scholarly journals A New Formulation of the Set Covering Problem for Metaheuristic Approaches

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Nehme Bilal ◽  
Philippe Galinier ◽  
Francois Guibault
Keyword(s):  
Optimization Problem ◽  
Set Covering ◽  
Covering Problem ◽  
Greedy Heuristic ◽  
Test Problems ◽  
Set Covering Problem ◽  
Computational Results ◽  
Unconstrained Optimization Problem ◽  
New Formulation ◽  
Neighbourhood Structure

Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times.

scholarly journals Exploring Further Advantages in an Alternative Formulation for the Set Covering Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Jose M. Lanza-Gutierrez ◽  
N. C. Caballe ◽  
Broderick Crawford ◽  
Ricardo Soto ◽  
Juan A. Gomez-Pulido ◽  
...  
Keyword(s):  
Optimization Problem ◽  
State Of The Art ◽  
Set Covering ◽  
Covering Problem ◽  
Limited Attention ◽  
Alternative Formulation ◽  
Search Process ◽  
Set Covering Problem ◽  
Np Complete ◽  
Complete Optimization

The set covering problem (SCP) is an NP-complete optimization problem, fitting with many problems in engineering. The traditional SCP formulation does not directly address both solution unsatisfiability and set redundancy aspects. As a result, the solving methods have to control these aspects to avoid getting unfeasible and nonoptimized in cost solutions. In the last years, an alternative SCP formulation was proposed, directly covering both aspects. This alternative formulation received limited attention because managing both aspects is considered straightforward at this time. This paper questions whether there is some advantage in the alternative formulation, beyond addressing the two issues. Thus, two studies based on a metaheuristic approach are proposed to identify if there is any concept in the alternative formulation, which could be considered for enhancing a solving method considering the traditional SCP formulation. As a result, the authors conclude that there are concepts from the alternative formulation, which could be applied for guiding the search process and for designing heuristic feasibilit\y operators. Thus, such concepts could be recommended for designing state-of-the-art algorithms addressing the traditional SCP formulation.

A self-adaptive biogeography-based algorithm to solve the set covering problem

2019 ◽  
Vol 53 (3) ◽  
pp. 1033-1059
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
Rodrigo Olivares ◽  
Luis Riquelme ◽  
Gino Astorga ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Industrial Applications ◽  
Original Version ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Control Parameters ◽  
Production Crew ◽  
Classical Optimization ◽  
Self Adaptive

Using the approximate algorithms, we are faced with the problem of determining the appropriate values of their input parameters, which is always a complex task and is considered an optimization problem. In this context, incorporating online control parameters is a very interesting issue. The aim is to vary the parameters during the run so that the studied algorithm can provide the best convergence rate and, thus, achieve the best performance. In this paper, we compare the performance of a self-adaptive approach for the biogeography-based optimization algorithm using the mutation rate parameter with respect to its original version and other heuristics. This work proposes altering some parameters of the metaheuristic according to its exhibited efficiency. To test this approach, we solve the set covering problem, which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, databases, among several others. We illustrate encouraging experimental results, where the proposed approach is capable of reaching various global optimums for a well-known instance set taken from the Beasleys OR-Library, and sometimes, it improves the results obtained by the original version of the algorithm.

A modified greedy heuristic for the Set Covering problem with improved worst case bound

1993 ◽  
Vol 48 (6) ◽  
pp. 305-310 ◽  
Author(s):  
Olivier Goldschmidt ◽  
Dorit S. Hochbaum ◽  
Gang Yu
Keyword(s):  
Set Covering ◽  
Covering Problem ◽  
Greedy Heuristic ◽  
Set Covering Problem ◽  
Worst Case

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 Multi-objective database queries in combined knapsack and set covering problem domains

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Sean A. Mochocki ◽  
Gary B. Lamont ◽  
Robert C. Leishman ◽  
Kyle J. Kauffman
Keyword(s):  
Relational Database ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Database Queries ◽  
Multi Objective ◽  
Data Representations ◽  
Np Hard Problem ◽  
Institute Of Technology ◽  
The One

AbstractDatabase queries are one of the most important functions of a relational database. Users are interested in viewing a variety of data representations, and this may vary based on database purpose and the nature of the stored data. The Air Force Institute of Technology has approximately 100 data logs which will be converted to the standardized Scorpion Data Model format. A relational database is designed to house this data and its associated sensor and non-sensor metadata. Deterministic polynomial-time queries were used to test the performance of this schema against two other schemas, with databases of 100 and 1000 logs of repeated data and randomized metadata. Of these approaches, the one that had the best performance was chosen as AFIT’s database solution, and now more complex and useful queries need to be developed to enable filter research. To this end, consider the combined Multi-Objective Knapsack/Set Covering Database Query. Algorithms which address The Set Covering Problem or Knapsack Problem could be used individually to achieve useful results, but together they could offer additional power to a potential user. This paper explores the NP-Hard problem domain of the Multi-Objective KP/SCP, proposes Genetic and Hill Climber algorithms, implements these algorithms using Java, populates their data structures using SQL queries from two test databases, and finally compares how these algorithms perform.

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