IFORS99 CONFERENCE August 1620 Beijing, China

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IFORS99 CONFERENCEAugust 16-20Beijing, China

• Presenter Gautam Mitra
• Brunel University and UNICOM Consultants

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Parallel Algorithms for Scenario Analysis and
Two-Stage Integer Stochastic Programming (ISP)

• Authors Gautam Mitra, Cormac Lucas,
• Chandra A. Poojari, Ali MirHassani.
• Brunel University

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Outline

• Introduction and Background
• Model and Data Instances
• Scenario Analysis in Parallel
• Two-Stage ISP in Parallel
• Discussions

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Introduction Background
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Model Data Instances (1)
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Model Data Instances (2)
P0
P1
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Model Data Instances (3)
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Scenario Analysis in Serial (1)
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Scenario Analysis in Serial (2)
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Scenario Analysis in Parallel (1)
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Scenario Analysis in Parallel (2)

• a collection of 5 high speed PCs
• connection by a 100 MB hub
• PVM, Geist, Beguelin et. al.(1994), is used as
  the message passing interface to achieve parallel
  processing.
• Each of the 5 PC stations is a 333 MHz Pentium
  II, 128MB RAM, VIGLEN computer and the operating
  system is windows NT4

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Two-Stage ISP
in Serial
P2
P3
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Two-Stage ISP
in Serial (2)
P4
Lagrangean Decomposition
P5
P6
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Two-Stage ISP
in Serial (3)
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Two - Stage ISP in Serial (4)
Step 0 Initialise BUB ?, BLB -?,
Pass 0, ?0 Step 1 Solve relaxation problem
Solve IP Problem P5 use BB Algorithm
Save new configuration
Solve LP Problem P6 use IPM Algorithm Step 2
Create a feasible solution Solve LP
Problem P3 use IPM while x is fixed to Step 3
Solution quality BLB Max BLB,
Obj_ValueP5 Obj_ValueP6 - ?h BUB
Min BUB, Obj_ValueP3 IF (Stopping
Criteria Satisfied) Then
s s 1 If (s gt Max No.
of Scenario) Stop Go To Step 0
Else Pass Pass
1 Go to Step 4 End
IF Step 4 Update Lagrangean multiplier
Compute step size
Update the multiplier values
Go to Step 1.
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Two-Stage ISP
in Parallel (5)
Stopping Criteria
1.
Pass ? Maximum Number of Iterations
2.
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Two - Stage ISP in Parallel (6)
N Number of Processors, n?N S Set of
Scenarios to be solved for generating
configurations. Sn Set of Scenarios to be
solved on Processor n. On each Processor n,
the following algorithm is run.
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Two-Stage ISP
The Approximation
APXP1
APXP0
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Two-Stage ISP in Serial

• a collection of 4 high speed PCs
• connection by a 100 MB hub
• PVM, Geist, Beguelin et. al.(1994), is used as
  the message passing interface to achieve parallel
  processing.
• Each of the 4 PC stations is a 500 MHz Pentium
  III, 128MB RAM, VIGLEN computer and the operating
  system is windows NT4

Two-Stage ISP (Approx.) by Direct Search over 590
config.
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Quality of the Approximation
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Two-Stage ISP (Approx.) by Direct Search over 590
config.
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Discussions
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End of Presentation