The Application of Memetic Algorithms for Forearm Crutch Design: A Case Study

Pseudocode 1

(1) //Initialization

(2) The set of final Pareto solutions 𝐹𝑃=∅;

(3) The set of GA population 𝑃𝑆=∅;

(4) The set of weights combination 𝑊𝑆=∅;

(5) Given N objective functions, we have ∑^𝑁_𝑖=1𝑤_𝑖𝐽_𝑖(𝐱_𝑖,𝐲)

(6) Begin (at facilitator agent level)

(7)  //Enumerate weights combination

(8)  Set 𝑤₁=𝑤₂=⋯=𝑤_𝑁−1=0;

(9)  Given weight step size 1/𝑊;

(10)  Let each 𝑤_𝑖(𝑖=1,…,𝑁−1) increases 1/𝑊, 𝑤_𝑁=1−𝑤₁−⋯𝑤_𝑁−1,

     and add (𝑤₁,𝑤₂,…,𝑤_𝑁) to WS;

(11)  //Weights Loop

(12)  For each weights combination (𝑤₁,𝑤₂,…,𝑤_𝑁) in 𝑊𝑆, ∑^𝑁_𝑖=1𝑤_𝑖𝐽_𝑖(𝐱_𝑖,𝐲) is

    constructed;

(13)    //GA loop

(14)    //Initialization

(15)    Generate random population of P solutions and add them to PS;

(16)    For 𝑛=1 to maximum # of generations for GA loop;

(17)     //Crossover and Mutation

(18)     Random select two parents 𝑝_𝑎 and 𝑝_𝑏 from PS;

(19)     Generate two offspring 𝑝^′_𝑎 and 𝑝^′_𝑏 by crossover operator;

(20)      if 𝑝^′_𝑎 and/or 𝑝^′_𝑏 are not feasible, generate new feasible offspring

(21)      𝑝_𝑎^′′ and/or 𝑝_𝑏^′′ using mutation operator;

(22)     //Selection

(23)     Using fitness function (∑^𝑁_𝑖=1𝑤_𝑖𝐽_𝑖(𝐱_𝑖,𝐲)) to evaluate the solution, update PS

       with improved solutions;

(24)     //Local Search Loop

(25)     For each chromosome 𝑝_𝑗 in 𝑃𝑆;

(26)      Call each Design Agent for local optimization on x (note different

        optimization engines can be employed based on the design

        disciplines);

(27)      Given updates from Design Agent on x, Facilitator agent employs

        sub-gradient algorithm [19] as local search algorithm to

        iteratively locate improved solution 𝑝^′_𝑗 with respect to y;

(28)     Next 𝑝_𝑗;

(29)     //Pareto Filter:

(30)     For each chromosome 𝑝_𝑗 in the set PS;

(31)      If 𝑝_𝑗 is not dominated by all the solutions in the set 𝐹𝑃;

(32)       Add 𝑝_𝑗 to the set 𝐹𝑃;

(33)      Else If there are solutions in the set 𝐹𝑃 are dominated by 𝑝_𝑗;

(34)      Remove those solutions in the set FP;

(35)      End If;

(36)    Next 𝑝_𝑗;

(37)    Next 𝑛;

(38) End;