optimization technique problem with different outputs

i am doing one optimization technique as there is a randomness in the technique i getting new value as a output every time some times repeated value if i run for 20 times i getting 20values some may be same now which value i need to choose correct value. is there any tool in matlab or any code to justify my problem?

[Ameer Hamza]

Which optimization function are you using? Have you written the function yourself? If you are using MATLAB's optimization toolbox functions, then probably every solution is a local minimum. In that case, you might try using global optimization toolbox: https://www.mathworks.com/help/gads/index.html?s_tid=CRUX_lftnav

[rajesh kumar]

every time i am executing the technique, i am getting optimal value, i am executed many times which optimum value i need to select, how can i justify that value is correct value, is there any concepts related to this one or any matlab tool.

[Walter Roberson]

Yes, the one and ONLY concept is that you select the configuration that gave you the best function value, even if it is only better only by 1E-278.

Note that unless you are using the symbolic toolbox, what you are optimizing at any time is not a formula, but rather an implementation of a formula. In floating point, A+B+C is not necessarily the same as C+A+B. So you choose the configuration or technique that gives you the best output for that implementation no matter how small the difference is.

This assumes that the configuration does not violate any constraints, even by a hair. If you permit a constraint violation at all, even just to take into account round-off error, then you need quite different reasoning about which solution to choose.

[Ameer Hamza]

Walter's answer explains the computational aspect of this issue. However, this might be the case that the system is underdetermined, and there are potentially infinite solutions to your optimization problem, each giving exactly the same optimal value. If this is the case, then you can consider adding some more constraint considering the underlying problem you are trying to solve. Anyway, the justification of a solution will depend on the problem you are trying to solve. If you just want to get a unique solution every time you run the code, you can just add

rng(0)

at the beginning of your code to seed the random number generator with the same value. You will get the same solution every time.

[Walter Roberson]

If you do find multiple solutions that are bit-for-bit identical in optimal function value, then in some cases you just pick one arbitrarily for illustration purposes; and in other cases you need to find the entire set of solutions or a formula to generate the entire set. In other cases for illustration you want to find the first few solutions for plotting purposes, where "first" typically refers to those with smallest positive independent variable to make it easier to plot. But if you are faced with something like sinc wave with infinite oscillations near 0 then your only "justification" for picking some has to do with giving nice separation in a low resolution diagram.

Answer 1

[Walter Roberson]

About the only test that can justify one optimization result compared to another, is to compare the value of the objective function, and choose the configuration that leads to the minimum or maximum as appropriate.

[rajesh kumar]

if there is no comparison with other method now how can i justify my answer, every time i am getting global value which value i need to select, is there any method or concepts or any matlab tool

[Walter Roberson]

By the way, if the question is which optimization technique is the best, then you need to define carefully what "best" means. If you have an optimization technique that produces a solution to (say) 45 bits accuracy in (say) 3 seconds, and you have a different technique that produces a solution to 48 bits accuracy (roughly one more decimal place) in (say) 3 hours, then which is best? How much extra time are you prepared to spend for each extra bit of accuracy?