Satellite Mission Scheduling With Dynamic Tasking

1
Satellite Mission Scheduling With Dynamic Tasking

• University of Colorado at Denver and Health
  Sciences Center
• Math Clinic, Spring 2006

2
Presentation Outline

• Problem Description
• Hybrid Double Chromosome Genetic Algorithms
• Dynamic Scheduling Methods
• Top Priority Path Dependent Algorithm
• Scatter Search/Path Relinking
• Summary/Conclusions
• Future Work

3
Satellite Mission Scheduling

• Satellite is equipped with camera for
  photographing earth-bound targets.
• Thousands of task requests...
• ...but only a few hundred can be performed.
• Problem Determine
• which tasks to perform
• and when to perform them.
• Constraints
• tasks cant overlap.
• tasks have time windows of opportunity
• Features
• order dependent slew time
• tasks are prioritized.

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Tasks

• Associated variables
• time window, preferred vs. effective
• priority (0-99)
• duration
• Monitoring vs. Simple

task
Preferred window
E f f e c t i v e w i n d o w
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Monitoring Tasks

• Require a specified number of revisits for image
  recapturing at given target
• Visits must occur at relatively evenly-spaced
  intervals
• A minimum and maximum number of revisits is given
• If revisits lt minimum, the monitoring task is not
  considered completed

6
The Schedule

• 2 Common Ways to Think of a Schedule
• Temporally (timeline)
• Geographically (nodes and arcs)

Task 3
Slew
Task 7
Task 1
Slew
Slew
Task 2
Task 4
Task 5
Task 8
Slew
2
3
slew time
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5
1
4
7
8
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Scheduling - Objectives

• Maximize number of tasks scheduled (images
  collected).
• Collect as many high priority tasks as possible.
• Be able to address incoming requests (dynamic
  tasking)

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Dynamic Scheduling

• Insert new tasks into initial schedule (on the
  fly)
• Must adjust remainder of schedule.

2
3
6
5
1
4
7
8
?
New task
?
?
Task 3
Slew
Task 7
Task 1
Slew
Slew
Task 2
Slew
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Team 1 A Hybrid Double Chromosome Genetic
Algorithm Approach to the Satellite Scheduling
Problem
Cliff Bainter, Nima Lekmine, Jeremy Noe, Leslie
Quinn, Whitney Rust, Dmitriy Vassilyev

• Math Clinic, Spring 2006

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Outline

• Double Chromosomes and Scheduler
• Genetic Algorithms Overview
• Hybrid GA Overview
• Future Work
• Conclusion

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Solving The Satellite Mission Scheduling Problem

• Combinatorial problem / NP-Hard
• There are many ways to approach this problem
  using heuristic algorithms involving permutation
  vectors
• Based on promising findings of the spring '05
  Math Clinic we chose to implement a Genetic
  Algorithm to solve the problem
• We used an approach that addresses the
  optimization of two things at once, priority and
  scheduling (hybrid).

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Hybrid Double Chromosome GA Approach
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Our Approach to the Satellite Problem Hybrid
Double Chromosome

• Double (Parallel) Chromosomes
• two chromosomes simultaneously run through the GA
• Chromosome 1
• represents the order that the scheduler will
  attempt to insert tasks into the schedule.
• Chromosome 2
• represents the chronological ordering of tasks
  (whether or not they are actually scheduled).
• e.g. if tasks i and j are scheduled, they will
  occur in the order they appear in this
  chromosome.
• Scheduler
• takes information from both chromosomes to
  develop optimal schedule
• fitness of double chromosomes measured by
  schedule evaluator

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Scheduler
Priority Order Chromosome
Time Order Chromosome
2
2
4
10
7
5
2
7
10
4
5
Start
End
Start
End
2
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Scheduler
Priority Order Chromosome
Time Order Chromosome
2
4
10
7
5
2
7
10
4
5
4
10
7
5
Start
2
Start
End
7
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Scheduler
Priority Order Chromosome
Time Order Chromosome
2
4
10
7
5
2
7
10
4
5
4
10
5
10
Start
2
7
Start
End
10
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Scheduler
Priority Order Chromosome
Time Order Chromosome
2
4
10
7
5
2
7
10
4
5
4
10
5
4
2
7
10
Start
End
4
7
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Scheduler
Priority Order Chromosome
Time Order Chromosome
2
4
10
7
5
2
7
10
4
5
4
10
5
4
2
7
10
Start
End
5
2
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Scheduler

• Uses input from both chromosomes to build
  schedule
• Selects from priority chromosome first
• Attempts to insert into schedule in order
  specified by time-order chromosome
• Schedules each task as early as possible
• Shifts already scheduled tasks as needed, but
  does not remove already scheduled tasks
• Resulting schedule is evaluated, and this becomes
  the fitness of the chromosome pair
• Scheduler ensures that all possible chromosome
  pairs correspond to a feasible schedule

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Evaluator (delete?)

