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Multi-Objective Planning and Scheduling with Astronomical Applications Mark Giuliano – Space Telescope Science Institute

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Talk Outline Why Multi-Objective Planning and Scheduling? Why Multi-Objective Planning and Scheduling? Motivation Implementation Approaches Implementation Approaches Genetic algorithms Example application Challenges Challenges Visualization tools Evaluating algorithms

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Overall Goal Schedule astronomical and other space science observations to optimize science return 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

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Goals Effective decision support tools that enable participants to optimize schedules in a collaborative manner... Effective decision support tools that enable participants to optimize schedules in a collaborative manner...

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Goals Effective decision support tools that enable participants to optimize schedules in a collaborative manner Effective decision support tools that enable participants to optimize schedules in a collaborative manner multiple objectives

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Goals Effective decision support tools that enable participants to optimize schedules in a collaborative manner Effective decision support tools that enable participants to optimize schedules in a collaborative manner multiple participants

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Goals Effective decision support tools that enable participants to optimize schedules in a collaborative manner Effective decision support tools that enable participants to optimize schedules in a collaborative manner enable integration with existing tools

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Multi-Objective Scheduling Effective scheduling of space based astronomy missions requires the ability to make trade-offs among competing mission objectives: 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 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 Objectives have different constituents lobbying for them e.g. mission science community versus engineering E.g. Solar system observers versus galaxy observers

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Traditional Approach The traditional approach to handling multiple objectives is to combine the weighted average of separate objectives The traditional approach to handling multiple objectives is to combine the weighted average of separate objectives ∑α i f i (x) But: combining objectives loses information and pre-determines the trade-offs among them! 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 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

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Multi-Objective Solution Approaches Multi-Objective Scheduling: 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

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Comparing the Approaches Traditional ApproachMulti Objective 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 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:The multi objective approach: - Automates steps that users would manually perform in the traditional approach; - Provides a more formal basis to select a solution.

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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 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 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, non- simultaneous users, domain-specific scheduling GUIs

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Implementation Approaches Evolutionary algorithms provide a natural fit for finding Pareto-surfaces 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

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Evolutionary Algorithms Based on models of animal Evolution Based on models of animal Evolution Core Algorithm; Core Algorithm; Generate the initial population Generate the initial population Evaluate the fitness of each member of the population Evaluate the fitness of each member of the population Repeat until termination 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

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GDE3 GDE3 is based on differential evolution optimization for single- objective problems (Price, et. al 2005) GDE3 is based on differential evolution optimization for single- objective 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 non- dominated sorting and crowding distance (to improve diversity along Pareto frontier)

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Typical System Architecture GDE3 - Implements multi- objective evolutionary algorithms Creates and evolves decision variable vectors SPIKE - Implements scheduling domain. Creates and evaluates schedules seeded by decision variable vectors

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Application: James Webb Telescope Application: James Webb Telescope Launch Launch Infrared sensors to detect the earliest star formation Infrared sensors to detect the earliest star formation L2 orbit 1.5 million km from Earth L2 orbit 1.5 million km from Earth 6.2 meter mirror 6.2 meter mirror Tennis court sized sun shield to protect science instruments Tennis court sized sun shield to protect science instruments

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Solar radiation pressure Sun normal to shield: minimal reaction wheel spin up Challenge: Momentum Scheduling

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Solar radiation pressure Sun not normal to shield: reaction wheel spin to maintain pointing

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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.

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JWST Momentum Challenges The model is a three dimensional vector space. The model is a three dimensional vector space. Momentum accumulation for an observation varies: Momentum accumulation for an observation varies: Over time in non-linear manner Momentum accumulation is additive in nature. 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. Momentum provides both a hard constraint due to a limited capacity, and a preference to consume as little resource as possible.

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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

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JWST Scheduling Engine (SPIKE) Multi-Objective Scheduler + JWST Application Map JWST Experiments Evaluated system using JWST Science Design Reference Mission Evaluated system using JWST Science Design Reference Mission Schedule observations to a quantum of 7 minutes in a 22- day momentum bin Schedule observations to a quantum of 7 minutes in a 22- day momentum bin Using GDE3 evolutionary algorithm (Java) with Lisp-based SPIKE JWST Scheduler Using GDE3 evolutionary algorithm (Java) with Lisp-based SPIKE JWST Scheduler Implemented parallel domain scheduler driver Implemented parallel domain scheduler driver Candidate vectors are executed in parallel up to the population size. Candidate vectors are executed in parallel up to the population size.

