  This paper defines multidimensional sequential optimization numbers and prove
that the unsigned Stirling numbers of first kind are 1-dimensional sequential
optimization numbers. This paper gives a recurrence formula and an upper bound
of multidimensional sequential optimization numbers. We proof that the
k-dimensional sequential optimization numbers, denoted by O_k (n,m), are almost
in {O_k (n,a)}, where a belong to[1,eklog(n-1)+(epi)^2/6(2^k-1)+M_1], n is the
size of k-dimensional sequential optimization numbers and M_1 is large positive
integer. Many achievements of the Stirling numbers of first kind can be
transformed into the properties of k-dimensional sequential optimization
numbers by k-dimensional extension and we give some examples. Shortest
weight-constrained path is NP-complete problem [1]. In the case of edge
symmetry and weight symmetry, we use the definition of the optimization set to
design 2-dimensional Bellman-Ford algorithm to solve it. According to the fact
that P_1 (n,m>M) less than or equal to e^(-M_1 ), where M=elog(n-1)+e+M_1, M_1
is a positive integer and P_1 (n,m) is the probability of 1-dimensional
sequential optimization numbers, this paper conjecture that the probability of
solving edge-symmetry and weight-symmetry shortest weight-constrained path
problem in polynomial time approaches 1 exponentially with the increase of
constant term in algorithm complexity. The results of a large number of
simulation experiments agree with this conjecture.
