In the present research, a type of permutation optimization was introduced. It is assumed that the cost function has an unknown probability distribution function. Since the solution space is inherently large, solving the problem of finding the optimal permutation is com More
In the present research, a type of permutation optimization was introduced. It is assumed that the cost function has an unknown probability distribution function. Since the solution space is inherently large, solving the problem of finding the optimal permutation is complex and this assumption increases the complexity. In the present study, an algorithm based on distributed learning automata was presented to solve the problem by searching in the permutation answer space and sampling random values. In the present research, in addition to the mathematical analysis of the behavior of the proposed new algorithm, it was shown that by choosing the appropriate values of the parameters of the learning algorithm, this new method can find the optimal solution with a probability close to 100% and by targeting the search using the distributed learning algorithms. The result of adopting this policy is to decrease the number of samplings in the new method compared to methods based on standard sampling. In the following, the problem of finding the minimum spanning tree in the stochastic graph was evaluated as a random permutation optimization problem and the proposed solution based on learning automata was used to solve it.
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