We completely characterize deterministic strategy-proof and group strategy-proof mechanisms on singlesinked public policy domain. The single-sinked domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the sink) in the interval, and the preferences are increasing as o...

Let T = (V,E) be a tree. A core of T is a path P , such that the sum of the weighted distances from all vertices to this path is minimized. In this paper we consider the semi-obnoxious case where the vertices have positive or negative weights. We prove that if the sum of the weights of vertices is negative the core must be a single vertex and when the sum of the weights of vertices is zero ther...

Evolutionary optimization algorithms have been used to solve multiple objective problems. However, most of these methods have focused on search a sufficient Pareto front, and no efforts are made to explore the diverse Pareto optimal solutions corresponding to a Pareto front. Note that in semi-obnoxious facility location problems, diversifying Pareto optimal solutions is important. The paper the...

in this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. let $t=(v,e)$ be a tree. the $(k,l)$-core of $t$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. we show that, when the sum of the weights of vertices is negative, t...

Unmanned Aerial Vehicle (UAV) have emerged as a promising technique to rapidly provide wireless services group of mobile users simultaneously. The paper aims address challenging issue that each user is selfish and may misreport his location or preference for changing the optimal UAV be close himself. Using algorithmic game theory, we study how determine final in 3D space, by ensuring all users'...

The problem considered in this paper is the weighted obnoxious facility location convex hull of demand points. objective function to maximize smallest distance between a and set Three new optimal solution approaches are proposed. Two variants Big Triangle Small global optimization method, procedure based on intersection points Apollonius circles. We also compared results with multi-start approa...