MapReduce machine covering problem on a small number of machines

2019 ◽  
Vol 38 (4) ◽  
pp. 1066-1076
Author(s):  
Yiwei Jiang ◽  
Ping Zhou ◽  
Wei Zhou
Keyword(s):  
Covering Problem ◽  
Machine Covering

Improved approaches to the exact solution of the machine covering problem

2016 ◽  
Vol 20 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Rico Walter ◽  
Martin Wirth ◽  
Alexander Lawrinenko
Keyword(s):  
Exact Solution ◽  
Covering Problem ◽  
Machine Covering

GRAPH ORIENTATION TO MAXIMIZE THE MINIMUM WEIGHTED OUTDEGREE

2011 ◽  
Vol 22 (03) ◽  
pp. 583-601 ◽  
Author(s):  
YUICHI ASAHIRO ◽  
JESPER JANSSON ◽  
EIJI MIYANO ◽  
HIROTAKA ONO
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Job Scheduling ◽  
Weighted Graph ◽  
Exact Algorithm ◽  
Covering Problem ◽  
Graph Orientation ◽  
Cactus Graph ◽  
New Variant ◽  
Machine Covering

We study a new variant of the graph orientation problem called MAXMINO where the input is an undirected, edge-weighted graph and the objective is to assign a direction to each edge so that the minimum weighted outdegree (taken over all vertices in the resulting directed graph) is maximized. All edge weights are assumed to be positive integers. This problem is closely related to the job scheduling on parallel machines, called the machine covering problem, where its goal is to assign jobs to parallel machines such that each machine is covered as much as possible. First, we prove that MAXMINO is strongly NP-hard and cannot be approximated within a ratio of 2 – ε for any constant ε > 0 in polynomial time unless P = NP , even if all edge weights belong to {1, 2}, every vertex has degree at most three, and the input graph is bipartite or planar. Next, we show how to solve MAXMINO exactly in polynomial time for the special case in which all edge weights are equal to 1. This technique gives us a simple polynomial-time [Formula: see text]-approximation algorithm for MAXMINO where wmax and wmin denote the maximum and minimum weights among all the input edges. Furthermore, we also observe that this approach yields an exact algorithm for the general case of MAXMINO whose running time is polynomial whenever the number of edges having weight larger than wmin is at most logarithmic in the number of vertices. Finally, we show that MAXMINO is solvable in polynomial time if the input is a cactus graph.

A new approach using a Binary Firefly Algorithm for the Set Covering Problem

2014 ◽  
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
Miguel Olivares-Suárez ◽  
Fernando Paredes
Keyword(s):  
Firefly Algorithm ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
New Approach

scholarly journals Q-Learnheuristics: Towards Data-Driven Balanced Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1839
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
José Lemus-Romani ◽  
Marcelo Becerra-Rozas ◽  
José M. Lanza-Gutiérrez ◽  
...  
Keyword(s):  
Combinatorial Problems ◽  
Set Covering ◽  
Covering Problem ◽  
Integration Framework ◽  
Q Learning ◽  
Whale Optimization ◽  
Sine Cosine Algorithm ◽  
Exploration Exploitation ◽  
Selection Of

One of the central issues that must be resolved for a metaheuristic optimization process to work well is the dilemma of the balance between exploration and exploitation. The metaheuristics (MH) that achieved this balance can be called balanced MH, where a Q-Learning (QL) integration framework was proposed for the selection of metaheuristic operators conducive to this balance, particularly the selection of binarization schemes when a continuous metaheuristic solves binary combinatorial problems. In this work the use of this framework is extended to other recent metaheuristics, demonstrating that the integration of QL in the selection of operators improves the exploration-exploitation balance. Specifically, the Whale Optimization Algorithm and the Sine-Cosine Algorithm are tested by solving the Set Covering Problem, showing statistical improvements in this balance and in the quality of the solutions.

scholarly journals An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 225
Author(s):  
José García ◽  
Gino Astorga ◽  
Víctor Yepes
Keyword(s):  
Transfer Functions ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Set Covering ◽  
Covering Problem ◽  
Perturbation Operator ◽  
K Nearest Neighbors ◽  
Combinatorial Optimization Problems ◽  
Box Plots ◽  
Metaheuristic Techniques

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

scholarly journals A fast $$(2 + \frac{2}{7})$$-approximation algorithm for capacitated cycle covering

2021 ◽  
Author(s):  
Vera Traub ◽  
Thorben Tröbst
Keyword(s):  
Vehicle Routing Problem ◽  
Covering Problem ◽  
Post Processing ◽  
Routing Problem ◽  
Cycle Cover ◽  
Disjoint Cycles ◽  
Processing Step ◽  
Number Of Cycles ◽  
Vertex Disjoint ◽  
Capacitated Vehicle

AbstractWe consider the capacitated cycle covering problem: given an undirected, complete graph G with metric edge lengths and demands on the vertices, we want to cover the vertices with vertex-disjoint cycles, each serving a demand of at most one. The objective is to minimize a linear combination of the total length and the number of cycles. This problem is closely related to the capacitated vehicle routing problem (CVRP) and other cycle cover problems such as min-max cycle cover and bounded cycle cover. We show that a greedy algorithm followed by a post-processing step yields a $$(2 + \frac{2}{7})$$ ( 2 + 2 7 ) -approximation for this problem by comparing the solution to a polymatroid relaxation. We also show that the analysis of our algorithm is tight and provide a $$2 + \epsilon $$ 2 + ϵ lower bound for the relaxation.

scholarly journals Symmetry Exploitation for Online Machine Covering with Bounded Migration

2020 ◽  
Vol 16 (4) ◽  
pp. 1-22
Author(s):  
Waldo Gálvez ◽  
José A. Soto ◽  
José Verschae
Keyword(s):  
Machine Covering

scholarly journals A Self-Adaptive Cuckoo Search Algorithm Using a Machine Learning Technique

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1840
Author(s):  
Nicolás Caselli ◽  
Ricardo Soto ◽  
Broderick Crawford ◽  
Sergio Valdivia ◽  
Rodrigo Olivares
Keyword(s):  
Machine Learning ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Set Covering ◽  
Covering Problem ◽  
Parameter Configuration ◽  
Self Tuning ◽  
Problem Solvers

Metaheuristics are intelligent problem-solvers that have been very efficient in solving huge optimization problems for more than two decades. However, the main drawback of these solvers is the need for problem-dependent and complex parameter setting in order to reach good results. This paper presents a new cuckoo search algorithm able to self-adapt its configuration, particularly its population and the abandon probability. The self-tuning process is governed by using machine learning, where cluster analysis is employed to autonomously and properly compute the number of agents needed at each step of the solving process. The goal is to efficiently explore the space of possible solutions while alleviating human effort in parameter configuration. We illustrate interesting experimental results on the well-known set covering problem, where the proposed approach is able to compete against various state-of-the-art algorithms, achieving better results in one single run versus 20 different configurations. In addition, the result obtained is compared with similar hybrid bio-inspired algorithms illustrating interesting results for this proposal.

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