A Novel Differential Evolution Invasive Weed Optimization Algorithm for Solving Nonlinear Equations Systems

Pseudocode 1

The pseudocode for DEIWO algorithm.

BEGIN

  Input: randomly initialize a population of DEIWO individuals.

 While (the termination criterion is not satisfied)

  Calculate every individual’s fitness 𝑓(𝑋);

  Calculate the number of every individual’s offspring

    weed_𝑛=𝑓−𝑓_min𝑓_max−𝑓_min(𝑠_max−𝑠_min)+𝑠_min;

  Update 𝜎_cur by

    𝜎_cur=(iter_max−iter)^𝑛(iter_max)^𝑛(𝜎_init−𝜎_final)+𝜎_final;

  Generate seeds over the search space by 𝑁(0,𝜎_cur),

  Add the generated seeds into the solution set;

   If (the number of all weeds and seeds equal the maximum population 𝑃_MAX)

     Sort the population in descending order by fitness;

     Truncate population of weeds with higher fitness until the number of set equal the

     maximum population;

   End If

  Mutate the individual by

    𝑉^𝑡_𝑖=𝑋^𝑡_𝑖+𝐹×(𝑋^𝑡_best−𝑋^𝑡_𝑖)+𝐹×(𝑋^𝑡_𝑟1−𝑋^𝑡_𝑟2);

  Cross the individual by

    𝑈^𝑡_𝑖,𝑗=𝑉^𝑡_𝑖,𝑗ifrand_𝑗[0,1]≤CRor𝑗=𝑗_rand𝑋^𝑡_𝑖,𝑗otherwise, 𝑗=1,2,…,𝑛;

  Select individual between 𝑈^𝑡_𝑖 and 𝑋^𝑡_𝑖

    𝑋_𝑖^𝑡+1=𝑈^𝑡_𝑖if𝑓(𝑈^𝑡_𝑖)<𝑓(𝑋^𝑡_𝑖)𝑋^𝑡_𝑖otherwise;

 End While

  Output the best individual and its fitness;

END