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...

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, a new model for the semi-obnoxious facility location problem is introduced. The new model is composed of a weighted minisum function to represent the transportation costs and a distance-based piecewise function to represent the obnoxious effects of the facility. A single-objective particle swarm optimizer (PSO) and a bi-objective PSO are devised to solve the problem. Results are ...

In this work, a semi-obnoxious facility must be located in the Euclidean plane to give service to a group of customers. Simultaneously, a set of populated areas, with shapes approximated via polygons, must be protected from the negative effects derived from that facility. The problem is formulated as a margin maximization model, following a strategy successfully used in Support Vector Machines....

This paper considers a bicriteria model to locate a semi-obnoxious facility within a convex polygon, while employing Euclidean push and pull covering criteria. The partial covering context is introduced into an ordinary bicriteria location framework. Although both objectives are neither concave nor convex, low complexity polynomial algorithms to find the efficient solutions and the tradeoffs in...

This study presents an endeavor to determine an optimal solution for the obnoxious facility location problem. Obnoxious materials are those which may cause harm to the health of human beings and pollute the environment. The obnoxious material management is a significant environmental issue. Since the social economical growth encourages to establishment of industrialization. While the waste mate...