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GPU-Accelerated Genetic Algorithms

GPU-Accelerated Genetic Algorithms. Rajvi Shah + , P J Narayanan + , Kishore Kothapalli ˆ IIIT Hyderabad Hyderabad, India. + : Center for Visual Information Technology ˆ : Center for Security, Theory and Algorithmic Research. GAs – an introduction. Genetic Algorithms

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GPU-Accelerated Genetic Algorithms

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  1. GPU-Accelerated Genetic Algorithms Rajvi Shah+, P J Narayanan+, KishoreKothapalliˆ IIIT Hyderabad Hyderabad, India + : Center for Visual Information Technology ˆ : Center for Security, Theory and Algorithmic Research

  2. GAs – an introduction • Genetic Algorithms • A class of evolutionary algorithms • Efficiently solves optimization tasks • Potential Applications in many fields • Challenges • Large execution time

  3. Typical flow of a GA User Specifies … Create Initial Population A representation for chromosome Select Parents GA Parameters Terminate? Crossover Operator No Create New Population Mutation Operator Termination Criteria Evaluate Fitness A method for fitness evaluation Yes Exit

  4. Accelerating Genetic Algorithms • High degree of parallelism • Fitness evaluation • Crossover • Mutation • Most obvious : • chromosome level parallelism • Same Operations on each chromosome • Use a thread per chromosome

  5. Gene-level Parallelism • Thread-per-chromosome model • Good enough for small to moderate sized multi-core • Doesn’t map well to a massively multithreaded GPUs • Solution : • identify and exploit gene-level parallelism

  6. CUDA

  7. Our Approach • A column of threads read a chromosome gene-by-gene and cooperate to perform operations • Results in coalesced read and faster processing Population Matrix in Memory Thread Blocks in a grid

  8. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Crossover Kernel Mutation Kernel

  9. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Population Crossover Kernel Scores Mutation Kernel

  10. Fitness Evaluation Partially parallel method Fully parallel method CUDA familiar user can effectively use 2D thread layout Use gene level Parallelism for fitness evaluation Benefit : Efficiency • Partially-parallel Method • User Specifies a serial code fragment for fitness evaluation. • Threads are arranged in a 1D grid. • Each thread executes user’s code on one chromosome. • Providing chromosome level parallelism. • Benefit : Abstraction

  11. Example – 0/1 Knapsack • Task : • Given weights , costs & knapsack capacity • Aim : maximize the cost. • Representation • 1D binary string • 0/1: Absence/Presence of an item, • W and C are total weight and Cost of given representation • Best Solution : One with max C given W < Wmax • Fully Parallel Method • Use a group of threads to compute total cost and weight in logarithmic time

  12. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Scores Crossover Kernel Statistics Mutation Kernel

  13. Statistics • Selection and Termination most often use Population Statistics • We use standard parallel reduce algorithm to calculate • Max, Min, Average Scores • We use highly optimized public library CUDPP • To sort and rank chromosomes

  14. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Selection Kernel Statistics Crossover Kernel Parents Mutation Kernel

  15. Selection • Selection Kernel • Uses N/2 threads • Each thread selects two parents for producing offspring • Uniform Selection : • Selects parents in a uniform random manner • Roulette Wheel Selection: • Fitness based approach, more the fitness, better the chance of selection

  16. Selection • Roulette Wheel • Sort fitness scores • Compute a roulette wheel array by doing a prefix-sum scan of scores and normalizing it. • Generate a random number in 0-1. • Perform binary search in roulette wheel array for the nearest smaller number to the randomly selected number. • Return the index of the result in array Image Courtesy : xyz

  17. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Old Population Crossover Kernel Crossover Kernel New Population Mutation Kernel

  18. Crossover GPU Global Memory Parent1 Crossover Parent2 03 04 02 02 08 13 12 07 02 04 19 05 15 14 01 Population Thread idy 12 Thread idy 2 Thread idy 3 Thread idy 4 02 08 13 02 12 07 02 05 19 02 04 Thread idx 1-L Thread idx 1-L Thread idx 1-L Thread idx 1-L 03

  19. Crossover GPU Global Memory Parent1 Crossover Parent2 02 03 04 13 02 08 02 07 12 05 19 04 14 15 01 Population Thread idy Thread idy Thread idy Thread idy 02 1 2 3 4 5 6 7 8 08 13 02 12 07 02 05 19 02 04 Thread idx 1-L Thread idx 1-L Thread idx 1-L Thread idx 1-L 03

  20. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel New Population Crossover Kernel New Population Mutation Kernel Mutation Kernel

  21. Mutation Thread Id y Flip Mutator • Each thread handles one gene and mutates it with probability of mutation Thread Id x X X X X X X X X X X X X X X X X X X X X x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Thread 1,4 x x x x x x x x x x x x x x x x x x x x Coin State X Population Gene Flip Coin Coin State T Gene

  22. Mutation Thread Id y Flip Mutator • Each thread handles one gene and mutates it with probability of mutation Thread Id x F F F F F F F F F F X X X X X X X X X X F F X X X F X X F F X X F X F F X F X F F F T F F F F F T F x x x x x x x x x x x x x F F F F x x T x x F F F x F F x x F F F F F T F F F F x x x x x x x x x x x F x x F F F F F x x x x x x F F F x F F F F F F F F F F F x x x x x x x x x x x x x F F x T F x F x x x F F F F x F x F F F T F F F F F T x x x x x x x x x x x F x F F x F x x F F F x x F F x x x F F F F F F F F F F F Thread 1,4 x x x x x x x x x x F x x F F F x x F x x F x x F x F x F F Coin State X Population Gene Flip Coin Coin State T Gene

  23. Program Execution Flow On CPU On GPU Parse GA Parameters Generate Random Numbers Generate Random Numbers Construct Initial Population Evaluation Kernel Statistics Update Kernel GPU Global Memory Random Numbers Old Population New Population Fitness Scores Statistics Selection Kernel Crossover Kernel Random No.s Mutation Kernel

  24. Random Number Generation • Extensive use of random numbers • No primitive for on the fly single random number generation • Solution: • Generate a pool of random numbers and copy it on GPU • We use CUDPP routine to generate a large pool of random numbers on GPU (faster) • If better quality random numbers are needed, this can be replaced by a CPU based routine

  25. Results • Test Device : • A quarter of Nvidia Tesla S1030 GPU • Test Problem : • Solve a 0/1 knapsack problem • Test Parameters: • Representation : A 1D Binary String • Crossover : One-point crossover • Mutation : Flip Mutation • Selection : Uniform and Roulette Wheel

  26. Results Ave. Run-time for 100 iterations (Uniform Selection) Growth in run-time for increase in NxL Ave. Run-time for 100 iterations (Roulette Wheel Selection) N: Population Size , L: Chromosome Length

  27. Scope • Our approach is modeled after GAlib and maintains structures for GA, Genome and Statistics • It is built with enough abstraction from user program so that user does not need to know CUDA architecture or programming. • This can be extended to build a GPU-Accelerated GA library

  28. Thank You rajvi.shah@research.iiit.ac.in pjn@iiit.ac.in kkishore@iiit.ac.in

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