Polynomial optimization techniques for activity scheduling (optimization based prototype scheduler) are presented in the form of the viewgraphs. The following subject areas are covered: agenda; need and viability of polynomial time techniques for SNC (Space Network Control); an intrinsic characteristic of SN scheduling problem; expected characteristics of the schedule; optimization based scheduling approach; single resource algorithms; decomposition of multiple resource problems; prototype capabilities, characteristics, and test results; computational characteristics; some features of prototyped algorithms; and some related GSFC references

Reddy, Surender

English

NASA Technical Reports Server

No2-1 og6
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR
ACTIVITY SCHEDULING
OPTIMIZATION BASED PROTOTYPE SCHEDULER
Surender Reddy
Computer Sciences Corporation
December 1990
Space Network Control Conference on
Resource Allocation Concepts and Approaches
Goddard Space Flight Center, Greenbelt MD
-- S Reddy GSFC / CSC --
R-I
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource AIIocalion Concepts and Approaches
Agenda
• Need and Viability of Polynomial Time Techniques for SNC
• Intrinsic Characteristic of SN Scheduling Problem
• Expected Characteristics of SN Resource Schedules
• Optimization Based Scheduling Approach
• Single Resource Algorithms
• Decomposition of Multiple Resource Problems
• Prototype Capabilities
• Prototype Test Results
• Computational Characteristics
• Prototype Characteristics
• Some Features of Prototyped Algorithms
• Some Related GSFC References
S Reddy
R-2
207 GSFC / CSC --
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https://ntrs.nasa.gov/search.jsp?R=19920001838 2020-03-17T15:12:29+00:00Z
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Need and Viability of
Polynomial Time Techniques for SNC
• Need for Efficient Scheduling Techniques such
as Polynomial Time Algorithms
Subjective scheduling decisions in an environment such as the
SN are necessary. However, producing a good initial schedule
based on subjective analysis is very labor intensive, impractical
and unnecessary. Initial schedules based on computationally
efficient approaches optimizing a general objective such as
maximizing requests can be the basis from which a final schedule
can be evolved through changes and fine tuning based on
subjective analysis and human interaction.
• Viability of Polynomial Time Algorithms for SNC
Recent R & D effort at GSFC has shown that polynomial time
algorithms for SN resource scheduling are viable and practical.
GSFC / CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts end Approaches
An Intrinsic Characteristic of
SN Scheduling Problem
Highly-coupled usage of resources for each request,
i.e., Each request uses all resources it requires
either simultaneously or in the immediate time frame
Request Window I
t Request Duration I" tIlIllllllllllll Illllll = i= = ===
Resource I Usage
Resource 2 Usage
Resource 3 Usage
-- S Reddy 208 GSFC / CSC --
R-4
POLYNOMIALOPTIMIZATIONTECHNIQUESFORACTIVITYSCHEDULING
SpaceNetworkControlConferenceonResourceAllocationConceptsendApproaches
E__x_pectedCharacteristics of the Schedule
Tight coupling of resource usage tends to force
schedules with the following characteristics
• General sequence (time-order) of scheduled
requests is nearly same for all resources
• Schedule for high-demand resources implicitly
control the schedule for resources with low -
demand
A multiple resource-usage request which is rejected
when attempted to be scheduled independently on a
low demand resource type is highly unlikely to be
scheduled on a high-demand resource type.
b S Reddy
R-5
GSFC / CSC
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
O__ptimization Based Schedulin Ag_Ap_proach
A combination of optimization and heuristic techniques
• Optimal and near optimal single resource
scheduling using polynomial time optimization
algorithms
• Heuristic reasoning for decomposing multiple
resource problems into a series of single resource
problems suitable for application of the
polynomial time single resource algorithms
--S Reddy 209 GSFC / CSC
1_-6
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Single Resource Algorithms
• First Algorithm (Does not consider activity priorities)
m Maximizes the number of scheduled activities
Generates sequence of scheduled activities with reduced
windows
Developed earlier last FY under SEAS task 20-122
• Second Algorithm (Considers activity priorities)
Maximizes the priority weighted number of scheduled
