Multiple-objective optimization for environment development systems

Abstract This paper deals with multiple-objective optimization problems for the environment development system. The model of the environment development system, which was introduced by Kulikowski, is described by a system of non linear differential equations which include interconnected n exogenous and m endogenous controlled factors or processes. The problem of multiple-objective optimization for the environment development system is formulated. A main difficulty of multiple-objective optimization is that it is no longer clear what one means by an optimal solution. A possible remedy for this situation is to refine the concept of optimal solution by introducing the so-called Pareto-optimal solution set. Then multiple-objective optimization problem boils down to determining the set of Pareto-optimal solutions. The Pareto-optimal solution set is related in a one-to-one manner to a family of auxiliary scalar index problems. For an unconstrained multiple-objective optimization problem for the environment development system, the entire Pareto-optimal set can be determined by solving the auxiliary scalar problem, using only one value of the weighting vector.