Dynamic Load Distributions for Adaptive Computations on MIMD Machines using Hybrid Genetic Algorithms (a subset)

Transcription

1 Dynamic Load Distributions for Adaptive Computations on MIMD Machines using Hybrid Genetic Algorithms (a subset) TIMOTHY H. KAISER PhD, Computer Science - UNM MS, Electrical Engineering - (Applied Physics) UCSD BS, Physics -UMR

2 Introduction Difficult talk to put together Subset of full dissertation defense Full dissertation can be found at Discuss parallel adaptive grid programs Dynamic load balancing - requirements for effectiveness Scope of research effort Genetic algorithms Sine qua nons for GA effectiveness Development Application 2

3 What are adaptive grid programs? Simulate a region of space and time using a grid of cells Often solving a PDE Weather modeling, fluid flow, aerodynamics Regions where higher spatial fidelity are required, have finer gridding Would want finer gridding at a weather storm front Would want finer gridding at a shock front New regions requiring higher spatial fidelity can move or be created Tornado Explosion Also called AMR or adaptive mesh refinement programs 3

4 4 An example grid program Numerical solution to Euler s equations U F G t x y + + =0 U u v E F u u p uv Eu pu G v uv v p Ev pv = = + + = + + ρ ρ ρ ρ ρ ρ ρ ρ ρ,, 2 2 ρ=density u=x velocity v=y velocity E= total energy These equations model the flow of fluids and gas

5 Parallelizing grid programs for speed up Assign portions of the grid to various processors Requires: Communication between processors Desirable Good load balanced Low communication cost Problem Getting perfect load balance and optimal communication is NP-Hard Various heuristics are used to solve this problem 5

6 Dynamic load balancing of adaptive grid programs Why is dynamic load balancing important? May start with balanced load and low communication The gird is refined in some region Processor holding refined region becomes heavily loaded Need to dynamically balance to get good performance Why is this difficult? Arbitrarily moving regions to new processors can cause high communication Must be done again when the grid changes Still NP-Hard 6

7 Scope of this research effort Needed to select a subset of all problems on which to work Adaptive grid program solves: Euler s fluid equations 2 dimensions Lower levels of parallelism Up to 16 nodes connected together by high speed network (SP1 and SP2) The committee felt such configurations are readily available Research should be applicable to other problems and architectures For very large problems framework would need modification 7

8 Thesis statement A genetic algorithm can be effectively used to decrease the run time of adaptive grid programs by maintaining good load balance and maintaining good communication performance. 8

9 Tools developed for thesis verification PLIFE - framework for a parallel adaptive grid or mesh program Darwin - framework for a parallel genetic algorithm Combined the two to create a parallel adaptive grid hydrodynamics simulation with dynamic load balancing and communication reduction 9

10 What is a Genetic Algorithm? An suboptimization system Find good, but maybe not optimal, solutions to difficult problems Often used on NP-Hard or combinatorial optimization problems Requirements Solution(s) to the problem represented as a string A fitness function Takes as input the solution string Output the desirability of the solution A method of combining solution strings to generate new solutions 10

11 More details on Genetic Algorithms Find solutions to problems by Darwinian evolution Potential solutions are thought of a living entities in a population The strings are the genetic codes of the individuals Individuals are evaluated for their fitness The fittest individuals are allowed to live and sexually reproduce There may be some mutation Parents die and kids start the next generation 11

12 Use of the GA After cells split, GA does the assignment of cells to processors For a particular potential assignment of cells to processors the GA: Counts the communication cost of the distribution Measures the imbalance of the distribution Fitness = weight of communication* (communication function) + weight of balance*(balance function) GAs have not been used in the past because they are too slow 12

13 For the GA to be effective Run fast Return good solutions Good load balance Low communication Key finding of dissertation: To enable fast and good solutions observe 2 sine qua nons Improvements must be made to the basic GA algorithm Domain specific knowledge must be used 13

14 Simulation used for the development of the sine qua nons Used a four node SP1 calculation Initial grid is 128 x 128 Each processor held a corner of the grid Exploded a bomb in the bottom left corner of the grid Restrictions One level of adaptation Only split cells are moved by the GA Cells are moved in clusters of 16 cells 14

15 First sine qua non - Use of domain specific knowledge Larger contiguous blocks cause less communication Clusters of cells are generated at irregular rates Future load can be estimated The most important piece of domain specific knowledge... 15

16 Cells split in the region of the shock front Shock wave propagating to the right. Boundary between split and unsplit cells across which communication will occur if the split cells are moved. 16

17 Cells split in the region of the shock front Implication Cells behind the shock split and may have been moved by the GA Cells in front of shock are not yet split and not yet moved by GA Conflict To balance load GA wants to move split cells To maintain low communication GA wants to not move cells Note: Next time GA is called more cells will have split Because shock propagates, cells in front of the shock will soon split GA will not want to move cells if those to the left have not moved 17

18 Exploitation of this domain specific knowledge Don t count communication between split and unsplit cells Sort term effect: Increases communication time GA is freer to move cells to balance load Long term effect: Contiguous blocks of cells on the same processor are larger Dramatic decrease in communication time 18

