The capacitated centred clustering problem

The capacitated centred clustering problem (CCCP) consists of defining a set of clusters with limited capacity and maximum proper similarity per cluster. Each cluster is composed of individuals from whom we can compute a centre value and hence, determine a similarity measure. The clusters must cover the demands of their individuals. This problem can be applied to the design of garbage collection zones, defining salesmen areas, etc. In this work, we present two variations (p-CCCP and Generic CCCP) of this problem and their mathematical programming formulations. We first focus our attention on the Generic CCCP, and then we create a new procedure for p  -CCCP. These problems being NP-HARD, we propose a two-phase polynomial heuristic algorithm. The first phase is a constructive phase for which we will propose two variants: the first technique uses known cluster procedures oriented by a log-polynomial geometric tree search, the other one uses unconstrained to constrained clustering. The second phase is a refinement of the variable neighbourhood search (VNS). We also show the results we have obtained for tests from the CCP literature, the design of garbage collection zones, and salesmen areas distribution using the approach implemented for the SISROT^®${\mathrm{SISROT}}^{\circledR }$ system.     

Optimal solutions for the balanced minimum evolution problem

Phylogenies are trees representing the evolutionary relationships of a set of species (called taxa). Phylogenies find application in several scientific areas ranging from medical research to drug discovery, epidemiology, systematics and population dynamics. In these applications the available information is usually restricted to the leaves of a phylogeny and is represented by molecular data extracted from the species analyzed. On the contrary, the information about the phylogeny itself is generally missing and must be determined by solving an optimization problem, called the phylogeny estimation problem (PEP), whose versions depend on the criterion used to select a phylogeny among plausible alternatives.     

An algorithm for computing the restriction scaffold assignment problem in computational biology

Let S and T be two finite sets of points on the real line with |S|+|T|=n and |S|>|T|. The restriction scaffold assignment problem in computational biology assigns each point of S to a point of T such that the sum of all the assignment costs is minimized, with the constraint that every element of T must be assigned at least one element of S. The cost of assigning an element si of S to an element tj of T is |si−tj|, i.e., the distance between si and tj. In 2003 Ben-Dor, Karp, Schwikowski and Shamir [J. Comput. Biol. 10 (2) (2003) 385] published an O(nlogn) time algorithm for this problem. Here we provide a counterexample to their algorithm and present a new algorithm that runs in O(n²) time, improving the best previous complexity of O(n³).     

Partition-distance: A problem and class of perfect graphs arising in clustering

Partitioning of a set of elements into disjoint clusters is a fundamental problem that arises in many applications. Different methods produce different partitions, so it is useful to have a measure of the similarity, or distance, between two or more partitions. In this paper we examine one distance measure used in a clustering application in computational genetics. We show how to efficiently compute the distance, and how this defines a new class of perfect graphs.     

An adaptive tabu search approach for buffer allocation problem in unreliable non-homogenous production lines

The buffer allocation problem, i.e. how much buffer storage to allow and where to place it within the line, is an important research issue in designing production lines. In this study, a novel adaptive tabu search approach is proposed for solving buffer allocation problem in unreliable and non-homogeneous production lines. The objective is to maximize the throughput of the line, which is constrained by the capacity of each buffer space and also the total buffer capacity to allocate to these spaces. Besides proposing a new strategy to tune the parameters of tabu search adaptively during the search, an experimental study is carried out to select an intelligent initial solution scheme among three alternatives so as to decrease the search effort to obtain the best solutions. The performance of the proposed approach is evaluated by computational tests and very promising results are obtained.     

eXploratory K-Means: A new simple and efficient algorithm for gene clustering

In this paper, a novel gene expression clustering method known as eXploratory K-Means (XK-Means) is proposed. The method is based on the integration of the K-Means framework, and an exploratory mechanism to prevent premature convergence of the clustering process. Experimental results reveal that the performance of XK-Means in grouping gene expressions, measured in terms of speed, error and stability, is superior to existing methods that are based on evolutionary algorithm. In addition, the complexity of the proposed method is lower and the method can be easily implemented in practice.     

