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Variable Neighborhood Search
, 1997
"... Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications a ..."
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Cited by 242 (24 self)
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Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications are briefly summarized. They comprise heuristic solution of a variety of optimization problems, ways to accelerate exact algorithms and to analyze heuristic solution processes, as well as computerassisted discovery of conjectures in graph theory.
Variable Neighborhood Search for Extremal Graphs 6. Analyzing Bounds for the Connectivity Index
, 2000
"... Recently, Araujo and De la Pe~na [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which ..."
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Cited by 23 (7 self)
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Recently, Araujo and De la Pe~na [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which are trees and the cyclomatic number of the graphs. The ramification index of a tree is first shown to be equal to the number of pending vertices minus 2. Then, in view of extremal graphs obtained with the system AutoGraphiX, all bounds of Araujo and De la Pe\~na [1] are improved, yielding tight bounds, and in one case corrected. Moreover, chemical trees of given order and number of pending vertices with minimum and with maximum connectivity index are characterized.
An integrated som fuzzy artmap neural system for the evaluation of toxicity
 J. Chem. Inf. Comput. Sci
, 2002
"... Selforganized maps (SOM) have been applied to analyze the similarities of chemical compounds and to select from a given pool of descriptors the smallest and more relevant subset needed to build robust QSAR models based on fuzzy ARTMAP. First, the category maps for each molecular descriptor and for ..."
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Cited by 12 (1 self)
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Selforganized maps (SOM) have been applied to analyze the similarities of chemical compounds and to select from a given pool of descriptors the smallest and more relevant subset needed to build robust QSAR models based on fuzzy ARTMAP. First, the category maps for each molecular descriptor and for the target activity variable were created with SOM and then classified on the basis of topology and nonlinear distribution. The best subset of descriptors was obtained by choosing from each cluster the index with the highest correlation with the target variable and then in order of decreasing correlation. This process was terminated when a dissimilarity measure increased, indicating that the inclusion of more molecular indices would not add supplementary information. The optimal subset of descriptors was used as input to a fuzzy ARTMAP architecture modified to effect predictive capabilities. The performance of the integrated SOMfuzzy ARTMAP approach was evaluated with the prediction of the acute toxicity LC50 of a homogeneous set of 69 benzene derivatives in the fathead minnow and the oral rat toxicity LD50 of a heterogeneous set of 155 organic compounds. The proposed methodology minimized the problem of misclassification of similar compounds and significantly enhanced the predictive capabilities of a properly trained fuzzy ARTMAP network.
Neural Network Based Quantitative Structural Property Relations (QSPRs) for Predicting Boiling Points of Aliphatic Hydrocarbons
 J. Chem. Inf. Comput. Sci
"... Quantitative structural property relations (QSPRs) for boiling points of aliphatic hydrocarbons were derived using a backpropagation neural network and a modified Fuzzy ARTMAP architecture. With the backpropagation model, the selected molecular descriptors were capable of distinguishing between di ..."
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Cited by 9 (4 self)
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Quantitative structural property relations (QSPRs) for boiling points of aliphatic hydrocarbons were derived using a backpropagation neural network and a modified Fuzzy ARTMAP architecture. With the backpropagation model, the selected molecular descriptors were capable of distinguishing between diastereomers. The QSPRs were obtained from four valance molecular connectivity indices (1łv,2łv,3łv,4łv), a secondorder Kappa shape index (2), dipole moment, and molecular weight. The inclusion of dipole moment proved to be particularly useful for distinguishing between cis and trans isomers. A backpropagation 741 architecture predicted boiling points for the test, validation, and overall data sets of alkanes with average absolute errors
A unified approach to extremal cacti for different indices
 MATCH Commun. Math. Comput. Chem
"... Many chemical indices have been invented in theoretical chemistry, such as Wiener index, MerrifieldSimmons index, Hosoya index, spectral radius and Randic ́ index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular gra ..."
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Cited by 5 (0 self)
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Many chemical indices have been invented in theoretical chemistry, such as Wiener index, MerrifieldSimmons index, Hosoya index, spectral radius and Randic ́ index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) the set of cacti of order n and with r cycles. Obviously, G (n, 0) is the set of all trees and G (n, 1) is the set of all unicyclic graphs. In this paper, we present a unified approach to the extremal cactus, which have the same or very similar structures, for Wiener index, MerrifieldSimmons index, Hosoya index and spectral radius. From our results, we can derive some known results. 1.