19 Results Without using this domain specific knowledge Communication time = 348 seconds Run time = 1510 seconds With domain specific knowledge in use Communication time = 228 seconds Run time = 1390 seconds Run time reduced by 2 minutes Show Movies 19

20 Second sine qua non - Improve the GA algorithm Run GA as a parallel application Developed a fast mutation methodology Use the Mansour-Fox algorithm Improve the Mansour-Fox algorithm 20

21 The Mansour-Fox algorithm Developed for static allocations Variable fitness function Initially put more weight on communication minimization In the end put more weight on balanced load About 50% - 75% through generations do the following: Call hill climbing routine for each member of GA population Greedy algorithm If cell has neighbors on different processor find best processor Increase mutation rate Mutate sections of gene which represent cells on boundaries 21

22 Mansour-Fox algorithm continued Problems: Slow because the hill climbing routine is slow Can not terminate early because of variable fitness function 22

23 Solution? Run as a parallel application Call the hill climbing routine every N generations with N>1 The hope is: Calling hill climbing routine every N generations speeds up routine Calling hill climbing routine every N generations will not greatly degrade the quality of the solution Hope was born out by experiment Improved Mansour-Fox algorithm reduced the run time of the adaptive grid simulation 23

24 What was learned to this point? What sine qua nons must be observed to make GA effective Use domain specific knowledge Improve the algorithm of the GA Important specifics: Ignore communication between split and unsplit cells in fitness function Use improved Mansour-Fox algorithm 24

25 Application of heuristics Problem run on 16 nodes of SP1 and SP2 Initial grid is 256 x 256 Multiple levels of adaptation Nonuniform distribution of mass 2 Pressure cycle= 0 t=0 pre 3.3 Nonuniform distribution of energy y x

26 Initial results using normal Mansour-Fox algorithm Parallel run time without GA = 1115 seconds Balance load only run time = 1240 seconds Mansour-Fox GA parameters: Population size = 320 Generations = 100 Adjusted weighting for cost of communication Weight Wall time Speed up GA Return Balance Comm. Time Run time with Mansour-Fox algorithm = 928 seconds with 44 seconds GA run time

27 Ran using the improved Mansour-Fox algorithm Allow the hill climbing routine to be called less often Tuned the GA Adjust to find optimum: Population size Number of generations Frequency of hill climbing routine in improved Mansour-Fox algorithm 27

28 Results with GA population size = 480 Often Size Gen Wall time Speed up GA Return Balance Comm. Time

29 Results with GA population size = 320 Often Size Gen Wall time Speed up GA Return Balance Comm. Time

30 Results with GA population size = 240 Often Size Gen Wall time Speed up GA Return Balance Comm. Time

31 Summary of results GA run time was in the range 18 to 117 seconds Simulation time was in the range of 1004 to 886 seconds Communication time was in the range of 283 to 325 seconds Run time reduced from 1115 seconds to 886 seconds by using the improved Mansour-Fox algorithm Speed up = 26% Population size = 320 Generations for GA =100 Frequency of calling hill climbing routine = 4 31

32 Improved Mansour-Fox algorithm By calling the hill climbing routine less often: GA run time is reduced from about 117 to about 2O seconds The algorithm still returned a good solution. Best run times with frequency of 4, longest with frequency of 1 Simulation run time (seconds) Generations=200 Generations=150 Generations= every 1 every 2 every 3 every 4 every 5 Frequency of hill climbing routine 32

33 Use of tuning the Genetic Algorithm Apply to other architectures Apply to other problems 33

34 Tuning for SP1 applied to SP2 Ran same simulation on the MHPCC SP2 Used same GA control parameters except: Conjecture is that we need a smaller weighting for communication down from Wall time Speed up GA Return Balance Comm. Time Weight Using tuning data from SP1 runs enabled 75% speed up on SP2 Conjecture is shown to be true Showed that tuning for one machine can be applied to another 34

35 Did comparison to bisection methods The Hybrid GA with improved Mansour-Fox algorithm produces the best results Machine Algorithm Run time Comm. Time Balance SP1 Best GA SP1 Centroid Bisection SP1 Coordinate Bisection SP2 Best GA SP2 Centroid Bisection SP2 Coordinate Bisection

36 Application to a different problem on SP1 Useful for performing trade studies Similar simulation Uniform blobs of energy and mass Deposited at different times Used best GA control parameters from the previous simulation (Frequency = 4, Size = 320, Generations = 100) Algorithm Wall time Speed up GA Return Balance Comm. Time Baseline Bisection GA Enabled 14% improvement in run time Recursive bisection caused a slow down 36

37 Future directions Using the GA Different architectures Have done simulations of SP2 SMP nodes 3d problems Oil field studies Improve the adaptive grid framework 3d Polygonal cells Edge based scheme 37

38 Summary Developed frameworks for Parallel adaptive mesh program Parallel Genetic Algorithm Studied the use of Genetic Algorithm to perform dynamic allocation of grids to processors Discovered two sine qua nons to enable the GA to be effective Use domain specific knowledge Improve the algorithm of the GA Showed the hybrid GA to be effective Using: Improved the Mansour-Fox algorithm Domain Knowledge of propagating shock waves Improved run time of an example calculation 75% 38