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### Highlights from GODLIKE - A robust single-& multi-objective optimizer

• GODLIKE.m
• GODLIKE_DEMO
• set_options(varargin)
• pop_single.m
• pop_multi
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# GODLIKE - A robust single-& multi-objective optimizer

### Rody Oldenhuis (view profile)

24 Jul 2009 (Updated )

GODLIKE combines 4 global optimizers for both single/multi-objective optimizations

File Information
Description

GODLIKE (Global Optimum Determination by Linking and Interchanging Kindred Evaluators) is a generization of various population-based global optimization schemes. Also, it handles both single- and multi-objective optimization, simply by adding additional objective functions.
GODLIKE solves optimization problems using relatively basic implementations of a genetic algorithm, differential evolution, particle swarm optimization and adaptive simulated annealing algorithms. Its power comes from the fact that these different algorithms run simultaneously (linked), and members from each population are occasionally swapped (interchanged) to decrease the chances of convergence to a local minimizer.

It is primarily intended to increase ROBUSTNESS, not efficiency as it usually requires more function evaluations than any of the algorithms separately. Its also inteded to do away with the need to fine-tune these algorithms each and every time you encounter an optimization problem, AND to generalize optimization itself (it's both a single and multi-objective optimizer), AND to generate simple plots to be used in quick reports etc.

BASIC EXAMPLES:

(single-objective)

% extended rosenbruck function
rosen = @(X) sum( 100*(X(:, 2:2:end) - X(:, 1:2:end-1).^2).^2 + (1 - X(:, 1:2:end-1)).^2, 2);

% call GODLIKE
GODLIKE(rosen, 250, -10*ones(1,10), 10*ones(1,10), 'ms')

will produce a reasonably accurate approximation to the global minimum of the 10-dimensional rosenbruck problem
( sol ~ ([1,1,1,...]), fval ~ 0 )

(multi-objective optimization)

% basic Sin-Cos Pareto front
GODLIKE({@sin;@cos}, 100, 0, 2*pi, [], 'display', 'plot')

will generate a nice plot of the problem's Pareto front. Some more examples are included in the GODLIKE_DEMO.m, included in the ZIP.

======================================
MAJOR CHANGES
(see the changelog for more detailed changes)
======================================
(06/Aug/2009)
- Objective functions can now accept any 2-dimensional input. Your objective function should accept arguments equal in size to either [lb] or [ub], and return a simple scalar.
- I discovered I made some *severe* mistakes in the implementation of the global optimization algorithms. This caused large inefficiencies or inaccurate results. Most (hopefully all) of these mistakes are corrected now.
- Added 2more options for the algorithms: NetWorkTopology & ReHeat (see doc)
- Changed the [MinDescent] criterion to the more MATLAB-style 'TolX' and 'TolFun' options

Acknowledgements

Nsga Ii: A Multi Objective Optimization Algorithm inspired this file.

MATLAB release MATLAB 7.7 (R2008b)
15 Jun 2015 Angelo Ambrisi

### Angelo Ambrisi (view profile)

I have to make a multi-objective optimization . I have a function called statement, my_obj , where there are 2 decision variables and 3 objective functions . Now I call this function by another m-file :

[ s0 , FVAL ] = GODLIKE ( @my_obj , PS , lb , ub , ' ASA ' , options) ;

but I always get this error :

??? Error using == > cellfun
Non - scalar in Uniform output , at index 1 , output 1 .
Set ' UniformOutput ' to false .

How should I give the 3 objective functions to algorithm GODLIKE ? In this moment I in the function statement, my_obj I have had write:

of1 = 1 -E ;
of2 = C ;
of3 = D ;

where E , ​​C , D are dependent on the 2 decision variables .

Who can help me? thanks

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21 Jan 2015 Cengiz Gunay

### Cengiz Gunay (view profile)

I forked the Github project and added parallel execution with a new "UseParallel" option:
https://github.com/cengique/FEX-GODLIKE/releases/tag/v0.5

07 Nov 2014 Alex Pavlides

### Alex Pavlides (view profile)

Hi, really great work. My only problem is getting the options to work. For example if I put 'MaxFunEvals',10 or 'Display','On' it seems to just ignore the option. Anyone know why this might be? Other than that it is running well.

