## ABSTRACT

Abstract In this chapter, we will be looking at the potential for using genetic algorithms to map a set of objects in a multidimensional space. Genetic algorithms have a couple of advantages over the standard multidimensional scaling procedures that appear in many commercial computer packages. We will see that the most frequently cited advantage of genetic algorithms, the ability to avoid being trapped in a local optimum, applies in the case of multidimensional scaling. Using a genetic algorithm, or at least a hybrid genetic algorithm, offers the opportunity to choose freely an appropriate objective function. This avoids the restrictions of the commercial packages, where the objective function is usually a standard function chosen for its stability of convergence rather than for its applicability to the user’s particular research problem. We will develop some genetic operators appropriate to this class of problem, and use them to build a genetic algorithm for multidimensional scaling with fitness functions that can be chosen by the user. We will test the algorithm on a realistic problem, and show that it converges to the global optimum in cases where a systematic hill-descending method becomes entrapped at a local optimum. We will also look at how considerable computation effort can be saved with no loss of accuracy by using a hybrid method. For hybrid methods, the genetic algorithm is brought in to “fine tune” a solution, which has first been obtained using standard multidimensional scaling methods. Finally, a full program description will be given allowing the reader to implement the program, or a modification, in a C or C++ environment.