Multi-objective negotiation of power profiles for datacenter powered - - PowerPoint PPT Presentation
Multi-objective negotiation of power profiles for datacenter powered with renewable energies Lo Grange University of Toulouse Institut de Recherche en Informatique de Toulouse (IRIT) July 2018 Context and overview Approach Methodology and
Léo Grange
University of Toulouse Institut de Recherche en Informatique de Toulouse (IRIT)
July 2018
Context and overview Approach Methodology and evaluation Conclusion
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 1 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Worldwide: 270 TWh in 2012
≈ Italy electricity consumption High economical and environmental costs
Possible mitigations
Improve energy efficiency, software and hardware Use renewable energy sources power
Solar, wind: intermittent and little predictability New challenges to make efficient use in datacenters
ANR Datazero: on-site renewable sources IT and electrical cooperation
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 2 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks
Power profile evaluation Power profile evaluation
Separated IT and electrical optimizations
Ability to evaluate power plan impact Internal objective (utility) Black box functions RT → R Computationally expensive
0:00 6:00 12:00 18:00 Time 2 4 6 8 10 12 Power
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 3 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks
Power profile evaluation Power profile evaluation
Separated IT and electrical optimizations
Ability to evaluate power plan impact Internal objective (utility) Black box functions RT → R Computationally expensive
0:00 6:00 12:00 18:00 Time 2 4 6 8 10 12 Power
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 3 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks
Power profile evaluation Power profile evaluation
Separated IT and electrical optimizations
Ability to evaluate power plan impact Internal objective (utility) Black box functions RT → R Computationally expensive
0:00 6:00 12:00 18:00 Time 2 4 6 8 10 12 Power Electrical utility
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 3 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks
Power profile evaluation Power profile evaluation
Separated IT and electrical optimizations
Ability to evaluate power plan impact Internal objective (utility) Black box functions RT → R Computationally expensive
0:00 6:00 12:00 18:00 Time 2 4 6 8 10 12 Power IT utility Electrical utility
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 3 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Each DM has one or more objectives to satisfy Objectives may differ between DM
QoS related for ITDM, environmental impact for PDM
Managing different objectives
Avoiding the problem: find common objective (money?) Scalarization (e.g. weighted sum) Finding a set of good solutions (set of possible trade-offs)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 4 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Each DM has one or more objectives to satisfy Objectives may differ between DM
QoS related for ITDM, environmental impact for PDM
Managing different objectives
Avoiding the problem: find common objective (money?) Scalarization (e.g. weighted sum) Finding a set of good solutions (set of possible trade-offs)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 4 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Each DM has one or more objectives to satisfy Objectives may differ between DM
QoS related for ITDM, environmental impact for PDM
Managing different objectives
Avoiding the problem: find common objective (money?) Scalarization (e.g. weighted sum) Finding a set of good solutions (set of possible trade-offs)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 4 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Find Pareto front (best trade-offs)
50 50 100 150 20 15 10 5 5 10 15
Electrical utility IT utility
Multi-Objective Evolutionary Algorithms
Well studied area, various approaches Focused on SPEA2 (genetic algorithm)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 5 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Find Pareto front (best trade-offs)
50 50 100 150 20 15 10 5 5 10 15
Electrical utility IT utility
0:00 12:00 0:00 Time Power
Multi-Objective Evolutionary Algorithms
Well studied area, various approaches Focused on SPEA2 (genetic algorithm)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 5 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Find Pareto front (best trade-offs)
50 50 100 150 20 15 10 5 5 10 15
Electrical utility IT utility
0:00 12:00 0:00 Time Power 0:00 12:00 0:00 Time Power
Multi-Objective Evolutionary Algorithms
Well studied area, various approaches Focused on SPEA2 (genetic algorithm)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 5 / 21
Context and overview Approach Methodology and evaluation Conclusion Context and overview of the problem
Find Pareto front (best trade-offs)
50 50 100 150 20 15 10 5 5 10 15
Electrical utility IT utility
0:00 12:00 0:00 Time Power 0:00 12:00 0:00 Time Power
Multi-Objective Evolutionary Algorithms
Well studied area, various approaches Focused on SPEA2 (genetic algorithm)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 5 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
1 2 Time step 2 4 6 Power
u = −0.29
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
1 2 Time step 2 4 6 Power
u = −0.29
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
1 2 Time step 2 4 6 Power
u = 0.41
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
1 2 Time step 2 4 6 Power
u = −1.2
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Evaluation of power profile is costly
Genetic algorithms require many evaluations
Workaround: Utility approximation
Fast approximation based on known solutions Evaluate only potentially good ones
Example: utility function, 2 time steps
1 2 3 4 5 6 2nd time slot power 1 2 3 4 5 6 1st time slot power
PDM utility for 2 time slots
2.0 1.6 1.2 0.8 0.4 0.0 0.4 0.8
Only 2 dimensions, easy
dimensions?