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08 Jul 2014 Joshua

### Joshua (view profile)

Hello again,
Just a comment: in addition to the modification I made below, I also require that a significant portions of the individual parameters be zero (which I call MAXNUMPAR), i.e. pop{1}.individuals = [ 0 0.2 0 0 0.5 0 0.3 ];. I initially included this change in the line before my previous modification.
This seems to cause problems with the genetic algorithm, as it returns NANs in some of the individuals.
I correct this by moving my MAXNUMPAR to before pop{i}.iterate;.
I'm not sure why the genetic algorithm does this (possibly combinations of the individuals results in an individual of all zeros), and isn't in need of a fix. Just an FYI in case someone else ever tries to do the same thing.

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10 Jun 2014 Joshua

### Joshua (view profile)

Thank you, Mario.
Thank you, Rody.
I managed to get the modification I wanted to GODLIKE, which makes me very glad, because this program seems very awesome.
To do it, I went to line 198 of GODLIKE and inserted the following code
X = size(pop{i}.individuals,1);
for j = 1:X
pop{i}.individuals(j,:) = ...
NORMTOTOTAL(pop{i}.individuals(j,:)));
end
clear X
where NORMTOTOTAL is a simple function I wrote to normalize each number in a row vector to the sum of the entire vector.
Thank you!

10 Jun 2014 Rody Oldenhuis

### Rody Oldenhuis (view profile)

@Joshua,

No, there is no easy way in GODLIKE to implement linear constraints like the one you have; GODLIKE is restricted to problems with bound-constraints only. It is fairly easy to devise a workaround (as suggested by Mario Castro Gama), however, if your problem is not too large, it might be easier to give a try to my minimize() function (just search my author page here on the FEX). This function also supports (non)linear constraints, and has global optimization capability (albeit rudimentary compared to GODLIKE).

Hope this helps, Rody Oldenhuis

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10 Jun 2014 MARIO CASTRO GAMA

### MARIO CASTRO GAMA (view profile)

Hello Joshua

Maybe you can try to implement http://www.mathworks.nl/matlabcentral/fileexchange/45490-generate-k-random-numbers-which-sum-m inside the godlike algortihm when the new population is created.

Best regards.

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09 Jun 2014 Joshua

### Joshua (view profile)

Hello,
I would like to run this code. My model parameters need to have a combined total of 1. I have tried modifying the code to include a function of mine that does this, but I keep finding new errors.
Is there a simple way to make this code keep the combined total of my model parameters equal to one?

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28 Oct 2013 Fabien

### Fabien (view profile)

nice job !

Dear Roddy

Thank you for sharing your great "godlike" optimisation code in matlab
central. I have two questions:
1. With the current "godlike" demo (set by you) the Multi-objective
optimisation is implemented. How can I set it to run just
single-objective optimisation?
2. How can I set it to run just one heuristic technique?

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08 Mar 2012 Christoph Feenders

### Christoph Feenders (view profile)

18 Nov 2011 Joe Ajay

### Joe Ajay (view profile)

Hello Rody, does this tool solve discrete optimization problems...do you have any update for solving discrete problems

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26 Aug 2011 Jeroen van Nugteren

### Jeroen van Nugteren (view profile)

23 Jun 2011 Sebastien PARIS

### Sebastien PARIS (view profile)

22 Jun 2011 Christopher

### Christopher (view profile)

I've found that this code is quite helpful in generating useful initial conditions for some constrained optimization problems that involve local minima. Are there any plans to handle nonlinear inequality constraints? Also, a useful addition to the code would be an option for a maximum run time. That way I can set it to run over the weekend easily.

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28 Jan 2011 Davide

### Davide (view profile)

When I try the multi-objective minimization I face some issues.
Let's take as an example this multiobjective function
function a = myfunc(x)
a(1) = sin(x)
a(2) = cos(x)

if I use GODLIKE like this:
GODLIKE({@sin,@cos},...)
it works fine

in this way
optfunc = @(x) myfunc(x)
GODLIKE(optfunc,...)
id does not.

