scholarly journals New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Himer Avila-George ◽  
Jose Torres-Jimenez ◽  
Vicente Hernández
Keyword(s):  
Simulated Annealing ◽  
Direct Methods ◽  
Combinatorial Structure ◽  
Covering Array ◽  
Covering Arrays ◽  
Construction Problem ◽  
Cooperative Approach ◽  
Benchmark Instances ◽  
Best Execution ◽  
Greedy Methods

A covering array (CA) is a combinatorial structure specified as a matrix ofNrows andkcolumns over an alphabet onvsymbols such that for each set oftcolumns everyt-tuple of symbols is covered at least once. Given the values oft,k, andv, the optimal covering array construction problem (CAC) consists in constructing a CA (N;t,k,v) with the minimum possible value ofN. There are several reported methods to attend the CAC problem, among them are direct methods, recursive methods, greedy methods, and metaheuristics methods. In this paper, There are three parallel approaches for simulated annealing: the independent, semi-independent, and cooperative searches are applied to the CAC problem. The empirical evidence supported by statistical analysis indicates that cooperative approach offers the best execution times and the same bounds as the independent and semi-independent approaches. Extensive experimentation was carried out, using 182 well-known benchmark instances of ternary covering arrays, for assessing its performance with respect to the best-known bounds reported previously. The results show that cooperative approach attains 134 new bounds and equals the solutions for other 29 instances.

New optimal covering arrays using an orderly algorithm

2018 ◽  
Vol 10 (01) ◽  
pp. 1850011 ◽  
Author(s):  
Idelfonso Izquierdo-Marquez ◽  
Jose Torres-Jimenez
Keyword(s):  
Small Subset ◽  
Computational Results ◽  
Covering Array ◽  
Covering Arrays ◽  
Computational Search ◽  
Minimum Number ◽  
Orderly Algorithm

A covering array [Formula: see text] is an [Formula: see text] array such that every [Formula: see text] subarray covers at least once each [Formula: see text]-tuple from [Formula: see text] symbols. For given [Formula: see text], [Formula: see text], and [Formula: see text], the minimum number of rows for which exists a CA is denoted by [Formula: see text] (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: [Formula: see text] for [Formula: see text], [Formula: see text], and [Formula: see text]. In addition, the new result [Formula: see text], and the already known existence of [Formula: see text], imply [Formula: see text].

Research Notes: Binary Test-Suites Using Covering Arrays

2018 ◽  
Vol 28 (09) ◽  
pp. 1321-1337 ◽  
Author(s):  
Jose Torres-Jimenez ◽  
Himer Avila-George ◽  
Ezra Federico Parra-González
Keyword(s):  
Software Testing ◽  
Test Generation ◽  
Software Systems ◽  
Combinatorial Testing ◽  
Covering Array ◽  
Covering Arrays ◽  
Almost All ◽  
Generation Problem ◽  
Test Suites

Software testing is an essential activity to ensure the quality of software systems. Combinatorial testing is a method that facilitates the software testing process; it is based on an empirical evidence where almost all faults in a software component are due to the interaction of very few parameters. The test generation problem for combinatorial testing can be represented as the construction of a matrix that has certain properties; typically this matrix is a covering array. Covering arrays have a small number of tests, in comparison with an exhaustive approach, and provide a level of interaction coverage among the parameters involved. This paper presents a repository that contains binary covering arrays involving many levels of interaction. Also, it discusses the importance of covering array repositories in the construction of better covering arrays. In most of the cases, the size of the covering arrays included in the repository reported here are the best upper bounds known, moreover, the files containing the matrices of these covering arrays are available to be downloaded. The final purpose of our Binary Covering Arrays Repository (BCAR) is to provide software testing practitioners the best-known binary test-suites.

