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Optimal path selection (OPS) with unique or multiple constraints is one of key issues in the dynamic networks, in which arc' weight metric is an interval number. Firstly, some existing solutions for this problem are analyzed, and some shortages and flaws are pointed out. Secondly, regularities of distribution of the summation of multiple independent random numbers with same and different distributions are analyzed and formulated by data simulating and fitting. Furthermore, an algorithm named DOPS_Const for the OPS with an additive arc weight is proposed based on the above analysis, and the randomness and subjectivity in path selection can be avoided according to the algorithm. Finally, the theoretical and statistical probabilities of the selected path satisfying the given constraint are compared, and our algorithm is feasible and valid to solve the OPS with constraint in the dynamic networks.