Sensitivity analysis of the knapsack sharing problem: Perturbation of the weight of an item

In this paper, we study the sensitivity analysis of the optimum of the knapsack sharing problem (KSP) to the perturbation of the weight of an arbitrary item. We determine the interval limits of the weight of each perturbed item using a heuristic approach which reduces the original problem to a series of single knapsack problems. A perturbed item belongs either to an optimal class or to a non-optimal class. We evaluate the performance of the proposed heuristic on a set of problem instances of the literature. Encouraging results are obtained.     

Newtonian clustering: An approach based on molecular dynamics and global optimization

Given a data set, a dynamical procedure is applied to the data points in order to shrink and separate, possibly overlapping clusters. Namely, Newton's equations of motion are employed to concentrate the data points around their cluster centers, using an attractive potential, constructed specially for this purpose. During this process, important information is gathered concerning the spread of each cluster. In succession this information is used to create an objective function that maps each cluster to a local maximum. Global optimization is then used to retrieve the positions of the maxima that correspond to the locations of the cluster centers. Further refinement is achieved by applying the EM-algorithm to a Gaussian mixture model whose construction and initialization is based on the acquired information. To assess the effectiveness of our method, we have conducted experiments on a plethora of benchmark data sets. In addition we have compared its performance against four clustering techniques that are well established in the literature.     

SID-GA: An evolutionary approach for improving observability and redundancy analysis in structural instrumentation design

In this paper the core of a genetic algorithm designed to define a sensor network for instrumentation design (ID) is presented. The tool has been incorporated into a decision support system (DSS) that assists the engineer during the ID process. The algorithm satisfactorily deals with non-linear mathematical models, and considers four design objectives, namely observability, cost, reliability and redundancy, exhibiting properties that were either never addressed by existing techniques or partially dealt with in the literature. Its performance was tested by carrying out the ID of an ammonia synthesis industrial plant. Results were statistically analysed. A face validity study on the fitness function’s soundness was also assessed by a chemical engineer with insight and expertise in this problem. The technique performed satisfactorily from the point of view of the expert in ID, and therefore it constitutes a significant upgrading for the DSS.     

Using instance-level constraints in agglomerative hierarchical clustering: theoretical and empirical results

Clustering with constraints is a powerful method that allows users to specify background knowledge and the expected cluster properties. Significant work has explored the incorporation of instance-level constraints into non-hierarchical clustering but not into hierarchical clustering algorithms. In this paper we present a formal complexity analysis of the problem and show that constraints can be used to not only improve the quality of the resultant dendrogram but also the efficiency of the algorithms. This is particularly important since many agglomerative style algorithms have running times that are quadratic (or faster growing) functions of the number of instances to be clustered. We present several bounds on the improvement in the running times of algorithms obtainable using constraints. A preliminary version of this paper appeared as Davidson and Ravi (2005b).     

New and efficient DCA based algorithms for minimum sum-of-squares clustering

The purpose of this paper is to develop new efficient approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) to perform clustering via minimum sum-of-squares Euclidean distance. We consider the two most widely used models for the so-called Minimum Sum-of-Squares Clustering (MSSC in short) that are a bilevel programming problem and a mixed integer program. Firstly, the mixed integer formulation of MSSC is carefully studied and is reformulated as a continuous optimization problem via a new result on exact penalty technique in DC programming. DCA is then investigated to the resulting problem. Secondly, we introduce a Gaussian kernel version of the bilevel programming formulation of MSSC, named GKMSSC. The GKMSSC problem is formulated as a DC program for which a simple and efficient DCA scheme is developed. A regularization technique is investigated for exploiting the nice effect of DC decomposition and a simple procedure for finding good starting points of DCA is developed. The proposed DCA schemes are original and very inexpensive because they amount to computing, at each iteration, the projection of points onto a simplex and/or onto a ball, and/or onto a box, which are all determined in the explicit form. Numerical results on real word datasets show the efficiency, the scalability of DCA and its great superiority with respect to k-means and kernel k-means, standard methods for clustering.     