What am I doing wrong in the second case? How should I use it?

07 Dec 2010 Ben

### Ben (view profile)

How to pass parameters to the objective function?

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27 Sep 2010 Davoud Safari

### Davoud Safari (view profile)

Thanks Rody...But I need the codes for integer programming. How can use these codes for that purpose.. i.e. which part of code, must be changed to achieve my purpose?

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03 Sep 2010 Vaibhav

### Vaibhav (view profile)

Developed function is very nice, but can i handle equality and inequality constraints in GODLIKE? In user manual, i couldn't find anything related to this.

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Is it possible to add more constraints into the optimization of godlike? for example: x(1)+x(2)-3*x(3)=10
How could I realize that in matlab?
Thanks

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10 Jul 2010 Robert

### Robert (view profile)

trade extra cpu cycles for fewer brain cycles.

15 Oct 2009 John

### John (view profile)

I would like to implement this code to fit a non-linear equation to a set of data. The non-linear equation takes 8 paramaters which I would like to optomize. Basically, the sum of least squares approach. Will GODLIKE achieve this? I have tried using it and the paramater guesses are all over the place and do not seem to converge. Thank you!

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29 Sep 2009 Roland Pihlakas

### Roland Pihlakas (view profile)

A bugfix.
set_options.m, at lines 456-457:

elseif strcmpi(option, 'SkipTest')
if ~isnumeric(value)

should be:

elseif strcmpi(option, 'SkipTest')
if ~ischar(value)

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08 Sep 2009 Rody Oldenhuis

### Rody Oldenhuis (view profile)

Daniel: I am most certainly planning to implement (non)-linear constraints in GODLIKE, that would be pretty convenient indeed! However, I'm VERY busy the next few weeks, so don't expect this change to come anytime soon :)

You could try my other tool OPTIMIZE (also on the file-exchange); it can also optimize problems globally. Perhaps that can give you some results...

Thanks for the 5 stars ! :)

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08 Sep 2009 Daniel

### Daniel (view profile)

Nice tool! Any plans for adding non-linear constraint handling? I'm messing with a Lagrangian barrier function (the method the original C++ implementation of NSGAII uses) inside a custom objective function, but it would be nice to have that kind of functionality implemented directly in the optimizer.

02 Sep 2009 Rody Oldenhuis

### Rody Oldenhuis (view profile)

Roland: Indeed, I overlooked that issue. It works great, thanks!

About the mex-file: I see no real need for it. Most of the time the real computational cost is in the objective functions, not this optimizer (as it should be)...except maybe for the NSGA-II part, but really I only notice that it's N2-complex if I use huge population sizes...that, and I'm really short on time these days :) But of course, you are more than welcome to do it!

So what changes did you make to allow ML2007a to run it? It would be perfect if more users could use GODLIKE! I think it's a great idea if you incorporate those changes, write a mex file and submit it as an improvement upon my version.

Thanks for the feedback.

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02 Sep 2009 Roland Pihlakas

### Roland Pihlakas (view profile)

Hi, You can make it orders of magnitude faster if You replace in pop_single.m this:

for i = 1:pop.dimensions
% convert column to decimal representation
temp_pop(:, i) = sum(convert_to_dec.*newpop(:, 1:NumBits), 2);
% delete entries
newpop(:, 1:NumBits) = [];
end

with this:

newpop_startcol = 1;
NumBits2 = NumBits-1;
for i = 1:pop.dimensions
% convert column to decimal representation
temp_pop(:, i) = sum(convert_to_dec.*newpop(:, newpop_startcol : newpop_startcol+NumBits2), 2);
% delete entries
newpop_startcol = newpop_startcol + NumBits;
end

Column/row deletion is very slow operation, its better to avoid it.

There were also some changes I had to make in order for the script to start in Matlab R2007a.

Are You considering to port it to mex file? I am going to do that but we may get the results sooner if we split the task.

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03 Aug 2009 André