This paper presents a new definition regarding inverse number sequence distance, proving that it satisfies five of the six conditions put forward by Cook and Seiford that sequence distance needs to meet. Sequence distance based on the absolute value has been separately used to solve minimum violation ranking scheduling problems that contained six variable sequences. Results have shown that the degree of overlap for the solution space of the two-distance scale was high; there were 176 optimal solutions through the use of the inverse number sequence distance. The proportion of the same solutions was 68.8%, and the sequence distance scales based on the absolute value were 228 and 42.0% respectively. The two-distance scale explains the sequence distance from different angles, but it can be seen from the data that the inverse number sequence distance explains the distance of sequence more fully than absolute distance, so the hit rate is relatively higher. Also we considered the sequence distance of n variables. The solution space is n!, the calculation is very large, so we have chosen the gravity optimization algorithm in order to solve it. Results show that using the proposed algorithm saves time and results in a good effect solution.
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