Some Heuristic and Deterministic Global Optimization Algorithms to Solve the Problem of Multidimensional Scaling

Multidimensional scaling (MDS) which is a fundamental problem in data analysis, can be formulated as a nonlinear global optimization problem. In order to solve it, some local, heuristic and global optimization methods are implemented. In another hand, to perform our new heuristic approach, the MDS problem is studied by using a multistart Levenberg-Marquardt method and, also for some small examples, by developping two rigourous global optimization algorithms. Nevertheless, these determinis-tic approaches have some identiied limits, which permit to extend these methods by making some accelerating or heuristic advices.