/27, coding as 01,ratios[1] = 20/27,coding as 11,ratios[2] = 4/27, coding as 01.
• Coding signal concerning critical path: 0111010000000000
Training LCS: number of correct matching scheduling algorithms to instances as function of
number of training cycles
Training LCS: population size of rules as function of a number of cycles
Training: summary of experiments
• Nontrained system correctly matched heuristics with scheduling instances in 40-50% cases
• The system was able to learn to match correctly in 100% heuristics to instances
• It means that information about the matching process was extracted during the learning process
• Classifiers contain this information and during the learning process the process of generalization of rules was observed
• Learning process is a costly process, but the gained information can be used in the scheduling
LCS-based scheduling system: normal operation mode
• Modification of instances (program graphs) from training set: testing set
• All computation and communication weights were scailed by 10
• Next, weights of k tasks or communications were changed by constant d
Experiment: k=1, d=1
Experiment: k=2, d=2
Experiment: k=3, d=3
Normal operation mode: summary of experiments
Number of correct matching heuristics to scheduling instances
Number k of modified weights (tasks or communications)
Difference d between initial weight value and
the value after modification
90% 1 1
80% 2 2
75% 3 3
Conclusions
• LCS has been proposed to learn optimal matching scheduling algorithms to instances
• Instances were represented by specially signatures• During the learning process the knowledge about matching was extracted
in the shape of LCS rules, and next generalized• Creating signatures is one of the most crucial issues in the proposed
approach • Performance of the system depends also on many parameters of LCS• We believe that encouraging results of experiments open new possibilities
in developing hyperheuristics