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This paper defines multidimensional sequential optimization numbers and provethat the unsigned Stirling numbers of first kind are 1-dimensional sequentialoptimization numbers. This paper gives a recurrence formula and an upper boundof multidimensional sequential optimization numbers. We proof that thek-dimensional sequential optimization numbers, denoted by O_k (n,m), are almostin {O_k (n,a)}, where a belong to[1,eklog(n-1)+(epi)^2/6(2^k-1)+M_1], n is thesize of k-dimensional sequential optimization numbers and M_1 is large positiveinteger. Many achievements of the Stirling numbers of first kind can betransformed into the properties of k-dimensional sequential optimizationnumbers by k-dimensional extension and we give some examples. Shortestweight-constrained path is NP-complete problem [1]. In the case of edgesymmetry and weight symmetry, we use the definition of the optimization set todesign 2-dimensional Bellman-Ford algorithm to solve it. According to the factthat P_1 (n,m>M) less than or equal to e^(-M_1 ), where M=elog(n-1)+e+M_1, M_1is a positive integer and P_1 (n,m) is the probability of 1-dimensionalsequential optimization numbers, this paper conjecture that the probability ofsolving edge-symmetry and weight-symmetry shortest weight-constrained pathproblem in polynomial time approaches 1 exponentially with the increase ofconstant term in algorithm complexity. The results of a large number ofsimulation experiments agree with this conjecture.

Sequential Optimization Numbers and Conjecture about Edge-Symmetry and Weight-Symmetry Shortest Weight-Constrained Path