Finding global minimum by using Ant Colony Optimization?

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Ozge Moral 2015-10-29

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https://ww2.mathworks.cn/matlabcentral/answers/251655-finding-global-minimum-by-using-ant-colony-optimization

回答： REMYA R suresh 2022-3-22

I want to apply Ant Colony Optimization to one variable function for finding a global minimum. But i'm confused how to implement it. Do you have any suggestion about article related this topic?

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Adam 2015-10-29

编辑：Adam 2015-10-29

Have you read papers on the subject? It's over 10 years since I wrote an ant colony algorithm, but I did it from papers as far as I can remember so there must be a lot more papers since then with details of the general algorithm that could be found via an internet search.

Ozge Moral 2015-10-29

Yes, i read many papers about ACO and application of TSP. Especially, i'm searching for finding global minimum. I already found two or three paper about this. i'm working on an algorithm with help these. i just wonder if i can reach anything else. I will add my code also in a few days, because i'm stuck. Thank you.

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Answer 1

Walter Roberson 2015-10-29

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There are ACO implementations in the File Exchange.

However, it can be shown that there is no algorithm that can always find the global minimum of a continuous "black box" function. In the discrete "black box function" case, the only algorithm that can always find the global minimum is to try every representable number in the range.

For functions that are available in analytic form rather than as "black box", analysis is sometimes able to find the global minima.

There are functions over the natural numbers for which it can be shown that knowing the value of the function for all values from 1 to N-1 does not allow you to predict the value of the function on N.

In other words, ACO can never be sure that it has found the global minima, and PSO and GA have the same difficulty.

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Ozge Moral 2015-10-29

I will look these implementations in the File Exchange again. I only reviewed the TSP application in the File Exchange. This is first step in my project, i will apply ACO on single-variable/ multi-variable cont. and discrete functions. I know it does not guarantee exact solution because it is a heuristic method, but i have to work with it. Thanks, i'm going on research.

Walter Roberson 2015-10-29

One implementation is:

http://www.mathworks.com/matlabcentral/fileexchange/52859-ant-colony-optimization--aco-

The difficulty I spoke of before still applies: none of these techniques can promise global minima without some analysis from the user to confine their search to the area where the local minima is somehow known to be the global minima

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