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 6 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Goal: find a function RT → R (profile to utility). Online learning with few training data
Utility function changes between negotiations
Curse of dimensionality...
RT is huge (T > 100 in many scenarios) Most regression method become impractical
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 7 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Goal: find a function RT → R (profile to utility). Online learning with few training data
Utility function changes between negotiations
Curse of dimensionality...
RT is huge (T > 100 in many scenarios) Most regression method become impractical
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 7 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks
Power profile evaluation Power profile evaluation
Improving negotiation for utility approximation
Estimator between negotiation algorithm and DM Acts like a smart cache
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 8 / 21
Context and overview Approach Methodology and evaluation Conclusion Utility approximation
Negotiation module Optimization algorithm Electrical infrastructure PDM Forecast IT infrastructure ITDM Tasks Estimator
Solution cache Approximation function
Estimator
Solution cache Approximation function
Improving negotiation for utility approximation
Estimator between negotiation algorithm and DM Acts like a smart cache
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 8 / 21
Context and overview Approach Methodology and evaluation Conclusion
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 8 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
New individuals Archive Archive New individuals Initial population Sorted individuals
Evaluate
Strength Pareto sorting
Eliminated Next archive
Selection
Next generation offspring (mutation & crossover)
Asynchronous approximation integration
Evaluation may be replaced by approximation Mix of evaluated and approximated individuals
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 9 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
New individuals Archive Archive New individuals Initial population Sorted individuals
Evaluate
Strength Pareto sorting
Eliminated Next archive
Selection
Next generation offspring (mutation & crossover)
Asynchronous approximation integration
Evaluation may be replaced by approximation Mix of evaluated and approximated individuals
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 9 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
Attribution of objective values
Lifetime associated to individuals Evaluated if conserved until lifetime is zero (archive)
Added to knowledge base
For each individual:
New individual?
Lifetime > 0
Decrement lifetime Miss? Done No Yes No Yes Yes No Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 10 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
Attribution of objective values
Lifetime associated to individuals Evaluated if conserved until lifetime is zero (archive)
Added to knowledge base
For each individual:
New individual?
Lifetime > 0
Decrement lifetime Miss? Done No Yes No Yes Yes No Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 10 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
Attribution of objective values
Lifetime associated to individuals Evaluated if conserved until lifetime is zero (archive)
Added to knowledge base
For each individual:
New individual?
Lifetime > 0
Decrement lifetime Miss? Done No Yes No Yes Yes No Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 10 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
Attribution of objective values
Lifetime associated to individuals Evaluated if conserved until lifetime is zero (archive)
Added to knowledge base
For each individual:
New individual?
Lifetime > 0
Decrement lifetime Miss? Done No Yes No Yes Yes No Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 10 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
SPEA2 not well adapted to asynchronous approximation
Limited archive of individuals Bad (optimistic) approximations → good solutions lost Still approximated solutions after ending condition reached
Pareto Objective 2 Objective 1
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 11 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
SPEA2 not well adapted to asynchronous approximation
Limited archive of individuals Bad (optimistic) approximations → good solutions lost Still approximated solutions after ending condition reached
Pareto Objective 2 Objective 1
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 11 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
SPEA2 not well adapted to asynchronous approximation
Limited archive of individuals Bad (optimistic) approximations → good solutions lost Still approximated solutions after ending condition reached
P a r e t
Objective 1
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 11 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
SPEA2 not well adapted to asynchronous approximation
Limited archive of individuals Bad (optimistic) approximations → good solutions lost Still approximated solutions after ending condition reached
Pareto Objective 2 Objective 1
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 11 / 21
Context and overview Approach Methodology and evaluation Conclusion Adapting MOEA for objective approximation
Modify SPEA2 to manage uncertain solutions (approximations) Add an archive of evaluated solutions (certain archive) Avoiding duplication of individuals Stopping USPEA2 at any time results in a set of valid solutions.
