1. Authors: M. Tomassini , M Oussaidene , B. Chopard and O. Pictet
Parallel Genetic Programming And Its Application To Trading Model Induction
Authors: M. Tomassini , M Oussaidene , B. Chopard and O. Pictet

2. Load Balancing Task : Fitness Computation of a Genetic Program
Task Size: Time Complexity of a Genetic Program to be Evaluated

3. Types of Load Balancing
Static
Round Robin Policy
ith Task assigned to Processor i/m
Dynamic
Greedy Heuristic
Processing Nodes Mi (i = 1…..m)
Tasks Tj (j = 1….p)
Size of Task Cj

4. Dynamic Load Balancing Algorithm
Sort Cj in Downward Order
Initialize workload li to zero
For all Tasks find Mi*, the least loaded processor such that li* <= lk , for all k
Assign Tj to Mi* , Li* = Li* + Cj

5. Parallel Programming Performance
For Speedup Measurement , they have a fixed problem size.
Speedup Measurement on two different problem instances for both scheduling algorithms :
Measurement n d p g A
1000 6
100 B 12 10

6. Parallel Programming Performance

7. Time Complexity and Scalability Analysis
Sequential Time :
Tseq = αmpC*
p : population size
n : problem size
C* : average population complexity
α : average time required to perform each arithmetic operation

8. Time Complexity and Scalability Analysis
Parallel Time :
lmax <= pC*/m + Cmax
Approximately :
lmax = pC*/m
Evaluation of G.P. for n fitness cases:
Tcomp = αnpC*/m

9. Time Complexity and Scalability Analysis
Communication Time :
Tcom = pтs + тdΘ(pC*)
Total Parallel Time :
Tpar = Tcomp + Tcom
Tpar ≈ αnpC*/m + ßpC*

10. Speedup Speedup on m processors:
S = αnm/(αn + ßm)
For Fixed problem size n, speedup saturates to n(α/ß).
For a given no. of processes m, nearly linear speedups are obtained.

11. Scalability Scalability: E = S/m = αn/(αn + ßm)
F(m) = n = (E/1 – E)(ß/α)m
where, isoefficiency function F(m) indicates how the problem size n must grow as the no. of processes m increases in order to obtain a given efficiency E.

12. Trading Model Performance