97-49
Vector Investor Problem and its Fractal Properties
by Girlich, E. (Magdeburg); Perepelitsa, V.A.; Sergeeva, L.N. (Zaporozhye)
Preprint series: 97-49, Preprints
- MSC:
- 90C27 Combinatorial optimization
- 90C29 Multi-objective and goal programming; vector optimization
Abstract: The paper dedicated to the research of properties of the two-criterial investor problem. The solution set is analysed at first time in the point of view of its capacity. The authors proved the property of completeness of two-criterial investor problem with criterion of MINSUM type and the property of quasi-completeness for the same problem but with the criterion of MINMAX type. For further analysis of the set of feasible solutions (SFS) it is convenient to consider in the form of its image in the criterion space. It is proposed two types of graphic imaginations of criterial space. Geometric structure of obtained image of the SFS is researched by fractal theory methods and by methods of theory of deterministic chaos. The proof of fractal structure of the SFS of vector investor problem is obtained by imitation modelling method.
Keywords: multiobjective discrete optimization, fractal theory, discrete optimization