activities when there are two priorities
For problems with > 2 priorities, algorithm is applied to
series of two priority problems
Generates sequence of scheduled activities with reduced windows
S Reddy
R-?
7 GSFC I CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
First Single Resource Algorithm
Provides ...
Optimal Solution
when windows exhibit
(Cascade Structure)
I ..... .J
I Activity Window
Activity Duration
Activity Flexibility
.......... j
L--- ..... I
L--- ..... I
Optimal Solution
when windows exhibit
(Triangular structure)
L.--- ........ 4
Near Optimal Solution
when windows exhibit
-- S Reddy
A general unrestricted structure
2]0 GSFC / CSC
R-8
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTWITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Second Single Resource Alqorithm
Provides optimal solution for a two priority
problem when activity windows within each
priority are non-overlapping
I Activity Window
Activity Duration
Activity Flexibility
Priority I I ---J t ---II
Priority 2 ........ JI _._11
..... i
-- S Reddy
R-9
9 GSFC / CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Decomposition of
Multiple Resource Problems
Schedule resources in increasing order of usability
Reason:
Given: Resources A and B
Activity set S(A) w Schedulable only on A
Activity set S(B) w Schedulable only on B
Activity set S(A or B) -- Schedulable on A or B
Scheduling as many of activities in S(A or B) as possible
on least usable of A and B tends to maximize the
availability of resources for highly resource specific
activities
-- S Reddy
R-IO
211 GSFC / CSC q
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Decomposition of
Multiple Resource Problems
(CONTINUED)
Example: S(A)=100 S(B)=20 S(AorB)=20
Scenario l mSchedule A first and schedule B second
70 of S(A) and 10 of S(A or B) scheduled on A
20 of S(B) and 10 of S(A or B) scheduled on B
Total scheduled: 100
Scenario 2--Schedule B first and schedule A second
20 of S(B) and 19 of S(A or B) scheduled on B
90 of S(A) scheduled on A
Total scheduled: 129
Scenario 2 maximizes the scheduled activities
-- S Reddy 11 GSFC / CSC --
R-ll
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource AIIocalion Concepts and Approaches
Prototype Capabilities
Scheduling of Specific and Generic Requests for:
• Tracking and Data Relay Satellites
• Deep Space Network
• Ground Network
• For Combination of Space and Ground Resources
-- S Reddy
R-12
212 GSFC / CSC m
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Prototype Test Results
First Algorithm (Disregard Priorities)
Second Algorithm (Consider Priorities)
Total Wall
Scheduled Upper Clock
Reqstd Events Bound Time
Events (Min.)
1584 1478 93.3% 98.7% 3.25
2960 2415 81.6% 86.% 21.1
1594 1499 94.6% 98.7% 18.5
Tested on
• PC/AT running at 12 MHz without a math coprocessor
-- S Reddy
R-13
13 GSFC / CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Computational Characteristics
Analytically determined computational
requirements of the prototyped algorithms is a
3rd order polynomial of the number of activities
3t=k*n
For n=1584
-3
t = 3.25 implies k = (1584) * (3.25)
For n = 2960
t = (1584)" 3. (3.25) * (2960) 3 = 21.2 Min
--S Reddy
R-14
213 GSFC / CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Prototype Characteristics
• COMPUTER: PC or PC (AT)
• LANGUAGE: MS-FORTRAN
• NUMBER OF LINES OF SOURCE CODE : 2000 Approx.
• EXECUTABLE MODULE: 520 Kbytes
• CAPACITIES: 8 Resource types
10 Resource Groups (TDRS/Ground Stations)
12000 Resource Intervals
3200 Instances
15 GSFC / CSC --
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts and Approaches
Some Features of
Prototyped Algorithms
Prototyped algorithms can be used for:
• Initial batch scheduling
• Batch rescheduling while limiting changes to any combination of:
-- restricted deletions for selected instances
-- restricted non-deletion schedule changes to selected Instances
-- allowable deletion of selected instances
-- S Reddy
R-I6
214 GSFC / CSC
POLYNOMIAL OPTIMIZATION TECHNIQUES FOR ACTIVITY SCHEDULING
Space Network Control Conference on Resource Allocation Concepts end Approaches
Some Related GSFC References
• Optimization Based Prototype Scheduler
DSTL-90-024, Available December 1990
• Single Resource Scheduling with Ready and Due Times
DSTL - 89 - 024, December 1989
• A Study of Optimization Techniques for Activity Scheduling
DSTL - 89 - 019
-- S Reddy
R-17
17 GSFC / CSC --
2]5



Polynomial optimization techniques for activity scheduling. Optimization based prototype scheduler

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