Fermat-weber location problem solving by the hyperbolic smoothing approach

2012 ◽  
Author(s):  
Vinicius, L. Xavier ◽  
Felipe, M. G. França ◽  
Adilson, E. Xavier ◽  
Priscila, M. V. Lima
Keyword(s):  
Problem Solving ◽  
Location Problem ◽  
Computational Experiments ◽  
Test Problems ◽  
Median Problem ◽  
Traditional Test ◽  
Hyperbolic Smoothing

The solution of the Fermat-Weber Location Problem, also known as the continuous p-median problem, is considered by using the Hyperbolic Smoothing approach. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments was performed, making use of traditional test problems described in the literature.

scholarly journals A SOLUTION ALGORITHM FOR p-MEDIAN LOCATION PROBLEM ON UNCERTAIN RANDOM NETWORKS

2020 ◽  
Vol 35 (1) ◽  
pp. 055
Author(s):  
Akram Soltanpour ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Optimization Model ◽  
Location Problem ◽  
Random Network ◽  
Solution Algorithm ◽  
Random Networks ◽  
Median Problem ◽  
Chance Theory ◽  
Numerical Example ◽  
Model Based ◽  
Uncertain Random Network

This paper investigatesthe classical $p$-median location problem in a network in which some of the vertex weights and the distances between vertices are uncertain and while others are random. For solving the $p$-median problem in an uncertain random network, an optimization model based on the chance theory is proposed first and then an algorithm is presented to find the $p$-median. Finally, a numerical example is given to illustrate the efficiency of the proposed method

An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

Solving the continuous multiple allocationp-hub median problem by the hyperbolic smoothing approach

Optimization ◽  
2014 ◽  
Vol 64 (12) ◽  
pp. 2631-2647 ◽  
Author(s):  
Adilson Elias Xavier ◽  
Claudio M. Gesteira ◽  
Vinicius Layter Xavier
Keyword(s):  
Median Problem ◽  
Hyperbolic Smoothing

scholarly journals An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ľuboš Buzna ◽  
Michal Koháni ◽  
Jaroslav Janáček
Keyword(s):  
Approximation Algorithm ◽  
Facility Location ◽  
Location Problem ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Exact Algorithm ◽  
General Purpose ◽  
Median Problem ◽  
Discrete Facility Location ◽  
Number Of Customers

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve thep-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

The Robustness of Two Common Heuristics for the p-Median Problem

1979 ◽  
Vol 11 (4) ◽  
pp. 373-380 ◽  
Author(s):  
K E Rosing ◽  
E L Hillsman ◽  
Hester Rosing-Vogelaar
Keyword(s):  
Heuristic Algorithms ◽  
Test Problems ◽  
Optimal Solutions ◽  
Problem Size ◽  
Median Problem ◽  
Robust Tests

Optimal p-median solutions were computed for six test problems on a network of forty-nine demand nodes and compared with solutions from two heuristic algorithms. Comparison of the optimal solutions with those from the Teitz and Bart heuristic indicates that this heuristic is very robust. Tests of the Maranzana heuristic, however, indicate that it is efficient only for small values of p (numbers of facilities) and that its robustness decreases rapidly as problem size increases.

Scheduling Jobs on Dedicated Parallel Machines

2013 ◽  
Vol 433-435 ◽  
pp. 2363-2366 ◽  
Author(s):  
Sang Oh Shim ◽  
Seong Woo Choi
Keyword(s):  
Completion Time ◽  
Parallel Machines ◽  
Computation Time ◽  
Computational Experiments ◽  
Test Problems ◽  
Scheduling Problem ◽  
Suggested Algorithm ◽  
Reasonable Amount ◽  
Scheduling Method

This paper considers scheduling problem on dedicated parallel machines where several types of machines are grouped into one process. The dedicated machine is that a job with a specific recipe should be processed on the dedicated machine even though the job can be produced on any other machine originally. In this process, a setup is required when different jobs are done consecutively. To minimize the completion time of the last job, a scheduling method is developed. Computational experiments are performed on a number of test problems and results show that the suggested algorithm give good solutions in a reasonable amount of computation time.

scholarly journals The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Longshu Wu ◽  
Joonwhoan Lee ◽  
Jianhua Zhang ◽  
Qin Wang
Keyword(s):  
Location Problem ◽  
Hamming Distance ◽  
Linear Time ◽  
Shopping Centers ◽  
Median Problem ◽  
Tree Networks ◽  
Total Cost ◽  
Negative Edge ◽  
Polynomial Time Algorithms ◽  
Np Hardness

Location problems exist in the real world and they mainly deal with finding optimal locations for facilities in a network, such as net servers, hospitals, and shopping centers. The inverse location problem is also often met in practice and has been intensively investigated in the literature. As a typical inverse location problem, the inverse 1-median problem on tree networks with variable real edge lengths is discussed in this paper, which is to modify the edge lengths at minimum total cost such that a given vertex becomes a 1-median of the tree network with respect to the new edge lengths. First, this problem is shown to be solvable in linear time with variable nonnegative edge lengths. For the case when negative edge lengths are allowable, the NP-hardness is proved under Hamming distance, and strongly polynomial time algorithms are presented underl1andl∞norms, respectively.

scholarly journals The Connected P -Median Problem on Cactus Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Chunsong Bai ◽  
Jianjie Zhou ◽  
Zuosong Liang
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Time Algorithm ◽  
Median Problem ◽  
Cactus Graph ◽  
Cactus Graphs

This study deals with the facility location problem of locating a set V p of p facilities on a graph such that the subgraph induced by V p is connected. We consider the connected p -median problem on a cactus graph G whose vertices and edges have nonnegative weights. The aim of a connected p -median problem is to minimize the sum of weighted distances from every vertex of a graph to the nearest vertex in V p . We provide an O n 2 p 2 time algorithm for the connected p -median problem, where n is the number of vertices.

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