Jafar Fathali
Department of Mathematics, Shahrood University of Technology, University Blvd., Shahrood, Iran
[ 1 ] - Unweighted p-center problem on extended stars
An extended star is a tree which has only one vertex with degree larger than two. The -center problem in a graph asks to find a subset of the vertices of of cardinality such that the maximum weighted distances from to all vertices is minimized. In this paper we consider the -center problem on the unweighted extended stars, and present some properties to find solution.
[ 2 ] - A hybrid algorithm for the path center problem
Let a graph G = (V;E) be given. In the path center problem we want to find a path P in G such that the maximum weighted distance of P to every vertex in V is minimized. In this paper a genetic algorithm and ahybrid of genetic and ant colony algorithms are presented for the path center problem. Some test problems are examined to compare the algorithms. The results show that for almost all exampl...
[ 3 ] - An efficient algorithm for finding the semi-obnoxious $(k,l)$-core of a tree
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...
[ 4 ] - The p-median and p-center Problems on Bipartite Graphs
Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...
[ 5 ] - مسائل معکوس مکان‌یابی تسهیلات 2- میانه پشتیبان با تغییر طول یال‌ها و وزن رئوس روی درخت و تغییر مختصات نقاط در صفحه
در این مقاله برای نخستین بار معکوسِ مسئلۀ بهینهسازی 2- میانۀ پشتیبان[i] بررسی شده است. در این مسئله تعدادی نقطه، مشتری در نظر گرفته می‌شوند و هدف این است که با تغییر پارامترهای مسئله، دو نقطۀ از پیش تعیین شده به‌سمت 2- میانه پشتیبان شدن برود. ابتدا مسائل معکوس (نوع محدودیت بودجهای و نوع حداقل هزینه) 2- میانه پشتیبان درحالت گسسته برای گرافهای عمومی مدلسازی ریاضی می‌شود. سپس درحالتی‌که گراف...
[ 6 ] - مسئله معکوسِ نوع محدودیت بودجه ایِ 2- میانه پشتیبان با تغییر در مختصات نقاط
In this paper we consider the reverse backup 2-median problem with variable coordinate of vertices in Rk. Let n points be given, then in reverse backup 2-median problem we want to change the coordinates of these points with a limited budget such that the two given points be the backup 2-median. We present a mathematical model for this problem and then solve an spatial case of this problem by ...
[ 7 ] - یک الگوریتم خطی برای مساله ی پیداکردن هسته ی درخت های بازه ای وزندار
In this paper we consider the problem of finding a core of weighted interval trees. A core of an interval graph is a path contains some intervals of graph so that the sum of distances from all intervals to this path is minimized. We show that intervals on core of a tree should be maximal, then a linear time algorithm is presented to find the core of interval trees
[ 8 ] - Single Facility Goal Location Problems with Symmetric and Asymmetric Penalty Functions
Location theory is an interstice field of optimization and operations research. In the classic location models, the goal is finding the location of one or more facilities such that some criteria such as transportation cost, the sum of distances passed by clients, total service time, and cost of servicing are minimized. The goal Weber location problem is a special case of location mode...
[ 9 ] - Solving single facility goal Weber location problem using stochastic optimization methods
Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities in a way such that some criteria such as transportation costs, customer traveling distance, total service time, and cost of servicing are optimized. In this paper, we investigate the goal Weber location problem in which the...
[ 10 ] - Inverse and Reverse 2-facility Location Problems with Equality Measures on a Network
In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...