A molecular structure matching problem

We study how to optimize a measure of similarity between two molecules A and B: each with the same number of atoms. The similarity measures are based upon the norm of the difference between the interatomic distance matrices D A and D B . We seek to find a permutation of the row and column indices of D B so that the normed difference of D A and the permuted matrix D B is as small as possible. The performance of two heuristics—simulated annealing and tabu search—are reported for 20 atom test cases. A novel method for generating initial permutations is shown to work well when the ( x, y, z) coordinates of the atoms of A and of B are related.