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demo's Introduction

DEMO "Toolbox"

Differential Evolution for Multiobjective Optimization

These codes were developed by Fillipe Goulart ([email protected]) during his M.Sc. at Universidade Federal de Minas Gerais, under the mentoring of Prof. Felipe Campelo ([email protected]).

The Octave-Matlab folder contains the implementations for Octave (which should work on Matlab too). The following algorithms are implemented:

  • A posteriori methods (without preferences):
    – DEMO [1]: the regular DEMO with non-dominated sorting;
    – IBEA [2]: DEMO using indicators instead.
  • A priori or interactive (with preferences):
    – R-DEMO [3]: R-NSGA-II but using the DEMO instead;
    – PBEA [4]: IBEA but using a reference point;
    – PAR-DEMO(nds) [5]: the method proposed by us, using nondominated sorting;
    – PAR-DEMO(ε) [5]: the same method, but using indicators instead.

Fillipe's M.Sc. thesis is available here, and contains an extensive review on multiobjective optimization and preference-based methods. It also contains a more extensive description and discussion of the Preference-based Adaptive Region-of-interest (PAR) framework.

If you use these codes in any way, please cite our paper [5]:

@article{Goulart2016,
  doi = {10.1016/j.ins.2015.09.015},
  url = {http://dx.doi.org/10.1016/j.ins.2015.09.015},
  year  = {2016},
  month = {feb},
  publisher = {Elsevier {BV}},
  volume = {329},
  pages = {236--255},
  author = {Fillipe Goulart and Felipe Campelo},
  title = {Preference-guided evolutionary algorithms for many-objective optimization},
  journal = {Information Sciences}
}

The description of the methods and examples of use are available in the Read me.pdf file.

References

  1. T Robic and B Filipic. DEMO: Differential evolution for multiobjective optimization. Evolutionary Multi-Criterion Optimization, 520–533, 2005.
  2. Eckart Zitzler and S Kunzli. Indicator-based selection in multiobjective search. Parallel Problem Solving from Nature-PPSN VIII, (i):1–11, 2004.
  3. Kalyanmoy Deb, J. Sundar, Rao N. Udaya Bhaskara, and Shamik Chaudhuri. Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms. International Journal of Computational Intelligence Research, 2(3):273– 286, 2006.
  4. Lothar Thiele, Kaisa Miettinen, PJ Korhonen, and Julian Molina. A preference- based evolutionary algorithm for multi-objective optimization. Evolutionary Computation, 17(3):411–436, 2009.
  5. Fillipe Goulart and Felipe Campelo. Preference-guided evolutionary algorithms for many-objective optimization. Information Sciences, 329:236 – 255, 2016. Special issue on Discovery Science.

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demo's Issues

Calculate Nadir point

Hi,
Dear Felipe Campelo,

Would you please explain how did you get these formulations to calculate Nadir point in In DTLZ5, 6 and Nadir, faux and zstar in DTLZ7?

case {'dtlz5', 'dtlz6'}
		zstar = zeros(M,1);
		znad = (1/sqrt(2)) .^ ([M-2, M-2:-1:0]');
	
case 'dtlz7'
		xaux = 0.85940;
		faux = 2*(M - (M-1)*xaux/2*(1 + sin(3*pi*xaux)));
		zstar = [zeros(M-1,1); faux];
		znad = [xaux(ones(M-1,1)); 2*M];

And how did you get this value xaux = 0.85940; in DTLZ7?

Thank you

Error in R-DEMO

Hi,

would you please check this error:

Error using bsxfun
Non-singleton dimensions of the two input arrays must match each other.

Error in rdemo_opt>selection (line 257)
aux = bsxfun(@minus, Fn, zrn);

Error in rdemo_opt (line 70)
   P = selection(P, O, zr, options);

I have used this:

zr = [0.6 0.2];
f = @(x) dtlz3(x, 2);
xrange = dtlz_range ('dtlz3', 2);

% R-DEMO:
>> [fopt1, xopt1] = rdemo_opt(f, zr, xrange);

Thank you

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