New functional representation for the strongly interacting systems is proposed which contains a new type of the coherent state. As a result the new algebraic structureso called ”tower of algebras” appears which gives the tower (or hierarchy) of models. 1 Functional approach. Consider Hubbard model (lattice version of Thirring model) [1]: H = −t ∑ ,σ αrσ + αr′σ + U ∑ r nr,↑nr,↓ = Hband = (1)

The Reference Point Method (RPM) is an interactive technique for multiple criteria optimization problems. It is based on optimization of the scalarizing achievement function built as the augmented maxmin aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average ac...

This paper examines the development of a Functional Model which will provide a unique framework to enable the objective identification, comparison and appraisal of procurement systems globally. The paper illustrates how the use of existing classification criteria for building procurement systems (CIB 1991) is uninformative in the context of an international investigation, since account is not t...

This paper presents a multiobjective linear integer programming model for supporting the choice of remote load control strategies in electric distribution network management. The model takes into account the main concerns in load management, considering three objective functions: minimization of the peak demand as perceived by the distribution network dispatch center, maximization of the utilit...

In this paper, an interactive version of the ParEGO algorithm is introduced for identifying most preferred solutions for computationally expensive multiobjective optimization problems. It enables a decision maker to guide the search with her preferences and change them in case new insight is gained about the feasibility of the preferences. At each interaction, the decision maker is shown a subs...

In the interactive algorithms for multicriteria optimization the decision maker (DM) may express his/her preferences among the separate Pareto optimal solutions with the help of the values of the scalarizing problem parameters. The DM must choose the final (most preferred) solution and be responsible for this selection. The interactive methods are the best developed and wide spread methods. Thi...

This article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation co...

The Reference Point Method (RPM) is a very convenient technique for interactive analysis of the multiple criteria optimization problems. The interactive analysis is navigated with the commonly accepted control parameters expressing reference levels for the individual objective functions. The final scalarizing achievement function is built as the augmented max-min aggregation of partial achievem...