Partitioning and Lipophilicity in Quantitative StructureActivity Relationships
"... The history of the relationship of biological activity to partition coefficient and related properties is briefly reviewed. The dominance of partition coefficient in quantitation of structureactivity relationships is emphasized, although the importance of other factors is also demonstrated. Various ..."
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The history of the relationship of biological activity to partition coefficient and related properties is briefly reviewed. The dominance of partition coefficient in quantitation of structureactivity relationships is emphasized, although the importance of other factors is also demonstrated. Various mathematical models of in vivo transport and binding are discussed; most of these involve partitioning as the primary mechanism of transport. The models describe observed quantitative structureactivity relationships (QSARs) well on the whole, confirming that partitioning is of key importance in in vivo behavior of a xenobiotic. The partition coefficient is shown to correlate with numerous other parameters representing bulk, such as molecular weight, volume and surface area, parachor and calculated indices such as molecular connectivity; this is especially so for apolar molecules, because for polar molecules lipophilicity factors into both bulk and polar or hydrogen bonding components. The relationship of partition coefficient to chromatographic parameters is discussed, and it is shown that such parameters, which are often readily obtainable experimentally, can successfully supplant partition coefficient in QSARs. The relationship of aqueous solubility with partition coefficient is examined in detail. Correlations are observed, even with solid compounds, and these can be used to predict solubility. The additive/constitutive nature of partition coefficient is discussed extensively, as are the available schemes for the calculation of
Combinatorial QSAR of ambergris fragrance compounds
 J. Chem. Inf. Comput. Sci
"... A combinatorial quantitative structureactivity relationships (CombiQSAR) approach has been developed and applied to a data set of 98 ambergris fragrance compounds with complex stereochemistry. The CombiQSAR approach explores all possible combinations of different independent descriptor collection ..."
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Cited by 4 (0 self)
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A combinatorial quantitative structureactivity relationships (CombiQSAR) approach has been developed and applied to a data set of 98 ambergris fragrance compounds with complex stereochemistry. The CombiQSAR approach explores all possible combinations of different independent descriptor collections and various individual correlation methods to obtain statistically significant models with high internal (for the training set) and external (for the test set) accuracy. Seven different descriptor collections were generated with commercially available MOE, CoMFA, CoMMA, Dragon, VolSurf, and MolconnZ programs; we also included chirality topological descriptors recently developed in our laboratory (Golbraikh, A.; Bonchev, D.; Tropsha, A. J. Chem. Inf. Comput. Sci. 2001, 41, 147158). CoMMA descriptors were used in combination with MOE descriptors. MolconnZ descriptors were used in combination with chirality descriptors. Each descriptor collection was combined individually with four correlation methods, including knearest neighbors (kNN) classification, Support Vector Machines (SVM), decision trees, and binary QSAR, giving rise to 28 different types of QSAR models. Multiple diverse and representative training and test sets were generated by the divisions of the original data set in two. Each model with high values of leaveoneout crossvalidated correct classification rate for the training set was subjected to extensive internal and external validation to avoid overfitting and achieve reliable predictive power. Two validation techniques were employed, i.e., the
The mconnectivity index of graphs
 MATCH Commun. Math. Comput. Chem
"... The mconnectivity index m χα(G) of an organic molecule whose molecular graph is G is the sum of the weights (di1 di2...dim+1)α, where i1 −i2 −...−im+1 runs over all paths of length m in G and di denotes the degree of vertex vi. We find upper bounds for m χα(G) when m ≥ 1 and α ≥ −1 (α � = 0) using ..."
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Cited by 4 (3 self)
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The mconnectivity index m χα(G) of an organic molecule whose molecular graph is G is the sum of the weights (di1 di2...dim+1)α, where i1 −i2 −...−im+1 runs over all paths of length m in G and di denotes the degree of vertex vi. We find upper bounds for m χα(G) when m ≥ 1 and α ≥ −1 (α � = 0) using the eigenvalues of the Laplacian matrix of an associated weighted graph. 1
Trees of extremal connectivity index
 Discrete Appl. Math
"... The connectivity index wα(G) of a graph G is the sum of the weights (d(u)d(v)) α of all edges uv of G, where α is a real number (α � = 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T ..."
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Cited by 3 (1 self)
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The connectivity index wα(G) of a graph G is the sum of the weights (d(u)d(v)) α of all edges uv of G, where α is a real number (α � = 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T). Also, for −1 ≤ α < 0, we give a sharp lower bound and a upper bound for wα(T).