A Tabu Search-Based Memetic Algorithm for Hardware/Software Partitioning

Algorithm 5

Path relinking (PR) procedure.

Require: An initiating solution 𝑥⁰, the current best solution 𝑥^∗.

Ensure: A solution 𝑦.

(1)    Initiate 𝑦=𝑥^∗, 𝐷=∅.

(2)   for  𝑖={1,…,𝑛}  do

(3)   if  𝑥⁰_𝑖≠𝑥^∗_𝑖  then

(4)    𝐷=𝐷∪{𝑖}.

(5)   end if

(6)   end for

(7)   while  𝐷≠∅  do

(8)   Calculate the flip gains 𝑔𝑎𝑖𝑛(𝑖,𝑥⁰),𝑖=1,…,𝑛.

(9)   𝑗 = argmax{𝑔𝑎𝑖𝑛(𝑖,𝑥⁰)|𝑖=1,…,𝑛}.

(10) if  𝐿(𝑥⁰)−𝑔𝑎𝑖𝑛(𝑖,𝑥⁰)<𝐿(𝑥^∗)  then

(11)   Let 𝑥⁰_𝑗=1−𝑥⁰_𝑗, and 𝑥^∗=𝑥⁰, 𝑦=𝑥^∗.

(12)  Break.

(13) else

(14)  𝑗 = argmax{𝑔𝑎𝑖𝑛(𝑖,𝑥⁰)|𝑖∈𝐷}.

(15)  Let 𝑥⁰_𝑗=1−𝑥⁰_𝑗, 𝐷=𝐷⧵{𝑗}.

(16) end if

(17) end while

(18) return  𝑦.