# How is it possible that gamultiobj gives worse solution when the number of MaximumGenerations is raised?

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Steffen Kuehl
on 14 Nov 2016

Commented: Steffen Kuehl
on 16 Nov 2016

Hi,

My muliobjective optimization modell (gamultiobj) does not get continuously better when I raise the number of MaximumGenerations. Sometimes a solution is worse than another solution which was generated with the same parameters, but a smaller number of MaximumGenerations. Since gamultiobj is a variant of NSGA-II( I can't find anything more specific in the Matlab-documentation), shouldn't the elitism of the algorithm make sure, that good solutions, that are calculated in early generations, are kept until the end?So, that it's not possible to get a worse solution when more generations are calculated?

I use the same starting/Initial Population for all my runs. I created my own Creation, Crossover and Mutation Function. Since the Elitism is supposed to be located in the Selection Function, I don't think that creating my own functions should interfer with the elitism.

I appreciate any idea and help. Thanks Steffen

And to clarify, here is some of my code.

These are the options for the Algorithm.

% code

options = optimoptions('gamultiobj',...

'UseParallel', true,...

'UseVectorized', false,...

'CreationFcn',@popFun,...

'CrossoverFcn',@crossoverBinary,...

'MutationFcn',@mutFun,...

'PopulationSize',InitPop,...

'MaxStallGenerations',MaxStallG,...

'MaxGenerations',MaxGamultiobj)

This is the Functioncall. A and B are linear constraints.

% code

[X,fval,exitflag] = gamultiobj(objFun,n,A,B,[],[],[],[],[],options);

This is my creation function.

% code

function Population = popFun(GenomeLength,~,options)

%Population function for example PopExample.

% This function must ensure that the linear constraints are met

global Zusatz

Population=zeros(options.PopulationSize,GenomeLength);

rng('default');

rng(Zusatz);

intcon=1:GenomeLength;

A=xlsread('Linearconstraints.xlsx','A2:MD86');

B=ones(85,1);

B(36,1)=-1;

lb=zeros(1,GenomeLength);

ub=ones(1,GenomeLength);

opts =optimoptions('intlinprog','IntegerTolerance',1e-06,'Display','off');

for a=1:options.PopulationSize

f= randn(GenomeLength,1);

[x,fval,exitflag]= intlinprog(f,intcon,A,B,[],[],lb,ub,opts);

Population(a,:)=x;

end

end

This is the Crossover function

if true

% code

end

function xoverKids = crossoverBinary(parents,options,GenomeLength,~,~,thisPopulation)

global Zusatz

rng('default');

rng(Zusatz);

% Extract information about linear constraints, if any

linCon = options.LinearConstr;

nKids = length(parents)/2;

index = 1;

xoverKids = nan(nKids,GenomeLength);

for k = 1:nKids

% Get the parents from the population

parent1 = thisPopulation(parents(index),:);

index = index + 1;

parent2 = thisPopulation(parents(index),:);

index = index+1;

% find locations where parents have a different genome

idx = randi(GenomeLength,1);

% Where genome is the same, keep it the same in the kids

xoverKids(k,1:idx) = parent1(1:idx);

xoverKids(k,idx+1:end) = parent2(idx+1:end);

% Ensure that kid astisfies constraints

flag = any(linCon.Aineq*(xoverKids(k,:)') > linCon.bineq,1);

while flag % Does not satisfy constraints

idx = randi(GenomeLength,1);

xoverKids(k,1:idx) = parent1(1:idx);

xoverKids(k,idx+1:end) = parent2(idx+1:end);

flag = any(linCon.Aineq*(xoverKids(k,:)') > linCon.bineq,1);

end

end

end

And the Mutation Function.

if true

% code

end

function mutationChildren = mutFun(parents, options, GenomeLength, ...

~, ~, ~, thisPopulation)

linCon = options.LinearConstr;

global Zusatz

rng('default');

rng(Zusatz);

% Initialize the output

mutationChildren = nan(length(parents),GenomeLength);

for k = 1:length(parents)

mut = thisPopulation(parents(k),:)';

idx = randi(GenomeLength,1);

mutated = mut;

if mutated(idx)==1

mutated(idx)=0;

else

mutated(idx)=1;

end

% Check that constraints are satisfied.

flag = any(linCon.Aineq*mutated > linCon.bineq,1);

while flag

idx = randi(GenomeLength,1);

mutated = mut;

if mutated(idx)==1

mutated(idx)=0;

else

mutated(idx)=1;

end

% Check that constraints are satisfied.

flag = any(linCon.Aineq*mutated > linCon.bineq,1);

end

mutationChildren(k,:) = mutated';

end

end

##### 5 Comments

### Accepted Answer

Brendan Hamm
on 15 Nov 2016

Ok. So there is an additional change you make in here that was not mentioned and is affecting the output. You change the MaxStallGenerations which was causing one of the solutions to run more iterations which were producing "better" results. While they may have been better with respect to some of the functions, they were not necessarily better with respect to others.

The basic idea is that if the average change in the best Objective Evaluations between the current generation and the Generation which occurred MaxStallGenerations ago is less than the FunctionTolerance (1e-4 by default), termination will occur.

So, I have a few suggestions:

- Keep the MaxStallGenerations the same between different runs.
- There is no need to change the rng in each function, in fact I would discourage this. Instead what you can do is get the 4th output of gamultiobj which contains the state of the RNG at the start of the algorithms run. See the link for information on this.
- Increase the population size. For a problem with this many variables I would consider having in the range of 500 different initial populations, this may provide you with a large enough "Elite" population to carry on to the next generation.

##### 4 Comments

Brendan Hamm
on 16 Nov 2016

### More Answers (2)

John D'Errico
on 14 Nov 2016

This is a stochastic solver. It generates points using random methods. As well, ANY numerical optimization tool can only find an approximate solution. They do not find an exact solution.

So there is no presumption that one optimization using a stochastic optimizer will always give as good a solution as another call to the same optimizer. Yes, by allowing it more iterations, you increase the chance that it will be able too improve, but it is only abetter chance, not an assurance of success.

Walter Roberson
on 14 Nov 2016

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