• Once schedule is built it is evaluated
• Two Implementations
• GA specific
• Uses lexicographical ordering based on last
  priority iteration
• General
• Compares two schedules using both lexicographical
  ordering and penalizes for scheduling outside
  preferred time

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Evaluator

• Motivation
• Equal Weights
• Evaluates one priority level at a time
• Time window penalty
• Determines the fitness of a given schedule
• Determines the best schedule
• This schedule is saved for later use

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Hybrid Double Chromosome GA Approach
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Traditional GA
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Background GA's

• Genetic Algorithm
• Search technique used in computer science to find
  an approximate solution to optimization problems
• Particular class of evolutionary algorithms that
  use techniques inspired by evolutionary biology
• inheritance
• mutation
• natural selection (survival of the fittest)
• recombination (cross-over)

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Background Traditional GA

• Many steps to Genetic Algorithm
• Initial Population
• Fitness Function
• function based on weighting of genes
• Selection of chromosomes for mating
• Recombination
• combining the genes of two selected (parent)
  chromosomes to develop offspring (child)
  chromosomes
• Mutation
• to ensure the population remains sufficiently
  diverse

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Selection

• Roulette Wheel strategy
• Population of double chromosomes scored by
  schedule evaluator
• Each chromosome is given a percent fitness based
  on total fitness of the population
• Probability of selection is proportional to
  fitness
• Two parents are chosen for mating (P1,P2)

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Cross-Over

• Syswerdas Crossover Operation
• Two (or more) random genes are chosen from P1
• Transferred to child chromosome in same gene
  positions
• Task numbers corresponding to those genes are
  then eliminated in P2
• Now all remaining tasks from P2 are transferred
  in the same order to the child chromosome
• Mutation
• Mutation will occur with a certain probability
  (swapping 2 genes, randomly selected).

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Current Population
02
03
04
06
05
01
06
01
02
05
04
03
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Current Population
06
01
02
05
04
03
02
03
04
06
05
01
03
05
06
01
02
04
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Current Population
06
01
02
05
04
03
02
03
04
06
05
01
06
01
02
04
06
03
02
01
05
04
New Population
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Hybrid Double Chromosome GA Approach
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Iterative Population Building

• Addresses schedule building by priority
• Iteratively cycles through tasks in priority
  order
• Filtering next priority tasks to most fit
  previous priority chromosome
• Allows other components to work faster

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Current Population
Task List (Next Priority)
Most Fit Chromosome
Random Priority 1 Task Chromosome
01
03
02
14
17
16
15
18
01
14
17
03
02
15
16
18
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Task List (Next Priority)
Current Population
Random Priority 1 Task Chromosome
Most Fit Chromosome
01
03
02
14
17
16
15
18
01
03
02
14
17
16
15
18
01
03
02
14
17
15
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New Population
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Hybrid Double Chromosome GA Approach
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Future Work

• Cross-over
• Try different algorithms (e.g. edge
  recombination)
• Scheduler
• Try scheduling for maximum flexibility
• Evaluator
• Account for more variables (e.g. distance between
  tasks, change in priority, etc)
• Overall
• Experiment w/more parameter variations

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Conclusion

• The Hybrid Double Chromosome approach to GA
  provides a novel method of traversing the
  solution space in an efficient manner
• Addressing the population iteratively helped
  reach solutions more quickly
• The scheduler proved to be extremely efficient
• Many ways to expand upon this approach in the
  future

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Scheduler

• Schedules are evaluated for fitness
• These fit schedules are fed back into the GA
  and the next priority level is added
• After a given priority level is scheduled, the
  scheduler will determine a best schedule and save
  it
• Uses previous schedule to its advantage
• The new population is fed into the scheduler and
  the cycle repeats, until all priority levels have
  been accounted for

