The use of conformity indices to optimize Gamma Knife planning is common, but does not address important tradeoffs between dose to tumor and normal tissue. Pareto analysis has been used for this purpose in other applications, but not for Gamma Knife (GK) planning. The goal of this work is to use computer models to show that Pareto analysis may be feasible for GK planning to identify dosimetric ...

Recent research on evolutionary multiobjective optimization has mainly focused on Pareto-fronts. However, we state that proper behavior of the utilized algorithms in decision/search space is necessary for obtaining good results if multimodal objective functions are concerned. Therefore, it makes sense to observe the development of Pareto-sets as well. We do so on a simple, configurable problem,...

Land-use allocation is of great significance in urban development. This type of allocation is usually considered to be a complex multi-objective spatial optimization problem, whose optimized result is a set of Pareto-optimal solutions (Pareto front) reflecting different tradeoffs in several objectives. However, obtaining a Pareto front is a challenging task, and the Pareto front obtained by sta...

In this paper we address the question of how many objective functions are really needed to decide whether a given point is Pareto optimal. We prove a reduction result for the case of quasi-convex objective functions and a convex feasible set. This result states that in order to decide whether a point x in the decision space is Pareto optimal it suuces to consider at most n + 1 objectives at a t...

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

Pareto efficiency is a widely used property in solution concepts for cooperative and non–cooperative game–theoretic settings and, more generally, in multi–objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the literature focuses on computing concise representations to approximate the Pareto curve or on explo...

We study Pareto optimal matchings in the context of house allocation problems. We present an O( √ nm) algorithm, based on Gale’s Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is N...

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...