Approximate ab initio calculations and the method of molecular fragments

A two stage approach to performing ab initio calculations on medium and large sized molecules is described. The first step is to perform SCF calculations on small molecules or molecular fragments using the OPIT Program. This employs a small basis set of spherical and p-type Gaussian functions. The Gaussian functions can be identified very closely with atomic cores, bond pairs, lone pairs, etc. The position and exponent of any of the Gaussian functions can be varied by OPIT to produce a small but fully optimised basis set. The second stage is the molecular fragments method. As an example of this, Gaussian exponents and distances are taken from an OPIT calculation on ethylene and used unchanged in a single SCF calculation on benzene. Approximate ab initio calculations of this type give much useful information and are often preferable to semi-empirical approaches, since the nature of the approximations involved is much better defined.

A New Genetic Algorithm for Set Covering Problems

An indirect genetic algorithm for the non-unicost set covering problem is presented. The algorithm is a two-stage meta-heuristic, which in the past was successfully applied to similar multiple-choice optimisation problems. The two stages of the algorithm are an ‘indirect’ genetic algorithm and a decoder routine. First, the solutions to the problem are encoded as permutations of the rows to be covered, which are subsequently ordered by the genetic algorithm. Fitness assignment is handled by the decoder, which transforms the permutations into actual solutions to the set covering problem. This is done by exploiting both problem structure and problem specific information. However, flexibility is retained by a self-adjusting element within the decoder, which allows adjustments to both the data and to stages within the search process. Computational results are presented.