In modern nonlinear programming the universal methods allowing solving arbitrary problems have not been elaborated yet. It is conditioned by the fact that real problems of minimization usually differ very much from each other both intrinsically and dimensionally. The basic idea of my research is the elaboration of a system connecting all optimization methods into a single one, so that the advantages of both first- and second-order methods speed and direct search methods universality remained. It is obvious that all the optimization algorithms are of the same specification - they get a function and initial point at the entry, ant at the output - return the found optimal point. This property allows us to combine them into one multiversion system.
The main idea of the multiversion programming is in the introduction of software redundancy due to using several various program modules equivalent on the functional purpose (got the name of multiversions), working in time parallel and getting the same data at the entry. The multiversion outputs are conformed by means of a particular multiversion voting algorithm. As a result, all the program module versions operate as an organic whole and return one coherent result irrespective of failures and errors of certain modules. Because of its high efficiency the given method has got a wide spread occurrence and development.
Having applied the multiversion programming ideology to the problem of several variables function optimization, we get the system, in which different optimization methods act as multiversions.
Methods of comparison of multiversions against each other:
- by the function value;
- by the search direction at the last step;
The influence of random search algorithms on the general result:
- the general search speed increases;
- there is no search process circling;
The influence of various voting methods on the efficiency of several variables functions optimization multiversion system:
- the overall majority voting method is invalid;
- the coherent majority voting method shows authentically high results;
- the coherent majority ill-defined voting method shows the best results;
- the weighted voting algorithms often end in results´ mismatch when using random search methods;
- the median voting results in the optimization process "circling".
As the carried out experiments showed, the multiversion system of several variables functions optimization doesn´t loose its efficiency compared to the best of all methods separately, while in some cases with a complex surface character, functions show even more rapid convergence speed.
It allows using the offered elaboration as a universal method of any several variables continuously differentiable functions optimization while solving academic and practical problems.
The work was submitted to international scientific conference «Innovation technologies», Thailand, February, 20-28, 2008, came to the editorial office 10.01.2008.