A Quasiphysics Intelligent Model for a Long Range Fast Tool Servo

Algorithm 1

The framework of the OSaRDE.

Parameters:

  (i) NP: Population size;

  (ii) F: Scaling factor;

  (iii) CR: Crossover control parameter;

  (iv) 𝑇_𝐶: The specified number of generations from when the replacement operation begins;

  (v) 𝑇_𝑃: The period during two replacement operations;

  (vi) G: The number of maximum generations.

Step 1. Initialization:

  S 1.1. Set the low and up boundaries of the searching space 𝐁∈[𝐌𝐈𝐍^𝐏, 𝐌𝐀𝐗^𝐏];

  S 1.2. Randomly sample NP vectors 𝐗⁰_𝑖=[𝑥⁰_𝑖,1,𝑥⁰_𝑖,2,𝑥⁰_𝑖,3…,𝑥⁰_𝑖,𝐷], 𝑖=1,2,…NP from B;

  S 1.3. Evaluate the fitness values of these individuals.

Step 2.  for 𝑘=1,2,…,𝐺, do:

  S 2.1. Mutation operation:

    Generate a mutant vector 𝐗^𝑘_𝑖=(𝑥^𝑘_𝑖,1,𝑥^𝑘_𝑖,2,𝑥^𝑘_𝑖,3…,𝑥^𝑘_𝑖,𝐷) via (16).

  S 2.2. Crossover operation:

    Execute the crossover operation to generate a trail vector 𝐘^𝑘_𝑖=(𝑦^𝑘_𝑖,1,𝑦^𝑘_𝑖,2,𝑦^𝑘_𝑖,3…,𝑦^𝑘_𝑖,𝐷) via (16).

  S 2.3. Constraint repair:

    if 𝐘^𝑘_𝑖 is not feasible (i.e. it is not in B), make it feasible via (26).

  S 2.4. Selection operation:

    S 2.4.1 if 𝐹_𝐶(𝐘^𝑘_𝑖)<𝐹_𝐶(𝐗^𝑘_𝑖), set 𝐗^𝑘_𝑖=𝐘^𝑘_𝑖, 𝐇𝐈(𝑖)=𝐹_𝐶(𝐘^𝑘_𝑖);

        else, set 𝐗^𝑘_𝑖=𝐗^𝑘_𝑖, 𝐇𝐈(𝑖)=𝐹_𝐶(𝐗^𝑘_𝑖).

    S 2.4.2 set 𝐩^𝑘_best∶=arg_𝐗𝑘min{𝐇𝐈,∀𝑖}, 𝐩^𝑘_worst∶=arg_𝐗𝑘max{𝐇𝐈,∀𝑖}, 𝐉_best(𝑘)=min(𝐇𝐈).

  S 2.5. Replacement operation:

     if 𝑘≥𝑇_𝐶 and 𝑘≠𝑇_𝐶 and (𝐺−𝑘)/𝑇_𝑃 == ceil((𝐺−𝑘)/𝑇_𝑃), do

      if 𝐗^𝑘_𝑖−𝐩^𝑘_worst≤Θ⋅Dis, Dis=𝐩^𝑘_best−𝐩^𝑘_worst;

        𝐗^𝑘_𝑖=𝐌𝐈𝐍^𝐏+𝐌𝐀𝐗^𝐏−𝐗^𝑘_𝑖; else 𝐗^𝑘_𝑖=𝐗^𝑘_𝑖.

  end for

Step 3. Output 𝐩^𝐺_best and 𝐉_best.