Operational Optimization of Large-Scale Parallel-Unit SWRO Desalination Plant Using Differential Evolution Algorithm

Algorithm 1

Pseudocode of TSDE.

Line     % Pseudocode of TSDE

(1)     Begin

(2)       Set NP = 100; 𝐷=20; 𝐺₁=300; 𝐺₂=700;

(3)     % Stage One

(4)       Initialize population 𝑥_𝑖,𝐺 (𝑖=1,2,…, NP) (the vectors which represent the status of RO are initialized

       randomly in the range of [0, 1]; the vectors which represent the amount of freshwater are

       initialized as constants, which equal the average capacity of each RO unit)

(5)        𝐺=1

(6)        For  𝐺=1 to 𝐺₁

(7)         For  𝑘=1 to 𝐾

(8)         For  𝑖=1 to NP

(9)          Randomly selected three integers 𝑟₁, 𝑟₂, and 𝑟₃ from the set {1,2,…, NP}

           (𝑟₁≠ 𝑟₂≠ 𝑟₃≠ 𝑖)

(10)          𝐹=0.2 * rand + 0.1

(11)          𝑣_𝑖,𝐺 = 𝑥_𝑟1,𝐺 + 𝐹 * (𝑥_𝑟2,𝐺−𝑥_𝑟3,𝐺)

(12)          Randomly selected index rnbr(𝑗) (rnbr(𝑗) ∈ {1,2,…,𝐷})

(13)          CR = rand * 0.2 + 0.7

(14)          For  𝑗=1 to 𝐷

(15)           If (rand < CR) or (𝑗 = rnbr(𝑗))

(16)            𝑢_{𝑖𝑗,𝐺} = 𝑣_{𝑖𝑗,𝐺}

(17)           Elseif

(18)            𝑢_{𝑖𝑗,𝐺} = 𝑥_{𝑖𝑗,𝐺}

(19)           End If

(20)           If (𝑢_{𝑖𝑗,𝐺} < 𝑥^𝐿_𝑖𝑗) or (𝑢_{𝑖𝑗,𝐺} > 𝑥^𝑈_𝑖𝑗)

(21)            𝑢_{𝑖𝑗,𝐺} = 𝑥^𝐿_𝑖𝑗 + rand * (𝑥^𝑈_𝑖𝑗−𝑥^𝐿_𝑖𝑗)

(22)           End If

(23)          End For

(24)          If  𝐹(𝑢_𝑖,𝐺) > 𝐹(𝑥_𝑖,𝐺)

(25)             𝑥_𝑖,𝐺+1 = 𝑢_𝑖,𝐺

(26)          Else

(27)           𝑥_𝑖,𝐺+1 = 𝑥_𝑖,𝐺

(28)          End If

(29)         End For

(30)        End For

(31)        End For

(32)     % Stage Two

(33)       Initialize population 𝑥_𝑖,𝐺 (𝑖=1,2,…, NP) (30 percent of them are remained the best values

        from Stage One and 70 percent are generated randomly)

(34)       𝐺=1

(35)       For  𝐺=1 to 𝐺₂

(36)        For  𝑘=1 to 𝐾

(37)         For  𝑖=1 to NP

(38)          Randomly selected three integers 𝑟₁, 𝑟₂, and 𝑟₃ from the set {1,2,…, NP}

           (𝑟₁≠ 𝑟₂≠ 𝑟₃≠ 𝑖)

(39)          𝐹=0.2 * rand + 0.1

(40)          𝑣_𝑖,𝐺 = 𝑥_𝑟1,𝐺 + 𝐹 * (𝑥_𝑟2,𝐺−𝑥_𝑟3,𝐺)

(41)          Randomly selected index rnbr(𝑗) (rnbr(𝑗) ∈ {1,2,…,𝐷})

(42)          CR = rand * 0.2 + 0.7

(43)          For  𝑗=1 to 𝐷

(44)           If  (rand < CR) or (𝑗 = rnbr(𝑗))

(45)            𝑢_{𝑖𝑗,𝐺} = 𝑣_{𝑖𝑗,𝐺}

(46)           Elseif

(47)            𝑢_{𝑖𝑗,𝐺} = 𝑥_{𝑖𝑗,𝐺}

(48)           End If

(49)           If (𝑢_{𝑖𝑗,𝐺} < 𝑥^𝐿_𝑖𝑗) or (𝑢_{𝑖𝑗,𝐺} > 𝑥^𝑈_𝑖𝑗)

(50)            𝑢_{𝑖𝑗,𝐺} = 𝑥^𝐿_𝑖𝑗 + rand * (𝑥^𝑈_𝑖𝑗−𝑥^𝐿_𝑖𝑗)

(51)           End If

(52)          End For

(53)          If  𝐹(𝑢_𝑖,𝐺) > 𝐹(𝑥_𝑖,𝐺)

(54)           𝑥_𝑖,𝐺+1 = 𝑢_𝑖,𝐺

(55)          Else

(56)           𝑥_𝑖,𝐺+1 = 𝑥_𝑖,𝐺

(57)          End If                                                            

(58)         End For

(59)        End For

(60)       End For

(61)     End