Transcript MUSE: A Multi-User Scheduling Environment for Multi

Multi-Objective Planning
and Scheduling with
Astronomical Applications
Mark Giuliano – Space Telescope Science
Institute
Talk Outline
• Why Multi-Objective Planning and Scheduling?
- Motivation
• Implementation Approaches
- Genetic algorithms
- Example application
• Challenges
- Visualization tools
- Evaluating algorithms
Overall Goal
•
Schedule astronomical and other space science observations to
optimize science return
- Reduce the cost of operations as well as enable more science
- Multiple mission phases and granularities
‣ Mission proof-of-concept versus operations
‣ Long range planning versus short term scheduling
-
Oversubscribed scheduling
‣ More science is approved than time is available
-
Dynamic environment ― change is the norm not the
exception
‣ Changing science goals
‣ Changing spacecraft capabilities
-
Multiple often conflicting goals with multiple constituents
‣ Science return, engineering, calibration, stability of the plan itself …
‣ Hard to quantify and make explicit goals - communication problem
Goals
•
Effective decision support tools that enable
participants to optimize schedules in a collaborative
manner...
Goals
•
Effective decision support tools that enable
participants to optimize schedules in a collaborative
manner
- multiple objectives
Goals
•
Effective decision support tools that enable
participants to optimize schedules in a collaborative
manner
- multiple participants
Goals
•
Effective decision support tools that enable
participants to optimize schedules in a collaborative
manner
- enable integration with existing tools
Multi-Objective Scheduling
•
Effective scheduling of space based astronomy missions
requires the ability to make trade-offs among competing mission
objectives:
- Time on target, minimizing use of consumables, minimizing
the use of critical mechanisms, preferring the higher priority
science, ...
•
Objectives are often competing in that improving one objective
means making another objective worse
•
In the short term getting more science done may decrease the
mission lifetime
Objectives have different constituents lobbying for them
- e.g. mission science community versus engineering
- E.g. Solar system observers versus galaxy observers
Traditional Approach
• The traditional approach to handling multiple
objectives is to combine the weighted average
of separate objectives
•
•
∑αi fi(x)
But: combining objectives loses information and
pre-determines the trade-offs among them!
In practice this approach requires users to run
the planning system multiple times each with
different weights for the objectives
- Users then compare solutions using ad-hoc
methods to select a solution for operations
-
Multi-Objective Solution Approaches
•
Multi-Objective Scheduling:
- Explicitly maintain and exploit multiple objectives
during scheduling
- Algorithms build up approximate Pareto optimal
frontier from a population of candidate schedules
‣ i.e. “non-dominated” solutions, such that no other candidate
is better, considering all objectives.
‣ Each point below represents a complete solution
Comparing the Approaches
Traditional Approach
• User determines criteria weights for
multiple planner/scheduler runs
• The planner/scheduler is run for each
set of criteria/weights
• The results of the runs are compared
using ad hoc methods to select a
solution for execution
Multi Objective Approach
• User performs a single
planner/scheduler run to produce a
Pareto surface of solutions
• The user explores the Pareto surface
to select a solution for execution
• The multi objective approach:
- Automates steps that users would
manually perform in the traditional
approach;
- Provides a more formal basis to select a
Tools for Selecting Solutions
• The Pareto frontier gives participants a powerful view
into the optimal trade-off space, but users still need to
agree on a particular candidate schedule
• Need to provide tools that will provide distributed
decision support
- Mixed-initiative planning
‣ support the end user in making trade offs
‣ Automate when possible but leave final control with the
user
-
Graphical internet-based tools that support multiple
participants
Challenges include: human factors, nonsimultaneous users, domain-specific scheduling
GUIs
Implementation Approaches
• Evolutionary algorithms provide a natural fit for finding
Pareto-surfaces
- Effective on a wide range of problems
- Capable of dealing with objectives that are not
mathematically well behaved (e.g. discontinuous,
non-differentiable).
- By maintaining a population of solutions they are
capable of representing the entire Pareto frontier at
any stage
- Lend themselves to parallelization
Evolutionary Algorithms
• Based on models of animal Evolution
• Core Algorithm;
• Generate the initial population
• Evaluate the fitness of each member of the population
• Repeat until termination
- Select the best-fit individuals for reproduction
- Breed New individuals through crossover and mutation
- Evaluate the individual fitness of new individuals
- Replace least-fit population with new individuals
GDE3
•
GDE3 is based on differential evolution optimization for singleobjective problems (Price, et. al 2005)
- For each member of the population, select three others and
calculate a candidate child vector by combining the three vectors
using binary crossover and a scaling factor
- Evaluate the candidate child vector and compare with the
original population member as follows:
-
‣
both infeasible: choose less violated
‣
one feasible, other infeasible: choose feasible
‣
both feasible: choose dominating if present, else choose both
If necessary, reduce population back to size N via nondominated sorting and crowding distance (to improve diversity
along Pareto frontier)
Typical System Architecture
GDE3 - Implements multiobjective evolutionary
algorithms
Creates and evolves decision
variable vectors
SPIKE - Implements scheduling
domain.