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Presentation Outline

• Problem Description
• Hybrid Double Chromosome Genetic Algorithms
• Dynamic Scheduling Methods
• Top Priority Path Dependent Algorithm
• Scatter Search/Path Relinking
• Summary/Conclusions
• Future Work

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Dynamic Rescheduling

• Tu Dinh
• Armen Zakharyan
• Scott Young
• Nadia Hamoude

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Outline

• Problem Description
• Genetic Algorithm Adaptation
• Max-Flexibility Task Swapping
• A Algorithm
• Conclusions

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Problem Description

• Assumptions
• Inputs static schedule and single dynamic task
• Goals
• Incorporate dynamic task into schedule
• Accommodate other tasks
• Optimize schedule

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Genetic Algorithm adaptation for dynamic tasking
(GAA)
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Overview

• Two chromosomes
• Time
• Priority
• Includes all possible tasks
• Scheduler benefits
• Accommodates as many tasks as possible
• Previously unscheduled tasks

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Overview

• Use GA chromosomes to produce a new optimal
  schedule, including dynamic task.
• Runtime should be fast
• Insertion time
• Scheduler time

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Overview

• Inputs
• Initial schedule
• Time and priority chromosomes
• Dynamic task
• Insertion of dynamic task
• Scheduler

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Dynamic Task Insertion

• Time chromosome

Dynamic Task
Time Chromosome
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Dynamic Task Insertion

• Time chromosome

Dynamic Task
Time window of DT
Time Chromosome
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Dynamic Task Insertion

• Resulting time chromosomes

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Dynamic Task Insertion

• Priority chromosome

Dynamic Task
Priority Chromosome
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Dynamic Task Insertion

• Priority chromosome

Priorities lt priority of dynamic task
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Dynamic Task Insertion

• Resulting priority chromosome

Priorities lt priority of dynamic task
Priorities gt priority of dynamic task
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Scheduler

• Chromosomes sent pairwise to scheduler

scheduler
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Conclusions on GAA

• Fast execution times.
• Inclusion of previously unscheduled tasks.

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Task Swapping with Max-Flexibility
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Background

• Laurence A. Kramer and Stephen F. Smith in 2003.
• USAF Air Mobility Command (AMC) scheduling
  problem.
• Used to improve an existing schedule by inserting
  additional lower priority tasks (no tasks are
  removed).
• In our problem we want to insert tasks that may
  have higher priorities (which may require
  removing tasks).

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The Basic Procedure

• Inputs initial schedule and a dynamic task.
• Uses iterative repair methods.
• Inserts the dynamic task by making space in the
  initial schedule.
• Retracts tasks with high flexibility to make the
  space needed.
• Apply the method recursively on the retracted
  tasks.

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Example

• Given the initial schedule and a dynamic task.
• Find a task with maximum flexibility (M.F.).
• Swap the dynamic and the M.F task.
• Repeat the procedure on the M.F task.

Dynamic task
Initial Schedule
M.F
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Retraction HeuristicMax-Flexibility

• Determines which task possesses the greatest
  potential for reassignment.
• Tasks with high flexibility are more capable for
  rescheduling in the future.
• Flexibility duration / effective time window.

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Area of interest

• Includes all the tasks from the old schedule
  that intersects with the dynamic tasks effective
  time window.

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Step by Step Procedure

• Calculate the area of interest.
• Calculate the flexibility.
• Chooses the task to retract Max-Flexibility
  and with priority less than the priority of the
  dynamic task.

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• Swap that task with the dynamic task.
• Mark the inserted task as protected.
• Apply same steps recursively using retracted task
  as new dynamic task.

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Conclusion

• The task swapping procedure was presented in the
  literature to be
• A fast algorithm.
• Attempts to preserve the initial schedule.

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A Algorithm

• Graph search algorithm finds path from start
  node to goal node.
• Ranks each node based upon best route through
  that node.
• Visits nodes in order of this rank.
• Finds shortest route, if one exists.

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A Algorithm

• An efficient heuristic algorithm for finding
  shortest paths between two points.
• Algorithm not examined beyond literature.
• We explored several ideas for application to
  dynamic scheduling.
• Very interesting idea but does not appear to be
  well-suited for our application.

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Conclusions

• GA adaptation
• Fast execution
• New task incorporation
• Max-Flexibility
• Fast algorithm
• Maintains much initial schedule
• A Algorithm
• Fast, but not well-suited for our problem.

