Multiple-Criteria Optimization for Environment Development System : Constrained Case

Abstract

This paper deals with the multiple-criteria optimization problem for environment development systems, where the global amounts of each exogenous factor are limited. The model of an environment development system, which was introduced by R. Kulikowski, is described by a system of nonlinear differential equations which include interconnected n endogenous factors and m×n exogenous factors. The problem of multiple-criteria optimization for an environment development system is formulated. A main difficulty of multiple-criteria optimization is that it is no longer clear what one means by an optimal solution. A possible remedy for this situation is to introduce an objective function which is expressed as some function of various criterions. Given the specific objective function, we first optimize the system with respect to another criterion which is a linear combination of the given criteria. For the special case when the systems have similar nonlinearities, the solution of the linear combination problem is obtained in an explicit manner, in terms of the weighting factors in the linear combination functional. A search procedure is then used to determine the optimum values of these weighting factors for the specified objective function.