Creates and evaluates schedules
seeded by decision variable
vectors
Application: James Webb Telescope
• Launch 2013 2014
• Infrared sensors
to detect the
earliest star
formation
• L2 orbit 1.5 million
km from Earth
• 6.2 meter mirror
• Tennis court sized
sun shield to
protect science
instruments
Challenge:
Momentum
Scheduling
Sun normal to shield:
minimal reaction
wheel spin up
Sun not normal to shield:
reaction wheel spin to
maintain pointing
Momentum Constraint
•
Solar radiation pressure on the sunshield is absorbed
as angular momentum in reaction wheels.
•
Wheels have a limited momentum capacity.
- Momentum dumping requires using non-renewable
fuel to fire thrusters.
- Potential limiting factor in the mission lifetime.
• Momentum accumulation for a target varies over time
and the spacecraft roll.
- Major factor in the quality of JWST schedules.
JWST Momentum Challenges
•
•
The model is a three dimensional vector space.
Momentum accumulation for an observation varies:
-
Over time in non-linear manner
•
Momentum accumulation is additive in nature.
- Scheduling an observation at a time can either add or
subtract from the overall momentum accumulation.
•
Momentum provides both a hard constraint due to a
limited capacity, and a preference to consume as little
resource as possible.
JWST Scheduling Objectives
•
Minimize Schedule Gaps - JWST Contract mandates
no more the 2.5% idle time
• Minimize Momentum Accumulation
• Minimize Observations that miss their last chance to
schedule
JWST Experiments
Multi-Objective
Scheduler +
JWST Application Map
JWST Scheduling
Engine (SPIKE)
• Evaluated system using JWST Science Design Reference
Mission
• Schedule observations to a quantum of 7 minutes in a 22day momentum bin
•Using GDE3 evolutionary algorithm (Java) with Lisp-based SPIKE
JWST Scheduler
• Implemented parallel domain scheduler driver
• Candidate vectors are executed in parallel up to the population
size.
Experimental Results
-The Blue and Red dots represent different search decompositions
- Hollow dots represent the Pareto surface.
- The use of parallel evaluations significantly sped up the search process
Evolutionary Algorithm Features
•
Can seed the initial set of candidate vectors
- Uniformly creates solutions with fewer dropped observations (i.e.
observations which miss their last chance to schedule)
•
The GDE framework allows constraint limits to be specified on
criteria values
‣ Will first evolve out of constraint violation space
‣ Will not consider solutions with violations for crossover if violation free
solutions exit
‣ Want variety in the search space but not at the expense of infeasible
solutions
-
Need to consider the depth versus the breadth of the search
space
‣ Is it better to have more generations but less elements in each generation
or to have less generations but more elements in each generation?
Selecting Solutions
•
So you have generated a Pareto-Surface of solutions
for a problem, now what do you do?
• Still have the problem of selecting a solution for
execution
•
Need to provide tools to end users that enable them
to explore the trade-offs in the Pareto Surface
- Trade off space can have a high dimensionality
making it hard for users to see patterns in the data
- Multi-objective problems often require multiple
users to be involved
‣ Each user contributes one or more objectives
Visualizing the trade-off space
• Traditional X-Y plots show trade offs between 2 objectives
• Hard to see relationships between the different graphs
• The number of plots increases rapidly as the number of
objectives increases
Parallel Coordinate Graphs
Parallel Coordinate Graphs
• Each solution is represented by a single line
• Creiteria values are plotted horizontally on a
normalized scale
•
Pros:
- Easy to see relationship between the criteria values
of different solutions
- Graphs scale linearly with the number of criteria
•
Cons:
- Not intuitive in that they need explantions
- Graphs can get crowded
Self Organizing Map
Self Organizing Maps
• Colors represent different criteria
• Circles with wedges represent solutions
• The map conveys information with:
- The geometry of the color coded shape
‣ correlation between criteria
- The placement of the circles on the map
‣ Correlation with criteria values
•
The size of the wedges within a circle represent
criteria values for solutions
The determination of a good self organizing map is
itself a multi-objective optimization problem
Crowding and Coordinate Plots
What Does this HST Plot tell us?
Interesting Solutions
•
Can use existing algorithms to display only the
interesting subset of a Pareto-surface.
• The genetic algorithm used in these experiments has
a crowding distance measure
- Used to reduce the number of candidates to the
population size at each generation
•
We reused the measure to display only the interesting
subset of a Pareto-surface.
A reduced Parallel Coordinate
chart
Shows the top 25% most interesting solutions
What Does this Plot tell us?