Solution of organic crystal structures from powder diffraction by combining simulated annealing and direct methods

2003 ◽  
Vol 36 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Angela Altomare ◽  
Rocco Caliandro ◽  
Carmelo Giacovazzo ◽  
Anna Grazia Giuseppina Moliterni ◽  
Rosanna Rizzi
Keyword(s):  
Monte Carlo ◽  
Simulated Annealing ◽  
Electron Density ◽  
Powder Diffraction ◽  
Direct Methods ◽  
Molecular Geometry ◽  
Molecular Structures ◽  
Chemical Information ◽  
Density Map ◽  
Electron Density Map

Theab initiocrystal structure solution from powder diffraction data can be attemptedviadirect methods. If heavy atoms are present, they are usually correctly located; then some crystal chemical information can be exploited to complete the partial structure model. Organic structures are more resistant to direct methods; as an alternative, their molecular geometry is used as prior information for Monte Carlo methods. In this paper, a new procedure is described which combines the information contained in the electron density map provided by direct methods with a Monte Carlo method which uses simulated annealing as a minimization algorithm. A figure of merit has been designed based on the agreement between the experimental and calculated profiles, and on the positions of the peaks in the electron density map. The procedure is completely automatic and has been included inEXPO; its performance has been validated and tested for a set of known molecular structures.

scholarly journals Simulated Annealing with Mutation Strategy for the Share-a-Ride Problem with Flexible Compartments

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2320
Author(s):  
Vincent F. Yu ◽  
Putu A. Y. Indrakarna ◽  
Anak Agung Ngurah Perwira Redi ◽  
Shih-Wei Lin
Keyword(s):  
Simulated Annealing ◽  
Upper Bounds ◽  
Computational Studies ◽  
Lower And Upper Bounds ◽  
Fixed Size ◽  
New Variant ◽  
Mutation Strategy ◽  
Benchmark Instances ◽  
Total Profit ◽  
Total Capacity

The Share-a-Ride Problem with Flexible Compartments (SARPFC) is an extension of the Share-a-Ride Problem (SARP) where both passenger and freight transport are serviced by a single taxi network. The aim of SARPFC is to increase profit by introducing flexible compartments into the SARP model. SARPFC allows taxis to adjust their compartment size within the lower and upper bounds while maintaining the same total capacity permitting them to service more parcels while simultaneously serving at most one passenger. The main contribution of this study is that we formulated a new mathematical model for the problem and proposed a new variant of the Simulated Annealing (SA) algorithm called Simulated Annealing with Mutation Strategy (SAMS) to solve SARPFC. The mutation strategy is an intensification approach to improve the solution based on slack time, which is activated in the later stage of the algorithm. The proposed SAMS was tested on SARP benchmark instances, and the result shows that it outperforms existing algorithms. Several computational studies have also been conducted on the SARPFC instances. The analysis of the effects of compartment size and the portion of package requests to the total profit showed that, on average, utilizing flexible compartments as in SARPFC brings in more profit than using a fixed-size compartment as in SARP.

Simulated Annealing for Constructing Mixed Covering Arrays

2012 ◽  
pp. 657-664 ◽  
Author(s):  
Himer Avila-George ◽  
Jose Torres-Jimenez ◽  
Vicente Hernández ◽  
Loreto Gonzalez-Hernandez
Keyword(s):  
Simulated Annealing ◽  
Covering Arrays

Mixed covering arrays on graphs of small treewidth

2021 ◽  
pp. 2150085
Author(s):  
Soumen Maity ◽  
Charles J. Colbourn
Keyword(s):  
Weighted Graph ◽  
Minimum Size ◽  
Index Formula ◽  
Covering Array ◽  
Covering Arrays ◽  
Combinatorial Objects ◽  
The Family ◽  
Positive Integers ◽  
Basic Graph ◽  
Test Suites

Covering arrays are combinatorial objects that have been successfully applied in design of test suites for testing systems such as software, hardware, and networks where failures can be caused by the interaction between their parameters. Let [Formula: see text] and [Formula: see text] be positive integers with [Formula: see text]. Two vectors [Formula: see text] and [Formula: see text] are qualitatively independent if for any ordered pair [Formula: see text], there exists an index [Formula: see text] such that [Formula: see text]. Let [Formula: see text] be a graph with [Formula: see text] vertices [Formula: see text] with respective vertex weights [Formula: see text]. A mixed covering array on[Formula: see text] , denoted by [Formula: see text], is a [Formula: see text] array such that row [Formula: see text] corresponds to vertex [Formula: see text], entries in row [Formula: see text] are from [Formula: see text]; and if [Formula: see text] is an edge in [Formula: see text], then the rows [Formula: see text] are qualitatively independent. The parameter [Formula: see text] is the size of the array. Given a weighted graph [Formula: see text], a mixed covering array on [Formula: see text] with minimum size is optimal. In this paper, we introduce some basic graph operations to provide constructions for optimal mixed covering arrays on the family of graphs with treewidth at most three.