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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 Experimental Results

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Evolutionary Algorithm Features Can seed the initial set of candidate vectors 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 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?

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Selecting Solutions So you have generated a Pareto-Surface of solutions for a problem, now what do you do? 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 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 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

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Visualizing the trade-off space Traditional X-Y plots show trade offs between 2 objectivesTraditional X-Y plots show trade offs between 2 objectives Hard to see relationships between the different graphsHard to see relationships between the different graphs The number of plots increases rapidly as the number of objectives increasesThe number of plots increases rapidly as the number of objectives increases

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Parallel Coordinate Graphs

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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

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Self Organizing Map

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Self Organizing Maps Colors represent different criteria Colors represent different criteria Circles with wedges represent solutions Circles with wedges represent solutions The map conveys information with: 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 The determination of a good self organizing map is itself a multi-objective optimization problem

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Crowding and Coordinate Plots What Does this HST Plot tell us?

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Interesting Solutions Can use existing algorithms to display only the interesting subset of a Pareto-surface. 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 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. We reused the measure to display only the interesting subset of a Pareto-surface.

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A reduced Parallel Coordinate chart Shows the top 25% most interesting solutions What Does this Plot tell us?

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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

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So you generated a Pareto Surface, Now what? Developers Challenges Need tools which allow developers to compare different multi-objective algorithms 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.

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Evaluating Algorithms Features of planning 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 multi- objective algorithms These features apply to both single and multi- objective algorithms Evaluating solution quality is different for multi- objective and single objective algorithms

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Evaluating Solution Quality Single objective algorithms produces a single solution for a problem instance 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 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

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Evaluating Surfaces (Zitzler 2003) There is no Unary function, F, on surfaces such that if F(surface 1 ) > F(surface 2 ) then surface 1 is better than surface 2 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

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Binary Evaluation Metric 1 You can construct binary evaluation functions that give metric comparisons between surfaces: 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. C is the combined Pareto surface of S1 and S2. In the example In the example F(A1,A2) = 4/5 F(A1,A2) = 4/5 F(A2,A1) = 1/5 F(A2,A1) = 1/5

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Binary Evaluation Metric 2 Define E(P 1,P 2 ) as the factor by which one Pareto surface is worse than another with respect to all objectives. Define E(P 1,P 2 ) as the factor by which one Pareto surface is worse than another with respect to all objectives. E(P 1,P 2 ) is the minimum factor e such that for any solution in P 2 there exists a solution in P 1 that is not worse by a factor of e in all objectives. If E(P 1,P 2 ) is smaller than E(P 2,P 1 ) then the indicator implies that P 1 is preferable to P 2.

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Formalism versus Graphics How well do the binary evaluation metrics perform compared to intuitions gained from graphic displays of Pareto-surfaces? 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 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

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Metrics vs Visualization (1) Schedule Run E-metricF-metric Blue Red Both of the metrics indicate a preference for the blue search. 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. 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 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 The broad blue search provides a better min gap values at the cost of a high number of dropped observations

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Metrics vs Visualization (2) Both of the metrics indicate a preference for the blue search.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. 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 metrics do not show features we can easily see from the charts: The delayed search is much better in terms of momentum. The delayed search is much better in terms of momentum. The two approaches are competitive if we do not consider momentum. The two approaches are competitive if we do not consider momentum. Schedul e Run E-metricF-metric blue red

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Metrics vs Visualization Take home thoughts: 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

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Evaluating Surfaces - Analogy Selecting an evolutionary algorithm out of a set of algorithms is like selecting a solution for execution out of a Pareto Surface 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 What is needed are tools that allow users to examine and manipulate Pareto-Surfaces Programmer Scheduler Which Algorithm Should I select? WhichSchedule Should I select?

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Overview Multi-Objective algorithms have advantages over the traditional approach of combining criteria with a weighted average 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 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 Challenges in providing dynamic visualization tools for exploring the surface and selecting solutions

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