1 Comparative Study of two Genetic Algorithms Based Task Allocation Models in Distributed Computing System Oğuzhan TAŞ 2005

2 Authors Deo Prakash Vidyarthi (India) Anil Kumar Tripathi (India) Biplab Kumer Sarker (Japan) Kirtil Rani (India) IEEE 2003

3 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

4 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

5 Objective and Previous Works Earlier, they have proposed a task allocation model to maximize the reliability of Distributed Computing System (DCS) using Genetic Algorithm. In this paper, they propose a task allocation model to minimize the Turnaround Time of the task submitted to Distributed Computing System for execution. Also, they use Simple Genetic Algorithms in this new task allocation model.

6 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

7 What are Genetic Algorithms? Genetic algorithms (GAs) provide a learning method motivated by an analogy to biological evolution. In the other words, a way to employ evolution in the computer Search and optimization technique based on variation and selection Genetic algorithms are a part of evolutionary computing, which is a rapidly growing area of artificial intelligence.

8 Evolutionary Algorithms

9 GA Vocabulary Gene – An single encoding of part of the solution space. A collection of genes is sometimes called a genotype A collection of aspects (like eye colour) is sometimes called a phenotype Chromosome – A string of “Genes” that represents a solution. Population - The number of “Chromosomes” available to test. GA Operations Reproduction Crossover Mutation

10 Genetic Algorithms (GA) The chromosomes in GA population generally take the form of bit strings. Bit strings ( ) Real numbers ( ) Permutations of element (E11 E3 E7... E1 E15) Lists of rules (R1 R2 R3... R22 R23) Program elements (genetic programming)... any data structure...

11 GA Operations - Crossover choose randomly some crossover point copy everything before this point from the first parent then copy everything after the crossover point from the other parent. Crossover probability is fixed =

12 GA Operations - Mutation Mutation means that the elements of DNA are a bit changed. Mutation probability is fixed. Bit inversion - selected bits are inverted =>

13 Fitness Function The GA requires a fitness function that assigns a score to each chromosome in the population. The fitness function in a GA is the objective function that is to be optimized. It is used to evaluate search nodes, thus it controls the GA.

14 Chromosome Selection Roulette Wheel Selection Boltzman Selection Tournament Selection Rank Selection Steady State Selection …..

15 Selection-Roulette Wheel Want to maintain an element of randomness but ‘fix’ the selection so that fitter individuals have better odds of being chosen Assign areas on a number line relative to each individuals fitness Generate a random number within the range of the number line Determine which individual occupies that area of the number line Choose that individual

16 Selection-Roulette Wheel This process can be described by the following algorithm. [Sum] Calculate the sum of all chromosome fitnesses in population - sum S. [Select] Generate random number from the interval (0,S) - r. [Loop] Go through the population and sum the fitnesses from 0 - sum s. When the sum s is greater then r, stop and return the chromosome where you are. Of course, the step 1 is performed only once for each population.

17 Selection-Roulette Wheel

18 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

19 Basic Genetic Algorithm 1. [Start] Generate random population 2. [Fitness] Evaluate the fitness f(x) of each chromosome 3. [New population] Create a new population by repeating following steps until the new population is complete 1. [Selection] Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected) 2. [Crossover] With a crossover probability cross over the parents to form new offspring (children). If no crossover was performed, offspring is the exact copy of parents. 3. [Mutation] With a mutation probability mutate new offspring at each locus (position in chromosome). 4. [Accepting] Place new offspring in the new population 4. [Replace] Use new generated population for a further run of the algorithm 5. [Test] If the end condition is satisfied, stop, and return the best solution in current population 6. [Loop] Go to step 2

20 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

21 Genetic Algorithms for Task Allocation *Calculation of Turnaround Time* The fitness function = turnaround time of the task submitted to the DCS for execution. The modules of the task allocated on the different nodes will be executed in parallel. Thus the node taking maximum time will furnish the turnaround time as all other nodes, taking less time, will complete the execution within the execution time of the task that takes maximum time. This time include the actual execution+communicate with other modules allocated on other computing nodes. The modules allocated on the same node will incur zero communication.

