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 Db-Scan Binarization Algorithm Applied to Matrix Covering Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
José García ◽  
Paola Moraga ◽  
Matias Valenzuela ◽  
Broderick Crawford ◽  
Ricardo Soto ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Optimization Problems ◽  
Metaheuristic Algorithms ◽  
Set Covering ◽  
Covering Problem ◽  
Random Operators ◽  
Combinatorial Optimization Problems ◽  
Hybrid Techniques ◽  
Area Of Interest

The integration of machine learning techniques and metaheuristic algorithms is an area of interest due to the great potential for applications. In particular, using these hybrid techniques to solve combinatorial optimization problems (COPs) to improve the quality of the solutions and convergence times is of great interest in operations research. In this article, the db-scan unsupervised learning technique is explored with the goal of using it in the binarization process of continuous swarm intelligence metaheuristic algorithms. The contribution of the db-scan operator to the binarization process is analyzed systematically through the design of random operators. Additionally, the behavior of this algorithm is studied and compared with other binarization methods based on clusters and transfer functions (TFs). To verify the results, the well-known set covering problem is addressed, and a real-world problem is solved. The results show that the integration of the db-scan technique produces consistently better results in terms of computation time and quality of the solutions when compared with TFs and random operators. Furthermore, when it is compared with other clustering techniques, we see that it achieves significantly improved convergence times.

scholarly journals Using machine learning to predict the number of alternative solutions to a minimum cardinality set covering problem

2021 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Brooks Emerick ◽  
Yun Lu ◽  
Francis J. Vasko
Keyword(s):  
Machine Learning ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Regression Trees ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Minimum Cardinality ◽  
Combinatorial Optimization Problems ◽  
Secondary Objective

Although the characterization of alternative optimal solutions for linear programming problems is well known, such characterizations for combinatorial optimization problems are essentially non-existent. This is the first article to qualitatively predict the number of alternative optima for a classic NP-hard combinatorial optimization problem, namely, the minimum cardinality (also called unicost) set covering problem (MCSCP). For the MCSCP, a set must be covered by a minimum number of subsets selected from a specified collection of subsets of the given set. The MCSCP has numerous industrial applications that require that a secondary objective is optimized once the size of a minimum cover has been determined. To optimize the secondary objective, the number of MCSCP solutions is optimized. In this article, for the first time, a machine learning methodology is presented to generate categorical regression trees to predict, qualitatively (extra-small, small, medium, large, or extra-large), the number of solutions to an MCSCP. Within the machine learning toolbox of MATLAB®, 600,000 unique random MCSCPs were generated and used to construct regression trees. The prediction quality of these regression trees was tested on 5000 different MCSCPs. For the 5-output model, the average accuracy of being at most one off from the predicted category was 94.2%. 

scholarly journals Hybrid differential evolution algorithms for the optimal camera placement problem

2018 ◽  
Vol 20 (4) ◽  
pp. 446-467 ◽  
Author(s):  
Mathieu Brévilliers ◽  
Julien Lepagnot ◽  
Lhassane Idoumghar ◽  
Maher Rebai ◽  
Julien Kritter
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Set Covering ◽  
Covering Problem ◽  
Placement Problem ◽  
Camera Placement ◽  
Content Type ◽  
Combinatorial Optimization Problems ◽  
Evolution Algorithms ◽  
Problem Instances

PurposeThis paper aims to investigate to what extent hybrid differential evolution (DE) algorithms can be successful in solving the optimal camera placement problem.Design/methodology/approachThis problem is stated as a unicost set covering problem (USCP) and 18 problem instances are defined according to practical operational needs. Three methods are selected from the literature to solve these instances: a CPLEX solver, greedy algorithm and row weighting local search (RWLS). Then, it is proposed to hybridize these algorithms with two hybrid DE approaches designed for combinatorial optimization problems. The first one is a set-based approach (DEset) from the literature. The second one is a new similarity-based approach (DEsim) that takes advantage of the geometric characteristics of a camera to find better solutions.FindingsThe experimental study highlights that RWLS and DEsim-CPLEX are the best proposed algorithms. Both easily outperform CPLEX, and it turns out that RWLS performs better on one class of problem instances, whereas DEsim-CPLEX performs better on another class, depending on the minimal resolution needed in practice.Originality/valueUp to now, the efficiency of RWLS and the DEset approach has been investigated only for a few problems. Thus, the first contribution is to apply these methods for the first time in the context of camera placement. Moreover, new hybrid DE algorithms are proposed to solve the optimal camera placement problem when stated as a USCP. The second main contribution is the design of the DEsim approach that uses the distance between camera locations to fully benefit from the DE mutation scheme.

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.

scholarly journals Adaptive Black Hole Algorithm for Solving the Set Covering Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
Ricardo Soto ◽  
Broderick Crawford ◽  
Rodrigo Olivares ◽  
Carla Taramasco ◽  
Ignacio Figueroa ◽  
...  
Keyword(s):  
Black Hole ◽  
Optimization Problems ◽  
Main Idea ◽  
Industrial Applications ◽  
Set Covering ◽  
Covering Problem ◽  
Problem Solver ◽  
Set Covering Problem ◽  
A New Technique ◽  
Black Hole Algorithm

Evolutionary algorithms have been used to solve several optimization problems, showing an efficient performance. Nevertheless, when these algorithms are applied they present the difficulty to decide on the appropriate values of their parameters. Typically, parameters are specified before the algorithm is run and include population size, selection rate, and operator probabilities. This process is known as offline control and is even considered as an optimization problem in itself. On the other hand, parameter settings or control online is a variation of the algorithm original version. The main idea is to vary the parameters so that the algorithm of interest can provide the best convergence rate and thus may achieve the best performance. In this paper, we propose an adaptive black hole algorithm able to dynamically adapt its population according to solving performance. For that, we use autonomous search which appeared as a new technique that enables the problem solver to control and adapt its own parameters and heuristics during solving in order to be more efficient without the knowledge of an expert user. In order to test this approach, we resolve the set covering problem which is a classical optimization benchmark with many industrial applications such as line balancing production, crew scheduling, service installation, and databases, among several others. We illustrate encouraging experimental results, where the proposed approach is able to reach various global optimums for a well-known instance set from Beasley’s OR-Library, while improving various modern metaheuristics.

