On the Identification of Coupled Pitch and Heave Motions Using Opposition-Based Particle Swarm Optimization

Algorithm 1

The process of OPSO.

  %% Initialization

(1) Initialize swarm size N and constant number 𝐶₁ and 𝐶₂; space dimension 𝐷; maximum

(2) Initialize the iteration number for opposition calculation 𝑐𝑜𝑛𝑁𝑢𝑚=0, 𝑠𝑒𝑡𝑛𝑢𝑚=100;

(3) for 𝑖=1:  𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑁𝑢𝑚

(4)   initialize 𝑋_𝑖 randomly with the search range (𝑋_min,𝑋_max)

(5)   initialize 𝑉_𝑖 randomly with the velocity range (𝑉_min,𝑉_max)

(6) End for

(7) Evaluate each particle’s fitness 𝑓_𝑖=𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑋_𝑖), and the best fitness 𝑃𝑏𝑒𝑠𝑡𝑉𝑎𝑙𝑢𝑒_𝑖=𝑓_𝑖

(8) Identify the best particle’s position 𝑃𝑔 and its fitness 𝐺𝑏𝑒𝑠𝑡𝑉𝑎𝑙𝑢𝑒=min(𝑃𝑏𝑒𝑠𝑡𝑉𝑎𝑙𝑢𝑒_𝑖); %%Loop

(9) While (𝑡<  𝑛_max)

(10)   If 𝑐𝑜𝑛𝑁𝑢𝑚>𝑠𝑒𝑡𝑁𝑢𝑚 then

(11)   for 𝑖=1 to 𝑁

(12)    Calculate the opposite particle 𝑋₀ using (8);

(13)    Evaluate fitness in opposite vector𝑓_𝑖𝑜=𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑋_𝑖𝑜);

(14)  end for

(15)  Select 𝑁 fittest particles 𝑁𝑒𝑤𝑓𝑖𝑡𝑛𝑒𝑠𝑠 from 𝐹(𝑓₁,𝑓₁,…,𝑓_𝑁) and 𝐹₀(𝑓_1𝑜,𝑓_1𝑜,…,𝑓_𝑁𝑜) to

(16)  create a population of size 𝑁;

(17)   Else

(18)  for 𝑖=1 to 𝑁

(19)   Calculate particle velocity 𝑉_𝑖(𝑡+1) using (5)

(20)   update particle position 𝑋_𝑖(𝑡+1) using (6)

(21)   Evaluate 𝑛𝑒𝑤𝑓𝑖𝑡𝑛𝑒𝑠𝑠_𝑖=𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑋_𝑖(𝑡+1))

(22)  End for

(23)   End if

(24)   update 𝑃𝑏𝑒𝑠𝑡_𝑖

(25)   for 𝑖=1 to 𝑁

(26)   if (𝑛𝑒𝑤𝐹𝑖𝑡𝑛𝑒𝑠𝑠<𝐺𝑏𝑒𝑠𝑡𝑉𝑎𝑙𝑢𝑒)

(27)     update 𝐺𝑏𝑒𝑠𝑡

(28)     𝑐𝑜𝑛𝑁𝑢𝑚=0;

(29)   end if

(30)   end for

(31)   𝑐𝑜𝑛𝑁𝑢𝑚=𝑐𝑜𝑛𝑁𝑢𝑚+1;

(32) end while