22 Genetic Algorithms for Task Allocation Different module of the task may take varying on the different computing nodes of DCS. The objective of this model will be to minimize this time computed by the abovesaid method.

23 Turnaround Time=Fitness Function n = number of processor in the distributed system. m=number of modules in the distributed system. X=an m x n matrix corresponding to a module assignment e ij = execution time of module m i on node P k C ij = communication between m i and m j x ik = an element of X; x ik =1 if module m i is assigned to P k, otherwise x ik =0.

24 Reliability Expression l pq = a link node P p and P q - R k (T,X)= Reliability of the processing node P k W pq = transmission rate of link l pq -R pq (T,X) = Reliability of the link l pq = failure rate of link l pq = failure rate of processing node P k

25 Algorithm Initial Schedule{ - Compute height for each module in the task graph - Keep modules of the same height (h) in the same group G(h) - Assign the modules of the same height from the same group G(h) onto different processors. If some modules are unassigned again assign it from the first processors in the same order. The assignment is to satisfy the system constraints. - Assign the modules of the G(h+1) in the same order of the processor as in 3. } many populations are generated by applying the Initial_Schedule and changing the order of the processors.

26 Algorithm Crossover { Two modules of different height are chosen for crossover site in a generated population and the portion of the string is swapped. } Mutation { Randomly alter 0 to 1 and 1 to 0 by keeping number of 0 and 1 same } Reproduction{ Use the fitness function. Choose few best strings which has good fitness value. }

27 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

28 Implementation - Case 1 Task Graph (TG) consists of 4 modules m 1,m 2,m 3 and m 4. also processor Graph (PG) consists of four modules p1, p2, p3 and p4.

29 Implementation - Case 1 p 1 –m 2, p 2 –nil, p 3 –m 4, p 4 –m 1,m 3 Turnaround time=14 unit Number of iterations=2 Reliability of allocation = Allocation with load balancing of maximum modules 2: same as above.

30 Implementation - Case 1 Allocation to Maximize Reliability: p 1 -nil, p 2 -m 1,m 2,m 4, p 3 -m 3, p 4 -nil Reliability for allocation= Number of iterations=2 Turnaround time=20 unit.

31 Execution Time Matrix of T 1 p1p1 p2p2 p3p3 p4p4 m1m1 53∞4 m2m m3m3 4∞25 m4m4 3452

32 IMC Matrix of T 1 m1m1 m2m2 m3m3 m4m4 m1m m2m m3m m4m4 2030

33 Implementation - Case 2

34 Implementation - Case 2 p 1 -m 1, m 3, p 2 -m 2, m 4, p 3 -nil, p 4 -nil Turnaraound time= 13 unit Number of iterations=2 Reliability of allocation= Allocation with load balancing of maximum modules 2: same as above.

35 Implementation - Case 2 Allocation to Maximize Reliability p 1 -nil, p 2 -m 1,m 2,m 3,m 4, p 3 -nil, p 4 -nil Reliability of the allocation= Number of iterations=3 Turnaround time=18 unit

36 Execution Time Matrix of T 2 p1p1 p2p2 m1m1 11 M2M2 35 M3M3 ∞4 M4M4 26

37 IMC Matrix of T 2 m1m1 m2m2 m3m3 m4m4 m1m m2m m3m m4m

38 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

39 Comparisons In this case, the minimum turnaround is found to be 14 unit and the reliability corresponding to this allocation slightly less than maximum possible reliability obtained their previous work for this example. The turnaround corresponding to max reliability 20 units which is more than minimum turnaround i.e. 14 unit

40 Outline Objective and Previous Works What are Genetic Algorithms? Genetic Algorithms for Task Allocation Implementation Examples and Comparisons Conclusion

41 Conclusion In conclusion, when we consider all the cases they found that when turnaround time is to be minimized the reliability of the DCS will sufer little. Load balancing factor produces better turnaround time of the task but further result in reliability reduction.

42 Questions Thank you. Questions?