How to Solve Triple-Objective Optimization Problems Using Matlab

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• Thanks

  • Good luck!

    • sir im applying this program code but always showing this errorIndex in position 1 exceeds array bounds.

      Error in Main_program (line 20)
      plot3(fval(1,:),fval(2,:),fval(3,:))
      , kindly make changes in my code so that ill get the graph.really need your help urgently

      function Output = multi_objective_function(Input)
      x(1) = Input(1); % variable 1
      x(2) = Input(2); % variable 2
      x(3) = Input(2); % variable 3
      x(4) = Input(2); % variable 4

      F1 = 84718*x(1)+72627.42*x(2)+41021.98*x(3)+58077.44*x(4); % objective 1
      F2 = -1124.424*x(1)-1004.247*x(2)-8.40858*x(3)-10.52292*x(4); % objective 2
      F3 = -51.524*x(1)-47.666*x(2)-19.136*x(3)-19.134*x(4); % objective 3
      Output = [F1 F2 F3];
      function [x,fval,exitflag,output,population,score] = multi_objective_genetic_algorithm_solver(nvars,Aeq,beq,Aineq,bineq,lb,ub,PopulationSize_Data,MaxGenerations_Data,MaxStallGenerations_Data,FunctionTolerance_Data,ConstraintTolerance_Data)
      options = optimoptions('gamultiobj');
      options = optimoptions(options,'PopulationSize', PopulationSize_Data);
      options = optimoptions(options,'MaxGenerations', MaxGenerations_Data);
      options = optimoptions(options,'MaxStallGenerations', MaxStallGenerations_Data);
      options = optimoptions(options,'FunctionTolerance', FunctionTolerance_Data);
      options = optimoptions(options,'ConstraintTolerance', ConstraintTolerance_Data);
      options = optimoptions(options,'CrossoverFcn', { @crossoverintermediate [] });
      options = optimoptions(options,'Display', 'off');
      [x,fval,exitflag,output,population,score] = ...
      gamultiobj(@multi_objective_function,nvars,Aeq,beq,Aineq,bineq,lb,ub,[],options);
      clc
      clear
      close all

      nvars = 4;
      Aineq =[1 1 1 1; 220.086 210.356 92.672 135.994; 464.75 203.194 261.548 206.638];
      bineq = [49.9; 660; 1136];
      lb = [0 0 0 0];
      ub = [];
      PopulationSize_Data = 500;
      MaxGenerations_Data = 100;
      MaxStallGenerations_Data = 100;
      FunctionTolerance_Data = 0;
      ConstraintTolerance_Data = 0;

      [x,fval,exitflag,output,population,score] = multi_objective_genetic_algorithm_solver(nvars,[],[],Aineq,bineq,lb,ub,PopulationSize_Data,MaxGenerations_Data,MaxStallGenerations_Data,FunctionTolerance_Data,ConstraintTolerance_Data);

      optimal_solution = x;
      objective_functions = fval;
      plot3(fval(1,:),fval(2,:),fval(3,:))
      unable to plot it kindly resolve my problem

      • Maybe your matlab version does not have GA toolbox

• thanks

• Thanks a lot.
  But two question!
  First, is it possible to increase the number of input variables to 3 or more?
  Second, is this method called NSGAII bult in algorithm from Matlab to solve optimization?

  • Hi, thanks for your interest! Yes, number of variables can be larger than 3. This is no NSGA II, this is multi objective genetic algorithm in Matlab. For NSGA II, please have a look other posts on this blog.

• Thank you so much.
  I have question about this procedure. when one of the objectives must be minimize and the rest of the objectives should be maximized in this case what to do?

  • Hi, interesting question! In that case, we need to convert the max objective to min one.

    • Thank you very much for your answer. How can I do this?

      • For example, max y = f(x) --> min y1 = 1/f(x)

• Thank you very much for your answer. How can I do this?

  • For example, max y = f(x) --> min y1 = 999999 - f(x)

  • Thank you Dr.

• Interesting example!

  I'm having the following issue:

  Error using optimoptions (line 124)
  Invalid solver specified. Provide a solver name or handle (such as 'fmincon' or @fminunc).
  Type DOC OPTIMOPTIONS for a list of solvers.

  Error in multi_objective_genetic_algorithm_solver (line 2)
  options = optimoptions('gamultiobj');

  I would appreciate some advice

  • Hi, your matlab does not have the solver. Install Matlab 2016a.

• How can I relate the objective functions in my case. i have three independent variables and one dependent variable. how can i set objective to find the optimal results for dependent variable that i have got. Is there any way to find the equations for this kind of problems. Really need some tips.

  • Use math equations to relate the components

• Hi, Its showing
  Invalid solver specified. Provide a solver name or handle (such as 'fmincon' or @fminunc).Type DOC OPTIMOPTIONS for a list of solvers.

  Error in multi_objective_genetic_algorithm_solver (line 2)
  options = optimoptions('gamultiobj');

  Error in Main (line 14)
  [x,fval,exitflag,output,population,score] =
  multi_objective_genetic_algorithm_solver(nvars,lb,ub,PopulationSize_Data,MaxGenerations_Data,MaxStallGenerations_Data,FunctionTolerance_Data,ConstraintTolerance_Data);
  It is not running.

  • Hello, that's because of Matlab version. Please use Matlab version 2016a.

    • Thank you very much, sir. Now it's running.

      • Great to hear that. Good luck!

• Thank you so much

• when i uused your program in my laptop; result showed the folowing error
  Undefined function or variable 'multi_objective_function'.

  Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)
  fcn_handle = @(x) fcn(x,FcnArgs{:});

  Error in gamultiobjMakeState (line 28)
  Score = FitnessFcn(state.Population(1,:));

  Error in gamultiobjsolve (line 8)
  state = gamultiobjMakeState(GenomeLength,FitnessFcn,ConstrFcn,output.problemtype,options);

  Error in gamultiobj (line 303)
  [x,fval,exitFlag,output,population,scores] = gamultiobjsolve(FitnessFcn,nvars, ...

  Error in multi_objective_genetic_algorithm_solver (line 11)
  gamultiobj(@multi_objective_function,nvars,[],[],[],[],lb,ub,[],options);

  Error in main_program (line 14)
  [x,fval,exitflag,output,population,score] =
  multi_objective_genetic_algorithm_solver(nvars,lb,ub,PopulationSize_Data,MaxGenerations_Data,MaxStallGenerations_Data,Function

  • Hello, that is because your matlab does not have GA solver.You should install Matlab version 2016a