Orthogonal Genetic Algorithm for Planar Thinned Array Designs

Algorithm 1

The pseudocode of OGA.

Initialize: population size NP, crossover rate 𝑃_crossover, mutation rate 𝑃_mutation, maximal number of

generations 𝐺_max and current generation counter 𝑔

Initialize randomly the initial population 𝑃₀ of size NP binary strings

Evaluate each individual 𝑥∈𝑃₀

WHILE stopping rule is not invoked DO

   Select a suitable two-level orthogonal array 𝐿_𝑛(2^𝑛−1) for matrix experiments

   // Orthogonal Crossover Operation

   FOR 𝑖=1 to NP

     IF random(0,1)<𝑃_crossover

      Select two random parents 𝑥_𝑎,𝑥_𝑏∈𝑃_𝑔

      Execute the matrix experiment for 𝑥_𝑎 and 𝑥_𝑏

      Calculate the function values of individuals generated by the matrix experiment

      Calculate the effects of the various factors (𝐸_𝑗1,𝐸_𝑗2) by using factor analysis,

      Generate an optimal individual 𝑥^†_𝑐

     END IF

    𝑋_𝑐←𝑥^†_𝑐

   END FOR

    NP_temp=size(𝑃_𝑔∪𝑋_𝑐)

    // Mutation Operation

    FOR 𝑖=1 to NP_temp

     IF random(0,1)<𝑃_mutation

      Select one random individual 𝑥_𝑚∈𝑃_𝑔∪𝑋_𝑐, and choose randomly two gene bits in this individual

      Change these two gens from 0 to 1 or vice versa, and generate a new individual 𝑥^†_𝑚

     END IF

       𝑋_𝑚←𝑥^†_𝑚

    END FOR

   // Select Operation

     Sort 𝑃_𝑔∪𝑋_𝑐∪𝑋_𝑚

     Copy the NP first solutions of 𝑃_𝑔∪𝑋_𝑐∪𝑋_𝑚, and retain the best individual

END WHILE