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 12 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
+1
0.5 1
Haar wavelet transform
Extract frequency and temporal features of a signal. Fast to compute Works well with discrete series ≈ successive mean between time steps Conserve euclidean distances
mean=7 mean=3
( 8, 6, 1, 5 ) Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 13 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
+1
0.5 1
Haar wavelet transform
Extract frequency and temporal features of a signal. Fast to compute Works well with discrete series ≈ successive mean between time steps Conserve euclidean distances
mean=7 mean=3
( 8, 6, 1, 5 ) Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 13 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
+1
0.5 1
Haar wavelet transform
Extract frequency and temporal features of a signal. Fast to compute Works well with discrete series ≈ successive mean between time steps Conserve euclidean distances
H2=[1,-2]
+1
+2
mean=7 mean=3
( 8, 6, 1, 5 ) Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 13 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
+1
0.5 1
Haar wavelet transform
Extract frequency and temporal features of a signal. Fast to compute Works well with discrete series ≈ successive mean between time steps Conserve euclidean distances
H1=[2]
+2
mean=5
H2=[1,-2]
+1
+2
mean=7 mean=3
( 8, 6, 1, 5 ) Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 13 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
+1
0.5 1
Haar wavelet transform
Extract frequency and temporal features of a signal. Fast to compute Works well with discrete series ≈ successive mean between time steps Conserve euclidean distances
H0=[5]
+5
H1=[2]
+2
mean=5
H2=[1,-2]
+1
+2
mean=7 mean=3
( 8, 6, 1, 5 ) Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 13 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
Distance between partial Haar representations from known solutions
Lowest frequencies features first
Select known solutions closer than a threshold If enough solutions: repeat with higher frequency Result: weighted average of close utilities Complexity: O(n log(n)) (n solutions in base)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 14 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
Distance between partial Haar representations from known solutions
Lowest frequencies features first
Select known solutions closer than a threshold If enough solutions: repeat with higher frequency Result: weighted average of close utilities Complexity: O(n log(n)) (n solutions in base)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 14 / 21
Context and overview Approach Methodology and evaluation Conclusion Multi-resolution Haar approximation
Distance between partial Haar representations from known solutions
Lowest frequencies features first
Select known solutions closer than a threshold If enough solutions: repeat with higher frequency Result: weighted average of close utilities Complexity: O(n log(n)) (n solutions in base)
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 14 / 21
Context and overview Approach Methodology and evaluation Conclusion
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 14 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
P a r e t
r
t Objective 2 (max) Objective 1 (max)
Hypervolume indicator
Area covered between Pareto front of solution set and any reference point. ≥ if solutions are better (dominate) ≥ if solution set is more spread
Generational distance
Average distance between approximation front and best known Pareto front Requires a good comparison set
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 15 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
Ref P a r e t
r
t Objective 2 (max) Objective 1 (max)
Hypervolume indicator
Area covered between Pareto front of solution set and any reference point. ≥ if solutions are better (dominate) ≥ if solution set is more spread
Generational distance
Average distance between approximation front and best known Pareto front Requires a good comparison set
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 15 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
Hypervolume
Hypervolume
Ref P a r e t
r
t Objective 2 (max) Objective 1 (max)
Hypervolume indicator
Area covered between Pareto front of solution set and any reference point. ≥ if solutions are better (dominate) ≥ if solution set is more spread
Generational distance
Average distance between approximation front and best known Pareto front Requires a good comparison set
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 15 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
Hypervolume
Hypervolume
Ref A p p r
f r
t Objective 2 (max) Objective 1 (max) Real Pareto front
Hypervolume indicator
Area covered between Pareto front of solution set and any reference point. ≥ if solutions are better (dominate) ≥ if solution set is more spread
Generational distance
Average distance between approximation front and best known Pareto front Requires a good comparison set
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 15 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
Simplified models, keep optimum computable
IT decision module
«Fluid» workload: total amount of CPU time Utility: revenue
Reward for each unit scheduled Incentive to execute unit early
Electrical decision module
Solar panels, batteries, electrical grid in/out Utility: equivalent CO2 emission
Zero for renewable Grid electricity average emission Battery aging, based on manufacturing cost
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 16 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
Simplified models, keep optimum computable
IT decision module
«Fluid» workload: total amount of CPU time Utility: revenue
Reward for each unit scheduled Incentive to execute unit early
Electrical decision module
Solar panels, batteries, electrical grid in/out Utility: equivalent CO2 emission
Zero for renewable Grid electricity average emission Battery aging, based on manufacturing cost
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 16 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