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Presentation Outline

• Problem Description
• Hybrid Double Chromosome Genetic Algorithms
• Dynamic Scheduling Methods
• Top Priority Path Dependent Algorithm
• Scatter Search/Path Relinking
• Summary/Conclusions
• Future Work

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Team 3 Satellite Mission Scheduling TPPA

• John Apodaca, George Shen
• Sara Morrison, Jennifer Zakotnik

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Presentation Outline

• Visual Representation of the Problem
• Motivation/Overview for Our Approach
• Task Insertion Algorithm
• Initial Path Algorithm
• Conclusions

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Top Priority Path Algorithm Overview

• Builds on idea from last years clinic.
• Tackle the problem in two steps
• Build an initial path through the highest
  priority tasks
• Traverse the initial path adding unscheduled
  tasks based on priority
• Motivation-Less Computation Time

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Initial Path
Red Priority Zero Black Priority One Blue
Priority Two
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Inserting Tasks

• Travel initial path and insert all possible
  priority one tasks
• Create new initial path
• Travel new initial path and insert all possible
  priority two tasks
• Create new initial path
• Etc.

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Initial Path
Red Priority Zero Black Priority One Blue
Priority Two
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Insertion Algorithm
X
X
Red Priority Zero Black Priority One Blue
Priority Two
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Insertion Algorithm
Red Priority Zero Black Priority One Blue
Priority Two
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Insertion Algorithm
X
Red Priority Zero Black Priority One Blue
Priority Two
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Insertion Algorithm
Red Priority Zero Black Priority One Blue
Priority Two
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Insertion Algorithm
Determine Highest Priority Unscheduled k
N
Y
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Building the Initial Schedule

• Goal build initial schedule with maximum
  flexibility, while scheduling as many priority 0
  tasks as possible

Scheduled Start Node pointer Next Node Node
pointer Previous Node Window Scheduled
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Terminology

• Distances represented as time
• Arc Path from one task (vertex) to another
• In-degree of arcs coming in to a vertex
• Out-degree of arcs going out of a vertex
• Wait-time time between arrival at a task and
  middle of preferred time window
• Flexibility measure used to determine if an arc
  should be chosen for the path
• Flexibility wait-time
• wait-time slew time

Scheduled Start Node pointer Next Node Node
pointer Previous Node Window Scheduled
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Initial Path Set Up

• Consider only priority 0 tasks
• Construct arcs in and out of every vertex to
  every other vertex
• Algorithm is based on
• cheapest edge algorithms
• cheapest most flexible

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Initial Path AlgorithmPre-Algorithm

• Delete impossible arcs (time window constraints)
• Search vertices for In-or Out-degree 0
• In-degree 0
• ? Starting Vertex of Path
• Out-degree 0
• ? Ending Vertex of Path
• Proceed to the algorithm

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Y
N
Y
N
Find best Flex Score
Choose Corresponding Arc
Delete Mirror and Unnecessary Arcs
Update Vertex Degrees
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Is in or out degree 1
Y
N
Y
N
Find best Flex Score
Choose Corresponding Arc
Delete Mirror and Unnecessary Arcs
Update Vertex Degrees
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Is in or out degree 1
Y
N
Y
N
Find best Flex Score
Choose Corresponding Arc
Delete Mirror and Unnecessary Arcs
Update Vertex Degrees
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Y
N
Y
N
Find best Flex Score
Choose Corresponding Arc
Delete Mirror and Unnecessary Arcs
Update Vertex Degrees
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Is in or out degree 1
Y
N
Is All in and out Degree 0
Y
N
Find best Flex Score
Choose Corresponding Arc
Delete Mirror and Unnecessary Arcs
Update Vertex Degrees
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Conclusions

• Initial Path Algorithm produces a path through
  priority 0 tasks
• Initial Path Algorithm can be modified to handle
  more priorities if desired
• Insertion Algorithm efficiently adds tasks to an
  original path

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Presentation Outline

• Problem Description
• Hybrid Double Chromosome Genetic Algorithms
• Dynamic Scheduling Methods
• Top Priority Path Dependent Algorithm
• Scatter Search/Path Relinking
• Summary/Conclusions
• Future Work

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Scatter Search and Path Relinking

• Armen Zakharyan

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Summary/Conclusions