Exploring the surface
•
•
No single view of the data is always best
Interface needs to provide multiple views that allow
users to dynamically explore the Pareto surface
- Allow users to adjust bounds on what is displayed
- Sort data and or to filter out data
- Link together different graphs by selecting solutions
So you generated a Pareto Surface, Now what?
Developers Challenges
•
Need tools which allow developers to compare
different multi-objective algorithms
- There are many variants for multiple objective
algorithms:
‣ High level search decomposition (choice of variables, values)
‣ Parameters controlling search
- Number of generations, size of each generation
-
Developers want to select the best algorithm variant
for their particular application domain.
Evaluating Algorithms
•
Features of planning algorithms:
- Runtime space and time performance
- Ease of system integration
- Transparency (easy to understand results)
- Maintainability of the code
- Quality of the solutions produced
•
These features apply to both single and multiobjective algorithms
- Evaluating solution quality is different for multiobjective and single objective algorithms
Evaluating Solution Quality
•
Single objective algorithms produces a single solution
for a problem instance
- Maximizes an objective function combining multiple
criteria
- Different single-objective algorithms can be directly
compared using the objective function
•
Multi-objective algorithm produces a Pareto-surface
of solutions where
- No solution is dominated by another solution for all
criteria
- Comparing algorithms for a problem requires
comparing Pareto-surfaces
Evaluating Surfaces
•
(Zitzler 2003) There is no Unary function, F, on surfaces such that if
F(surface1) > F(surface2) then surface1 is better than surface2
•
You can construct binary evaluation functions that detect domination between
surfaces
-Let C
be the Pareto surface
obtained by combining surfaces
S1 and S2
-The following function detects
domination:
‣If Intersect(S1,C) == S1 and
intersect(S2,C)== NULL then S1
dominates S2
‣ Algorithms 1 dominates Algorithm 2
Binary Evaluation Metric 1
•
You can construct binary evaluation functions that give metric
comparisons between surfaces:
- Define F(S1,S2) = Length(Intersect(S1,C)) / Length(S1)
• C is the combined Pareto
surface of S1 and S2.
• In the example
•F(A1,A2) = 4/5
• F(A2,A1) = 1/5
Binary Evaluation Metric 2
•
Define E(P1,P2) as the factor by which one Pareto
surface is worse than another with respect to all
objectives.
- E(P1,P2) is the minimum factor e such that for any
solution in P2 there exists a solution in P1 that is not
worse by a factor of e in all objectives.
- If E(P1,P2) is smaller than E(P2,P1) then the
indicator implies that P1 is preferable to P2.
Formalism versus Graphics
•
How well do the binary evaluation metrics perform
compared to intuitions gained from graphic displays of
Pareto-surfaces?
- Can we use metrics to evaluate algorithms?
•
We compare results for two sets of experiments
- For the purpose of this talk we will just compare the
blue algorithm with the red algorithm
Metrics vs Visualization (1)
• Both of the metrics
indicate a preference for the
blue search.
• This agrees with our visual
intuition as we see more
blue than red in the plots.
• The metrics do not show
features we can easily
see from the charts:
• The broad blue search
provides a better min gap
values at the cost of a high
number of dropped
observations
Schedule
Run
E-metric
F-metric
Blue
1.61
0.58
Red
3.45
0.42
Metrics vs Visualization (2)
•Both of the metrics indicate a
preference for the blue search.
• This agrees with our visual
intuition as we see more blue
than red in the plots.
• The metrics do not show
features we can easily see
from the charts:
• The delayed search is much
better in terms of momentum.
• The two approaches are
competitive if we do not
consider momentum.
Schedul
e Run
E-metric
F-metric
blue
1.58
0.6
red
1.98
0.4
Metrics vs Visualization
•
Take home thoughts:
- Metrics can provide a high level comparison of
Pareto-surfaces
- Metrics miss intuitions that can be gained through
the use of visualization tools.
- Use both techniques
Evaluating Surfaces - Analogy
Programmer
Which
Algorithm
Should I
select?
Scheduler
Which
Schedule
Should I
select?
• Selecting an evolutionary algorithm out of a set of algorithms
is like selecting a solution for execution out of a Pareto
Surface
- If there is a dominating algorithm/solution then it will be
selected
- If there is no domination then it is up to the user to
otherwise it is up to user to select a algorithm/solution
• What is needed are tools that allow users to examine and
manipulate Pareto-Surfaces
Overview
•
Multi-Objective algorithms have advantages over the
traditional approach of combining criteria with a
weighted average
- Do not pre-determine trade-offs between criteria
- Provide end users with a Pareto surface of
solutions to select from
- Automate manual steps of adjusting criteria weights
•
Existing Multi-Objective Algorithms are effective in
building uniformly sampled approximations of the
Pareto surface
•
Challenges in providing dynamic visualization tools
for exploring the surface and selecting solutions