Distributed Query Plan Generation Using Multiobjective Genetic Algorithm

Algorithm 1

NSGA-II based DQPG algorithm.

Input: 𝑅_𝑖: Relations participating in the query, 𝑃_𝑐: Probability of crossover,

𝑃_𝑚: Probability of mutation, 𝐺: Pre-defined number of generations, 𝑃_size: Population Size

Output: Top-n query plans.

Method:

Initialize a random parent population of query plans PP

where chromosome length “len” is the number of relations accessed in the query and the gene at the 𝑘th position in the

chromosome represents the site of the 𝑘th relation.

WHILE generation ≤ 𝐺  DO

Step  1. Evaluate each query plan in PP on the following objective functions

       𝑚₁: Minimize TCC=∑^{𝑖=𝑢−1,𝑗=𝑢}_{𝑖=1,𝑗=𝑖+1}CC_𝑖𝑗×𝑏_𝑖,

       𝑚₂: Minimize TPC=∑^𝑢_𝑖=1LPC_𝑖×𝑎_𝑖,

where 𝑢 is the number of sites accessed by the query plan in ascending order of cardinality per site, CC_𝑖𝑗 is the communication

cost per byte between sites 𝑖 and 𝑗, LPC_𝑖 is the local processing cost per byte at site 𝑖, 𝑏_𝑖 is the bytes to be communicated from

site 𝑖 and 𝑎_𝑖 is the bytes to be processed at site 𝑖.

Step  2. Perform Non-Dominated (ND) Sort  on PP for “𝑚₁” and “𝑚₂” separately and place each query plan (QP)

into corresponding ND  fronts “Ŧ_𝑖” and sort the QPs within each “Ŧ_𝑖”

Step  3. Evaluate Crowding Distance Function  𝐼(𝑑)   for each objective function

Assign 𝐼(𝑑)=∞ for smallest and highest values in each front “Ŧ_𝑖”.

For the remaining QPs, 𝐼(𝑑) is calculated as:

      𝐼𝑑_𝑘=𝐼𝑑_𝑘+𝐼(𝑘+1)_𝑚−𝐼(𝑘−1)_𝑚𝑓_𝑚^max−𝑓_𝑚^min,

where 𝐼(𝑘)_𝑚 is the value of 𝑚th objective function of 𝑘th query plan in Front Ŧ_𝑖 and 𝑓_𝑚^max and 𝑓_𝑚^min are the

maximum and minimum values obtained for the objective function 𝑚.

Step  4. Perform Selection from PP using binary tournament selection using crowded comparison operator ≺_𝑛

Step  5. Perform random single point crossover on selected chromosomes with crossover probability 𝑃_𝑐

Step  6. Apply mutation on resulting population with mutation probability 𝑃_𝑚

Let the resulting child population be CP

Step  7. Append CP into PP, and let the resulting intermediate population be IP

Step  8. Repeat Step  1 and Step  2 for population IP

Step  9. Form the population PP for the next generation by picking query plans Front-wise from IP till the

population size = 𝑃_size.

Step  10. Increment Generation by 1

END DO

Return Top-𝐾 Query Plans from population PP