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 DA and DB. We seek to find a permutation of the row and column indices of DB so that the normed difference of DA and the permuted matrix DB 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.