3 days scenarios Workload: 75% of maximum data center capacity
ExcessRenew: sunny days, initial battery 50% Normal: less sunny days FewRenew: almost no sun, initial battery at 25%
12 24 36 48 60 72 Time (hours) 5 10 15 20 Power (kW)
Optimal formulation → comparison Pareto front (U)SPEA2 ending condition: budget of utility evaluations
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 17 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
3 days scenarios Workload: 75% of maximum data center capacity
ExcessRenew: sunny days, initial battery 50% Normal: less sunny days FewRenew: almost no sun, initial battery at 25%
12 24 36 48 60 72 Time (hours) 5 10 15 20 Power (kW)
Optimal formulation → comparison Pareto front (U)SPEA2 ending condition: budget of utility evaluations
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 17 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
3 days scenarios Workload: 75% of maximum data center capacity
ExcessRenew: sunny days, initial battery 50% Normal: less sunny days FewRenew: almost no sun, initial battery at 25%
12 24 36 48 60 72 Time (hours) 5 10 15 20 Power (kW)
Optimal formulation → comparison Pareto front (U)SPEA2 ending condition: budget of utility evaluations
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 17 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
3 days scenarios Workload: 75% of maximum data center capacity
ExcessRenew: sunny days, initial battery 50% Normal: less sunny days FewRenew: almost no sun, initial battery at 25%
12 24 36 48 60 72 Time (hours) 5 10 15 20 Power (kW)
Optimal formulation → comparison Pareto front (U)SPEA2 ending condition: budget of utility evaluations
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 17 / 21
Context and overview Approach Methodology and evaluation Conclusion Methodology
3 days scenarios Workload: 75% of maximum data center capacity
ExcessRenew: sunny days, initial battery 50% Normal: less sunny days FewRenew: almost no sun, initial battery at 25%
12 24 36 48 60 72 Time (hours) 5 10 15 20 Power (kW)
Optimal formulation → comparison Pareto front (U)SPEA2 ending condition: budget of utility evaluations
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 17 / 21
Context and overview Approach Methodology and evaluation Conclusion Results
Scenario Normal, 80 time steps
50 100 200 400 800 1600 Evaluation budget (log scale) 0.55 0.60 0.65 0.70 0.75 Normalized Hypervolume SPEA2 + MHT SPEA2 only USPEA2 + MHT USPEA2 only 50 100 200 400 800 1600 Evaluation budget (log scale) 0.110 0.115 0.120 0.125 0.130 0.135 Distance to Pareto front
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 18 / 21
Context and overview Approach Methodology and evaluation Conclusion Results
Budget of 100 evaluations 80 time steps
ExcessRenew Normal FewRenew Scenarios 0.50 0.55 0.60 0.65 Normalized Hypervolume SPEA2 + MHT USPEA2 + MHT SPEA2 only USPEA2 only ExcessRenew Normal FewRenew Scenarios 0.35 0.40 0.45 0.50 Normalized Hypervolume SPEA2 + MHT USPEA2 + MHT SPEA2 only USPEA2 only
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 19 / 21
Context and overview Approach Methodology and evaluation Conclusion Results
Budget of 100 evaluations 80 time steps
ExcessRenew Normal FewRenew Scenarios 0.50 0.55 0.60 0.65 Normalized Hypervolume SPEA2 + MHT USPEA2 + MHT SPEA2 only USPEA2 only
320 time steps
ExcessRenew Normal FewRenew Scenarios 0.35 0.40 0.45 0.50 Normalized Hypervolume SPEA2 + MHT USPEA2 + MHT SPEA2 only USPEA2 only
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 19 / 21
Context and overview Approach Methodology and evaluation Conclusion Results
Initial profiles: Best profiles from each DM
ExcessRenew Normal FewRenew Scenarios 0.84 0.86 0.88 0.90 Normalized Hypervolume USPEA2 + MHT SPEA2 only
Approximation method AD: naive and usually ≈ baseline
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 20 / 21
Context and overview Approach Methodology and evaluation Conclusion Results
Initial profiles: Best profiles from each DM
ExcessRenew Normal FewRenew Scenarios 0.84 0.86 0.88 0.90 0.92 Normalized Hypervolume USPEA2 + MHT USPEA2 + AD SPEA2 only
Approximation method AD: naive and usually ≈ baseline
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 20 / 21
Context and overview Approach Methodology and evaluation Conclusion
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 20 / 21
Context and overview Approach Methodology and evaluation Conclusion
Find set of trade-offs power plans Approximation of power profile utility valuable
More objective space covered Similar hypervolume for 1/3rd to 1/5th evaluations Difficult to predict performances in advance...
USPEA2 ensure stable results with approximation
Similar to SPEA2 without approximation
Future works
Repeated planning policies: choosing a solution Better understanding of MOEA/approximation relationship
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 21 / 21
Context and overview Approach Methodology and evaluation Conclusion
Find set of trade-offs power plans Approximation of power profile utility valuable
More objective space covered Similar hypervolume for 1/3rd to 1/5th evaluations Difficult to predict performances in advance...
USPEA2 ensure stable results with approximation
Similar to SPEA2 without approximation
Future works
Repeated planning policies: choosing a solution Better understanding of MOEA/approximation relationship
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 21 / 21
Context and overview Approach Methodology and evaluation Conclusion
Find set of trade-offs power plans Approximation of power profile utility valuable
More objective space covered Similar hypervolume for 1/3rd to 1/5th evaluations Difficult to predict performances in advance...
USPEA2 ensure stable results with approximation
Similar to SPEA2 without approximation
Future works
Repeated planning policies: choosing a solution Better understanding of MOEA/approximation relationship
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 21 / 21
Context and overview Approach Methodology and evaluation Conclusion
Léo Grange (IRIT- University of Toulouse) GreenDays@Toulouse 2018 21 / 21