Identifying Optimal Trade-Offs between CPU Time Usage and Temporal Constraints
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This document describes a method for identifying optimal trade-offs between CPU time usage and temporal constraints in software integration using multi-objective search. The method models the problem as a constrained optimization problem to minimize CPU time usage and number of time slots while satisfying timing constraints. A multi-objective genetic algorithm searches over task offset vectors to find Pareto optimal solutions representing different trade-offs. The approach is evaluated on a large automotive case study with 430 tasks, finding solutions that reduce CPU usage by 60-70% compared to a naive approach.
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Identifying Optimal Trade-Offs between CPU Time Usage and Temporal Constraints
- 1. Identifying Optimal Trade-Offs between CPU Time Usage and Temporal Constraints Using Search" Shiva Nejati, Lionel C. Briand" SnT Centre, University of Luxembourg" " "
- 2. Today’s cars are developed in a distributed way 2
- 3. Integration of software from different sources is essential in most embedded software industries 3
- 4. Software integration involves multiple stakeholders 4 Car Makers Software Part Suppliers Software Integrator
- 5. Software integrators have to fulfill conflicting objectives 5 Car Makers Part Suppliers Objective: Effective execution and synchronization of runnables Some runnables should execute simultaneously or in a certain order Objective: Effective usage of CPU time The CPU time used by all the runnables should remain as low as possible over time
- 6. It is challenging to satisfy all objectives Car Makers r0 r1 r2 r3 Part Suppliers Minimize CPU time usage Execute r0 to r3 close to one another. 0ms 5ms 10ms 15ms 20ms 25ms 30ms 0ms 5ms 10ms 15ms 20ms 25ms 30ms 0ms 5ms 10ms 15ms 20ms 25ms 30ms 6 4ms 3ms 2ms 1 slot 2 slots 3 slots
- 7. 7 An multi-objective decision support approach # of slots 2ms 3ms 4ms CPU time usage 3 2 1 Pareto Front Solutions/ Tradeoff Solutions Car Makers Part Suppliers
- 8. Constrained Optimization Problem (COP) 8 Objective Function(s): Minimizing CPU time usage Minimizing # of time slots Constraint model: Tasks and their timing properties Scheduling policy Search Space: Vectors of Task Offsets
- 9. • Tasks and their timing properties • Static Cyclic Scheduling 0ms 5ms 10ms 15ms 20ms 25ms 30ms 9 Constraint model period = 5ms period = 10ms
- 10. 10 4ms 3ms Search Space Vectors of task offsets (initial delays) r0 r1 r2 r3 o0=0, o1=0, o2=0, o3=0 0ms 5ms 10ms 15ms 20ms 25ms 30ms o0=0, o1=5, o2=5, o3=0 0ms 5ms 10ms 15ms 20ms 25ms 30ms
- 11. (1) CPU time usage 0ms 5ms 10ms 15ms 20ms 25ms 30ms 11 Objective Functions (2) Number of Time slots 0ms 5ms 10ms 15ms 20ms 25ms 30ms Runnables r0, r1, r2, and r3 run in within at most two consecutive time slots infinitely often iff for every ri, rj 2 {r0, r1, r2, r3}, for some l < 2 oi ⌘ oj + l ⇥ 5 mod(gcd(periodi, periodj)) 3ms
- 13. 13 Multi-Objective Search algorithm Non-dominated Sorting Genetic Algorithm version 2 (NSGA-II) Solution Representation a vector of offset values: o0=0, o1=5, o2=5, o3=0 Search operators Selection: Binary tournament selection with replacement Crossover: uniform cross over Mutation: o0=0, o1=5, o2=5, o3=0 à o0=0, o1=5, o2=10, o3=0 Fitness Functions max CPU time usage per time slot, and number of time slots during which the tasks run
- 14. 14 Case Study and Experiments An automotive software project with 430 tasks. These 430 tasks can be scheduled in almost 10^320 different ways.
- 15. 15 Naïve execution of the runnables 5.34ms 5.34ms 5 ms Time CPU time usage (ms) CPU time usage exceeds the size of the slot (5ms)
- 16. 16 After applying our work 5 ms ms) (usage [2.04ms … 1.45ms] time CPU Time Depending on the number of slots, CPU time usage is between 2.04ms to 1.45ms. So, around 60% to 70% of each time slot is guaranteed to be free.
- 17. 17 Research Questions RQ1 Sanity Check Do we do better than a trivial (random search) solution? RQ2 Effectiveness Are we able to find solutions that are close to known lower bounds? RQ3 Performance How long does it take to compute solutions? RQ4 Usefulness Are we able to find useful trade-off solutions?
- 18. 18 RQ2: Effectiveness most relaxed temporal constraint (# of time slots = ∞) most restricted temporal constraint (# of time slots for each group = 1) 1.43 ms 2.03 ms most relaxed temporal constraint (# of time slots = ∞) 1.45 ms most restricted temporal constraint (# of time slots for each group = 1) 2.04 ms Our Results Ideal CPU usage
- 19. 19 RQ3: Performance Our approach generates optimal results in about 5 min 90 80 min) (Time 70 60 50 40 NSGA-II(25,000) Random(25,000) Time (min) 8 7 6 5 4 NSGA-II(250,000) Random(250,000)
- 20. 20 RQ4: Usefulness # of slots 1.452.04 CPU time usage (ms) 21 14 12 1.56 1 2 3 Boundary Trade Offs Interesting Solutions
- 21. Related Work • Feasibility analysis – Schedulable or not? v We perform optimization by finding the best solutions among all the feasible ones • Logical models – Correct/incorrect? v We provide an explicit time model enabling us to perform a quantitative analysis • Symbolically represent the model and rely on model-checkers or constraint solvers – State explosion problem v We scale to very large search spaces: 10^320 21
- 22. Our Contributions 22 Casting a schedulability analysis problem as a multi-objective constrained optimization problem Objective Functions Constraint models Search Space Scaling to a very large industry case study Search Space of 10^320 Our approach is applicable to similar CPU utilization problems if Tasks timing properties are known although tasks may come from third parties A constraint model capturing the scheduling policy can be defined