Direct methods and simulated annealing: a hybrid approach for powder diffraction data

2008 ◽  
Vol 41 (1) ◽  
pp. 56-61 ◽  
Author(s):  
Angela Altomare ◽  
Rocco Caliandro ◽  
Corrado Cuocci ◽  
Carmelo Giacovazzo ◽  
Anna Grazia Giuseppina Moliterni ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Diffraction Data ◽  
Degrees Of Freedom ◽  
Molecular Model ◽  
Hybrid Approach ◽  
Direct Methods ◽  
Heavy Atoms ◽  
The Monte Carlo Method ◽  
Structure Solution ◽  
Electron Density Map

The solution of crystal structures from powder data using direct methods can be very difficult if the quality of the diffraction pattern is low and if no heavy atoms are present in the molecule. On the contrary, the use of direct-space methods does not require good quality diffraction data, but if a molecular model is available, the structure solution is limited principally by the number of degrees of freedom used to describe the model. The combination of the information contained in the electron density map (direct methods) with the Monte Carlo method, which uses simulated annealing as a global minimization algorithm (direct-space techniques), can be a useful tool for crystal structure solution, especially for organic structures. A modified and improved version of this approach [Altomareet al.(2003),J. Appl. Cryst.36, 230–238] has been implemented in theEXPO2004program and is described here.

Temperature phase changes in solid bicyclo[3.3.1]nonane-2,6-dione and bicyclo[3.3.1]nonane-3,7-dione from powder X-ray diffraction data

2007 ◽  
Vol 40 (4) ◽  
pp. 702-709 ◽  
Author(s):  
Michela Brunelli ◽  
Marcus A. Neumann ◽  
Andrew N. Fitch ◽  
Asiloé J. Mora
Keyword(s):  
Simulated Annealing ◽  
Crystal Structures ◽  
Phase Ii ◽  
Diffraction Data ◽  
Direct Methods ◽  
Temperature Phase ◽  
Molecular Orbital Calculations ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray

The crystal structures of bicyclo[3.3.1]nonane-2,6-dione and bicyclo[3.3.1]nonane-3,7-dione have been solved by direct methods and by direct-space simulated annealing, respectively, from powder synchrotron X-ray diffraction data. Both compounds have a transition to a face-centred-cubic orientationally disordered phase (phase I) near 363 K, as shown by differential scanning calorimetry and powder diffraction measurements. Phase II of bicyclo[3.3.1]nonane-2,6-dione, which occurs below 363 K, is monoclinic, space groupC2/c, witha= 7.38042 (4),b= 10.38220 (5),c= 9.75092 (5) Å and β = 95.359 (1)° at 80 K. Phase II of bicyclo[3.3.1]nonane-3,7-dione, which occurs below 365 K, is tetragonal, space groupP41212, witha= 6.8558 (1) andc= 16.9375 (1) Å at 100 K. This phase coexists in a biphasic mixture with a minor monoclinic phase II′ [a= 11.450 (6),b = 20.583 (1),c= 6.3779 (3) Å, β = 94.7555 (5)°, at 100 K] detected in the sample, which impeded indexing with standard programs. The crystal structures of phases II were solved by direct methods and by direct-space simulated annealing, employing powder synchrotron X-ray diffraction data of increased instrumental intensity and resolution from the ID31 beamline at the ESRF, and novel indexing algorithms.Ab initiomolecular orbital calculations on the two systems are reported. In the solid state, the molecules pack in chair–chair conformation; molecular structures and packing are discussed.

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