Two approaches for solving the buffer allocation problem in unreliable production lines

This paper presents an integrated approach to solve the buffer allocation problem in unreliable production lines so as to maximize the throughput rate of the line with minimum total buffer size. The proposed integrated approach has two control loops; the inner loop and the outer loop. While the inner loop control includes an adaptive tabu search algorithm proposed by Demir et al. [8], binary search and tabu search are proposed for the outer loop. These nested loops aim at minimizing the total buffer size to achieve the desired throughput level. To improve the efficiency of the proposed tabu search, alternative neighborhood generation mechanisms are developed. The performances of the proposed algorithms are evaluated by extensive computational experimentation, and the results are reported.     

Particle Swarm Clustering in clustering ensembles: Exploiting pruning and alignment free consensus

A clustering ensemble combines in a consensus function the partitions generated by a set of independent base clusterers. In this study both the employment of particle swarm clustering (PSC) and ensemble pruning (i.e., selective reduction of base partitions) using evolutionary techniques in the design of the consensus function is investigated. In the proposed ensemble, PSC plays two roles. First, it is used as a base clusterer. Second, it is employed in the consensus function; arguably the most challenging element of the ensemble. The proposed consensus function exploits a representation for the base partitions that makes cluster alignment unnecessary, allows for the combination of partitions with different number of clusters, and supports both disjoint and overlapping (fuzzy, probabilistic, and possibilistic) partitions. Results on both synthetic and real-world data sets show that the proposed ensemble can produce statistically significant better partitions, in terms of the validity indices used, than the best base partition available in the ensemble. In general, a small number of selected base partitions (below 20% of the total) yields the best results. Moreover, results produced by the proposed ensemble compare favorably to those of state-of-the-art clustering algorithms, and specially to swarm based clustering ensemble algorithms.     

Inverse resistivity problem: Geoelectric uncertainty principle and numerical reconstruction method

Mathematical model of vertical electrical sounding by using resistivity method is studied. The model leads to an inverse problem of determination of the unknown leading coefficient (conductivity) of the elliptic equation in R²$R^2$ in a slab. The direct problem is obtained in the form of mixed BVP in axisymmetric cylindrical coordinates. The additional (available measured) data is given on the upper boundary of the slab, in the form of tangential derivative. Due to ill-conditionedness of the considered inverse problem the logarithmic transformation is applied to the unknown coefficient and the inverse problem is studied as a minimization problem for the cost functional, with respect to the reflection coefficient. The Conjugate Gradient method (CGM) is applied for the numerical solution of this problem. Computational experiments were performed with noise free and random noisy data.     

Bee colony optimization for the p-center problem

Bee colony optimization (BCO) is a relatively new meta-heuristic designed to deal with hard combinatorial optimization problems. It is biologically inspired method that explores collective intelligence applied by the honey bees during nectar collecting process. In this paper we apply BCO to the p-center problem in the case of symmetric distance matrix. On the contrary to the constructive variant of the BCO algorithm used in recent literature, we propose variant of BCO based on the improvement concept (BCOi). The BCOi has not been significantly used in the relevant BCO literature so far. In this paper it is proved that BCOi can be a very useful concept for solving difficult combinatorial problems. The numerical experiments performed on well-known benchmark problems show that the BCOi is competitive with other methods and it can generate high-quality solutions within negligible CPU times.     

