1 Introduction

Observations of interacting galaxies provide important information about galactic structure and evolution. Due to the long time scales (compared to the lifetime of a human) involved in interactions between galaxies, one can only obtain a single snapshot of an interacting system. Dynamical modelling of such systems therefore constitutes an important complement to observations, and can naturally be divided into two parts: Modelling of the individual galaxies participating in an interaction, and determination of the orbital parameters. Advances in the techniques for modelling of individual galaxies in interacting systems has led to a greatly increased understanding of features such as bars, rings, and spiral arms.

In order to understand the dynamics of an interacting system of galaxies it is, however, equally important to know the parameters of the relative orbit of the two galaxies. Determination of orbital parameters has only been carried out for a small fraction of all observed interacting galaxies. An example of a system that has been much studied is the M 51 system (for recent results, see Engström & Athanassoula 1991; Howard & Byrd 1990, and Hernquist 1990). The fact that several authors have arrived at very different orbits shows the difficulties involved in modelling even a well-observed system such as M 51.

Some of the main problems encountered when numerical simulations are used for determining orbital parameters are that the parameter space that needs to be searched is often very large, and that the results of each simulation must be compared with the observational data. While methods for automatic comparison of data between observations and simulations have been used in some cases (e.g. Engström & Athanassoula 1991), very little has been done to find an efficient method for reducing the amount of searching necessary in order to find the orbit in a general case. In this paper, an efficient search method will be presented and evaluated using artificial data.

Science often benefits from the sharing of information between different disciplines. One example of this is the invention of genetic algorithms (Holland 1975). With natural evolution as the inspiration, genetic algorithms (hereafter GAs) use artificial selection and the genetic crossover and mutation operators to manipulate strings of numbers which encode the variables of the problem, thereby reaching better and better solutions to the problem. GAs are used in many branches of science (see the Appendix). However, in astrophysics there have, as yet, only been a few applications of GAs, in the fields of solar coronal modelling (Gibson & Charbonneau 1996), helioseismology (Tomczyk et al. 1995), pulsar planet searching (Lazio 1997), eclipsing binary stars (Hakala 1995), and gamma-ray astronomy (Lang 1995). For an excellent review of GAs in astronomy and astrophysics, see Charbonneau (1995).

In this paper, a GA will be used for searching the space of possible orbital parameters for pairs of interacting galaxies. Section 2 contains a description of the problem, and the method of solution is presented in Sect. 3. The results are given in Sects. 4 and 5. The method is discussed in Sect. 6, and the conclusions are presented in Sect. 7. The Appendix contains a brief description of the essential features of the GA used in the paper, as well as some references for further reading.