surrogateopt multi-objective function output

I have a function in a .p file called AuxModel.p. To call the function it it simply @(x) AuxModel(x). I need to implement a surrogate based strategy to find a good approximation of the entrie pareto front. The problem I am having is using surrogateopt, the output of the function must be a scalar value, while AuxModel returns a output as a vector with two elements. Is is possible to create a wrapper function so that surrogateopt can work with the AuxModel function? I did something similiar previously to find the global minimum of each function value. I cannot use gamultiobj, as I used this for a previous question in the assignment and the strategy must be surrogate based.

% Define the wrapper function
function scalar_value = AuxModelWrapper(x)
    % Call the original function
    vec = AuxModel(x);
    % Compute a scalar value from the output
    scalar_value = vec(1);
end

[Mario Malic]

The question is unclear.

What is the output (those two elements)? Are those the optimization variables?

If not, are you trying to minimize those elements? Are you trying to maximize them? Do you care only about the first one? Is the second element much more important than the first one?

scalar_value = vec(1) + vec(2); % or something appropriate

[Max Fawcett]

I am trying to find the pareto front of the minimum value for both elements of the function output. Both functions take as input a design vector bounded as:

• Lower bounds LB = [-10, -50, -200, -1000, -5000]
• Upper bounds UB = [10, 50, 200, 1000, 5000]

Answer 1

[Alan Weiss]

I do not understand why you want to use surrogateopt to help solve a multiobjective problem. I think that gamultiobj or paretosearch would be more efficient.

But, if you insist, you can use a single-objective solver to create a Pareto front. See Generate and Plot Pareto Front. You can easily use surrogateopt instead of fgoalattain. Basically, you solve a series of single-objective problems of the form

where α goes from 0 through 1.

Alan Weiss

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