The most important issue in multi-objective optimization problems is to determine the Pareto points along the Pareto frontier. If the optimization problem involves multiple conflicting objectives, the results obtained from the Pareto-optimality will have the trade-off solutions that shaping the Pareto frontier. Each of these solutions lies at the boundary of the Pareto frontier, such that the i...

I. Pireto surfaces and attainable sets of complexity 1 (i.e., those having a l-coiumodi*/ representation and no O-comcodity representation) are treated. An implicit characterization of these sets is given, and various of their properties are derived. In particular, Pareto surfaces of complexity a^ raost 1 are always closed ses.

designer is solving an optimization problem, which involves different disciplines and where all design criteria have to be optimized simultaneously. Mathematically this problem can be reduced to a vector optimization problem. The solution of this problem is not unique and is represented by a Pareto surface in the space of the objective functions. Once a Pareto solution is obtained, it may be ve...

PURPOSE To eliminate or reduce the error to Pareto optimality that arises in Pareto surface navigation when the Pareto surface is approximated by a small number of plans. METHODS The authors propose to project the navigated plan onto the Pareto surface as a postprocessing step to the navigation. The projection attempts to find a Pareto optimal plan that is at least as good as or better than t...

In multidisciplinary optimization a designer solves a problem where there are different criteria usually contradicting each other. In general, the solution of such a problem is not unique. When seeking an optimal design, it is natural to exclude from the consideration any design solution which can be improved without deterioration of any discipline and violation of the constraints; in other wor...

the photocatalytic activity of nano-bi2o3 was evaluated in degradation of rhodamine b (rhb) as a model of dye pollutant from waste waters. nano sized bi2o3 was synthesized using the chemical precipitation method. the as-prepared sample was characterized by x-ray diffraction (xrd), scanning electron microscopy (sem) and fourier transform infrared spectrometry (ft-ir). structural analysis reveale...

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable...

We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set...