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

Algorithm 2

General structure of TSMA.

Require: A directed acyclic graph;

Ensure: Approximate global maximal solution 𝑥^∗;

(1)    Initial 𝑈=∑^𝑛_𝑖=1𝑎ℎ_𝑖, 𝑥^∗=(1,…,1).

(2)    Generate randomly a population 𝑃={𝑥¹,…,𝑥^𝑝}.

(3)    for  𝑘={1,…,𝑝}  do

(4)    Use the local search procedure (see Section 4.3) to minimize problem (𝑈𝐼𝑃2) from

      every individual 𝑥^𝑘, also denote the obtained solution by 𝑥^𝑘.

(5)     if  𝐿(𝑥^𝑘)<𝑈  then

(6)      Let 𝑈=𝐿(𝑥^𝑘), and 𝑥^∗=𝑥^𝑘.

(7)     end if

(8)    end for

(9)    while termination criteria (see Section 4.6) do not meet do

(10)   Use the crossover operator (see Section 4.2) to generate a new offspring 𝑥⁰, and

    apply the local search procedure to refine 𝑥⁰, also denote it by 𝑥⁰.

(11)   if  𝐿(𝑥⁰)<𝑈  then

(12)    Let 𝑈=𝐿(𝑥⁰), and 𝑥^∗=𝑥⁰.

(13)   end if

(14)   if  𝑥⁰=𝑥^∗  then  

(15)       𝑦=𝑥⁰.

(16)   else

(17)       Use the path relinking procedure PR (see Section 4.4) to the solution

        𝑥⁰ and the current best solution 𝑥^∗ to obtain a solution 𝑦.

(18)   end if

(19)   if  𝐿(𝑦)<𝑈  then

(20)    Let 𝑈=𝐿(𝑦), and 𝑥^∗=𝑦.

(21)   end if

(22)  Use the population updating method (see Section 4.5) to update the population that is

    to decide if 𝑦∈𝑃.

(23) end while

(24) return  𝑥^∗ and 𝑓(𝑥^∗) as an approximate discrete global minimizer and global minimal

   value of problem (𝐼𝑃), respectively.