A hill-jump algorithm of Hopfield neural network for shortest path problem in communication network

In this paper, we present a hill-jump algorithm of the Hopfield neural network for the shortest path problem in communication networks, where the goal is to find the shortest path from a starting node to an ending node. The method is intended to provide a near-optimum parallel algorithm for solving the shortest path problem. To do this, first the method uses the Hopfield neural network to get a path. Because the neural network always falls into a local minimum, the found path is usually not a shortest path. To search the shortest path, the method then helps the neural network jump from local minima of energy function by using another neural network built from a part of energy function of the problem. The method is tested through simulating some randomly generated communication networks, with the simulation results showing that the solution found by the proposed method is superior to that of the best existing neural network based algorithm.     

A combined algorithm for weighting the variables and clustering in the clustering problem

One problem in clustering (classification) analysis relates to whether or not the original variables should be transformed in some way before they are used by the clustering algorithm. More often than not, the original variables do require some transformation. The purpose of the transformation may be a desire to have more compact clusters in the space of the transformed variables, to take into account the different nature and/or units of the variables involved, to allow for the different or equal ‘importance’ of different variables, to minimize the number of variables used, etc. Among the linear transformations of variables we distinguish two groups - those which change only the scales of the variables (they are often called weighting procedures), and those which also rotate the space of variables (a good example would be the method of principal components⁽¹⁾). This paper addresses the former group of transformations.One strong reason for using the weighted variables (as opposed to their linear combinations) is that when using them one can interpret the results of the classification in terms of the original (physical) variables. Unfortunately, weighting the variables can result in ‘spoiling’ the compactness of the clusters in the space of the weighted variables if the weighting procedure being used ‘does not care’ about the results of clustering (in other words if the weighting is done prior to and independently of the clustering).A method of weighting the variables which is a part of the classification procedure and thus guarantees an improvement of the cluster clarity is suggested in this paper. The weights of variables and the clusters of objects produced by the algorithm correspond to a local minimum of some classification criterion. Because of this, the resultant weights can be interpreted as a measure of ‘importance’ of the variables for the classification purpose. These weights are compared with such popular weighting procedures as equal variance⁽⁶⁾ and Mahalanobis distance⁽⁷⁾ methods. Two examples of the performance of the algorithm are presented.     

A novel approach for clustering sentiments in Chinese blogs based on graph similarity

Blog clustering is an important approach for online public opinion analysis. The traditional clustering methods, usually group blogs by keywords, stories and timeline, which usually ignore opinions and emotions expressed in the blog articles. In this paper, an integrated graph-based model for clustering Chinese blogs by embedded sentiments is proposed. A novel graph-based representation and the corresponding clustering algorithm are applied on the Chinese blog search results. The proposed model SoB-graph considers not only sentiment words but also structural information in blogs. Experimental results show that comparing with the traditional graph-based document representation model and vector space document representation model, the proposed SoB-graph model has achieved better performance in clustering sentiments in Chinese blog documents.     

A network flow model for clustering segments and minimizing total maintenance and rehabilitation cost

Because of shrinking budgets, transportation agencies are facing severe challenges in the preservation of deteriorating pavements. There is an urgent need to develop a methodology that minimizes maintenance and rehabilitation (M&R) cost. To minimize total network M&R cost of clustering pavement segments, we propose an integer programming model similar to an uncapacitated facility location problem (UFLP) that clusters pavement segments contiguously. Based on the properties of contiguous clustered pavement segments, we have transformed the clustering problem into an equivalent network flow problem in which each possible clustering corresponds to a path in the proposed acyclic network model. Our proposed shortest-path algorithm gives an optimal clustering of segments that can be calculated in a time polynomial to the number of segments. Computational experiments indicate our proposed network model and algorithm can efficiently deal with real-world spatial clustering problems.     

Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering

In this paper, we develop a family of solution algorithms based upon computational intelligence for solving the dynamic multi-vehicle pick-up and delivery problem formulated under a hybrid predictive adaptive control scheme. The scheme considers future demand and prediction of expected waiting and travel times experienced by customers.