关于求最优分批问题的全部解

<正> 在文章2],3],4],5]中已对任何N>n>1及0≤δ≤1/2(以下总假设上列不等式满足)研究了最优分批问题的满足2]中定理5.1的条件组

ON THE FINDING OF ALL SOLUTIONS FOR THE OPTIMAL BLOCK SEARCH

It is proved by Wu Fang, in 1974, that we can certainly find a solution for the optimal block search which satisfies the conditions:Ⅰ.k_1 is an even number.Ⅱ. |k_i-k_j|≤2(1≤i, j≤n);Ⅲ. All even numbers in k_2, k_3,…, k_n are equal.All optimal solutions satisfying these conditions are found by recent works 2]-6]. Now we investigate the cases where these conditions are not satisfied. The main results are as follows. Theorem 3. If n = 2, k_1 + k_2 = N, then(1) When N = 4u, (2u, 2u) is optimal for any δ, and (2u + 1, 2u - 1) is optimal for δ = 0.(2) When N = 4u + 1, (2u, 2u + 1) is optimal for any δ, and (2u +2, 2u-1) is optimal for δ = 0.(3) When N = 4u + 2, (2u + 1 ± 1, 2u + 1 1) is optimal for any δ, and (2u + 3, 2u-1) and (2u+1, 2u+1) is optimal for δ=0.(4) When N = 4u + 3, (2u + 2, 2u + 1) is optimal for any δ.Theorem 6. If n > 2, conditions (1) are necessary for the solution (k_1, k_2,…, k_n) to be optimal, except that when δ = 0,(1) (2u-2, 2u, 2u-3), are optimal.