Transcript Document

Project BNB-Grid: solving large scale
optimization problems in a distributed
environment
M. Posypkin (ISA RAS)
GLOBAL OPTIMIZATION
Given f :
f :G  
Find x0:
f ( x )  min f ( x) , x  G
0
APPLICATIONS OF GLOBAL
OPTIMIZATION
VLSI design
Automated theorem proving
Constructing optimal transport networks
Selecting a best investment package
Computational chemistry: finding
molecular conformations
OFTEN HARD TO SOLVE !
BRANCH-AND-BOUND METHOD
BRANCHING
SUB-PROBLEM
DISCARDED SUBPROBLEM:
1.
NO SOLUTION
2.
KNOWN OPTIMUM
3.
OPTIMUM IS NOT
BETTER THAN
INCUMBENT (ALREADY
FOUND)
BRANCHING TREE
BNB parallelization
HIGH COMPLEXITY
 TREE-LIKE STRUCTURE
SUITABLE FOR DECOMPOSITION
SUITS FOR DISTRIBUTED
COMPUTING
DISTRIBUTED ENVIRONMENT
BNB-Grid: ARCHITECTURE
CE-AGENT #1
CE-AGENT #2
IARnet
CE-AGENT #3
MASTER
AGENT
AGENT FUNCTIONALITY
COMPUTING ELEMENT AGENT
 Start solver
 Interact with the CE
batch system
 Load initial data
 Monitor computing
element
 Send and receive
sub-problems
MASTER AGENT
 Manage distributed
application
 Manage load
balancing
 Monitor and visualize
computational
process
INSIDE A COMPUTING ELEMENT
CE Agent
BNB-Proxy
BNB-Solver
Interaction with BNB-Solver.
A library for solving optimization
problems on multiprocessor and
uni-processor systems
FAULT-TOLERANCE in BNB-Grid
Dynamically changing computing space:
nodes may leave or join at run-time
BNB-Grid backs up sub-problems and resubmits them
In the case of the node failure
EXPERIMENTAL RESULTS: PLATFORM
1048 x PowerPC 970 2,2 GHz,
2096 GB,
Myrinet
256 x Itanium 2 1.6 GHz,
256 GB,
Myrinet
Workstation
(ISA)
МВС 15000 BM
(JSCC)
МВС 6000 IM
(CC)
EXPERIMENTAL RESULTS: KNAPSACK
PROBLEM
We are given n items with weights wi and profits pi
and a knapsack with capacity C. The objective:
select a subset of items such that the total profit is
maximized and the total weight does not exceed C:
n
f ( x)   pi xi  max
i 1
n
w x
i 1
i i
C
xi  0,1 i  1,2,...,n
EXPERIMENTAL RESULTS: DATA
The hard knapsack
instance (introduced
by Finkelshtejn):
32
 2x
i 1
i
 max,
n
2 xi  2   1

2
i 1
32
8 CPU on
MVS 15000
BM
5.57 min
8CPU on
MVS 6000 IM
6.04 min
8CPU on MVS
15000 BM + 8
CPU on MVS
6000 IM
3.15 min
CONCLUSIONS
Usage a number of supercomputers in
BNB-Grid does increase performance for
large scale optimization problems
IARnet framework makes development of
complex distributed applications rather
simple
THANK YOU!
КЛАССИЧЕСКИЕ МОДЕЛЬНЫЕ ЗАДАЧИ
ОПТИМИЗАЦИИ
 Задача коммивояжера
 Задачи о покрытиях и разрезаниях графов
 Задача о ранце (одномерная и
многомерная)
 Задачи транспортного типа
 Поиск глобального экстремума функции
многих переменных
…
ДЛЯ РЕШЕНИЯ ТРЕБУЮТСЯ БОЛЬШИЕ
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