Analyses of Simple Hybrid Algorithms for the Vertex Cover Problem

2009 ◽  
Vol 17 (1) ◽  
pp. 3-19 ◽  
Author(s):  
Tobias Friedrich ◽  
Jun He ◽  
Nils Hebbinghaus ◽  
Frank Neumann ◽  
Carsten Witt
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Hybrid Methods ◽  
Vertex Cover ◽  
Optimization Methods ◽  
Theoretical Understanding ◽  
Combinatorial Optimization Problems ◽  
Vertex Cover Problem ◽  
The Subject ◽  
Cover Problem

Hybrid methods are very popular for solving problems from combinatorial optimization. In contrast, the theoretical understanding of the interplay of different optimization methods is rare. In this paper, we make a first step into the rigorous analysis of such combinations for combinatorial optimization problems. The subject of our analyses is the vertex cover problem for which several approximation algorithms have been proposed. We point out specific instances where solutions can (or cannot) be improved by the search process of a simple evolutionary algorithm in expected polynomial time.

scholarly journals Genetic Algorithms as Computational Methods for Finite-Dimensional Optimization

2021 ◽  
pp. 5-14
Author(s):  
Nataliya Gulayeva ◽  
Volodymyr Shylo ◽  
Mykola Glybovets
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Numerical Methods ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Direct Search ◽  
Mathematical Programming Problem ◽  
Combinatorial Optimization Problems

Introduction. As early as 1744, the great Leonhard Euler noted that nothing at all took place in the universe in which some rule of maximum or minimum did not appear [12]. Great many today’s scientific and engineering problems faced by humankind are of optimization nature. There exist many different methods developed to solve optimization problems, the number of these methods is estimated to be in the hundreds and continues to grow. A number of approaches to classify optimization methods based on various criteria (e.g. the type of optimization strategy or the type of solution obtained) are proposed, narrower classifications of methods solving specific types of optimization problems (e.g. combinatorial optimization problems or nonlinear programming problems) are also in use. Total number of known optimization method classes amounts to several hundreds. At the same time, methods falling into classes far from each other may often have many common properties and can be reduced to each other by rethinking certain characteristics. In view of the above, the pressing task of the modern science is to develop a general approach to classify optimization methods based on the disclosure of the involved search strategy basic principles, and to systematize existing optimization methods. The purpose is to show that genetic algorithms, usually classified as metaheuristic, population-based, simulation, etc., are inherently the stochastic numerical methods of direct search. Results. Alternative statements of optimization problem are given. An overview of existing classifications of optimization problems and basic methods to solve them is provided. The heart of optimization method classification into symbolic (analytical) and numerical ones is described. It is shown that a genetic algorithm scheme can be represented as a scheme of numerical method of direct search. A method to reduce a given optimization problem to a problem solvable by a genetic algorithm is described, and the class of problems that can be solved by genetic algorithms is outlined. Conclusions. Taking into account the existence of a great number of methods solving optimization problems and approaches to classify them it is necessary to work out a unified approach for optimization method classification and systematization. Reducing the class of genetic algorithms to numerical methods of direct search is the first step in this direction. Keywords: mathematical programming problem, unconstrained optimization problem, constrained optimization problem, multimodal optimization problem, numerical methods, genetic algorithms, metaheuristic algorithms.

Combinatorial Optimization Problems in Multimedia Delivery

2018 ◽  
pp. 67-92
Author(s):  
Tibor Szkaliczki
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Multimedia Systems ◽  
Multimedia Data ◽  
Discrete Mathematics ◽  
Resource Assignment ◽  
Multimedia Delivery ◽  
Combinatorial Optimization Problems ◽  
Problems And Solutions

The amount of multimedia data (video, audio, images, animation, etc.) delivered through the Internet is continuously increasing. There is a wide range of application possibilities of optimization methods in the multimedia systems such as adapting multimedia objects, replication of multimedia elements, resource assignment, etc. This chapter introduces selected combinatorial optimization problems arising during the operation of multimedia delivery systems. The efficient solution of the problems considered can enhance significantly the performance of the servers and improve the quality of the provided services. This chapter provides an overview of the algorithms that can be used in multimedia delivery. Both heuristics and adaptation of well-known combinatorial optimization algorithms can be applied to solve the problems concerned. The approaches are related to typical problems and solutions in discrete mathematics such as facility location problem, knapsack problem, monotonic optimization, linear programming, evolutionary algorithms, etc.

scholarly journals Application of the Artificial Bee Colony Algorithm for Solving the Set Covering Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
Rodrigo Cuesta ◽  
Fernando Paredes
Keyword(s):  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Formal Model ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Solution Quality ◽  
Bee Colony ◽  
Unicost Set Covering Problem

The set covering problem is a formal model for many practical optimization problems. In the set covering problem the goal is to choose a subset of the columns of minimal cost that covers every row. Here, we present a novel application of the artificial bee colony algorithm to solve the non-unicost set covering problem. The artificial bee colony algorithm is a recent swarm metaheuristic technique based on the intelligent foraging behavior of honey bees. Experimental results show that our artificial bee colony algorithm is competitive in terms of solution quality with other recent metaheuristic approaches for the set covering problem.

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