Daniel Aloise

NP-hardness of Euclidean sum-of-squares clustering

A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al. (Mach. Learn. 56:9–33, 2004), is not valid. An alternate short proof is provided.

Scheduling workover rigs for onshore oil production

Many oil wells in Brazilian onshore fields rely on artificial lift methods. Maintenance services such as cleaning, reinstatement, stimulation and others are essential to these wells. These services are performed by workover rigs, which are available on a limited number with respect to the number of wells demanding service. The decision of which workover rig should be sent to perform some maintenance service is based on factors such as the well production, the current location of the workover rig in relation to the demanding well, and the type of service to be performed. The problem of scheduling workover rigs consists in finding the best schedule for the available workover rigs, so as to minimize the production loss associated with the wells awaiting for service. We propose a variable neighborhood search (VNS) heuristic for this problem. Computational results on real-life problems are reported and their economic impacts are evaluated.

A simple and effective genetic algorithm for the two-stage capacitated facility location problem ☆

This paper presents a simple and effective Genetic Algorithm (GA) for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem which arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying demand and capacity constraints of its agents. For this purpose, a GA is proposed and computational results are reported comparing the heuristic results with those obtained by two state-of-the-art Lagrangian heuristics proposed in the literature for the problem.

Reactive Search strategies using Reinforcement Learning, local search algorithms and Variable Neighborhood Search

Abstract Optimization techniques known as metaheuristics have been applied successfully to solve different problems, in which their development is characterized by the appropriate selection of parameters (values) for its execution. Where the adjustment of a parameter is required, this parameter will be tested until viable results are obtained. Normally, such adjustments are made by the developer deploying the metaheuristic. The quality of the results of a test instance [The term instance is used to refer to the assignment of values to the input variables of a problem.] will not be transferred to the instances that were not tested yet and its feedback may require a slow process of “trial and error” where the algorithm has to be adjusted for a specific application. Within this context of metaheuristics the Reactive Search emerged defending the integration of machine learning within heuristic searches for solving complex optimization problems. Based in the integration that the Reactive Search proposes between machine learning and metaheuristics, emerged the idea of putting Reinforcement Learning, more specifically the Q-learning algorithm with a reactive behavior, to select which local search is the most appropriate in a given time of a search, to succeed another local search that can not improve the current solution in the VNS metaheuristic. In this work we propose a reactive implementation using Reinforcement Learning for the self-tuning of the implemented algorithm, applied to the Symmetric Travelling Salesman Problem.

Adaptive memory in multistart heuristics for multicommodity network design

This paper focuses on the use of different memory strategies to improve multistart methods. A network design problem in which the costs are given by discrete stepwise increasing cost functions of the capacities installed in the edges is used to illustrate the contributions of adaptive memory and vocabulary building strategies. Heuristics based on shortest path and maximum flow algorithms are combined with adaptive memory in order to obtain an approximate solution to the problem in the framework of a multistart algorithm. Furthermore, a vocabulary building intensification mechanism supported by the resolution of a linear program is also explored. Numerical experiments have shown that the proposed algorithm obtained the best known solutions for some instances in the literature. These results show the contribution of each memory component and the effectiveness of their combination.

A model for clustering data from heterogeneous dissimilarities

Clustering algorithms partition a set of n objects into p groups (called clusters), such that objects assigned to the same groups are homogeneous according to some criteria. To derive these clusters, the data input required is often a single n × n dissimilarity matrix. Yet for many applications, more than one instance of the dissimilarity matrix is available and so to conform to model requirements, it is common practice to aggregate (e.g., sum up, average) the matrices. This aggregation practice results in clustering solutions that mask the true nature of the original data. In this paper we introduce a clustering model which, to handle the heterogeneity, uses all available dissimilarity matrices and identifies for groups of individuals clustering objects in a similar way. The model is a nonconvex problem and difficult to solve exactly, and we thus introduce a Variable Neighborhood Search heuristic to provide solutions efficiently. Computational experiments and an empirical application to perception of chocolate candy show that the heuristic algorithm is efficient and that the proposed model is suited for recovering heterogeneous data. Implications for clustering researchers are discussed.

On the Weber facility location problem with limited distances and side constraints

The objective in the continuous facility location problem with limited distances is to minimize the sum of distance functions from the facility to the customers, but with a limit on each of the distances, after which the corresponding function becomes constant. The problem has applications in situations where the service provided by the facility is insensitive after a given threshold distance. In this paper, we propose a global optimization algorithm for the case in which there are in addition lower and upper bounds on the numbers of customers served.

A VNS heuristic for escaping local extrema entrapment in normalized cut clustering

Normalized cut is one of the most popular graph clustering criteria. The main approaches proposed for its resolution are spectral clustering methods and a multilevel approach of Dhillon et al. (TPAMI 29:1944-1957, 2007), called graclus. Their aim is to obtain good solutions in a small amount of time for large instances. Metaheuristics are general frameworks for stochastic searches often employed in global optimization to improve the solutions obtained by other heuristics. Variable neighborhood search (VNS) is a metaheuristic which exploits systematically the idea of neighborhood change during the search. In this paper, we propose a VNS heuristic for normalized cut segmentation. Computational experiments show that in most cases this VNS heuristic improves significantly, and in moderate time, the solutions obtained by the current state-of-the-art algorithms, i.e., graclus and a spectral method proposed by Yu and Shi (ICCV, 2003).

A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering

Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of n points into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Peng & Xia (2005) established the equivalence between 0-1 semidefinite programming (SDP) and MSSC. In this paper, we propose a branch-and-cut algorithm for the underlying 0-1 SDP model. The algorithm obtains exact solutions for fairly large data sets with computing times comparable with those of the best exact method found in the literature.

Extracting Summary Piles from Sorting Task Data

In a sorting task, consumers receive a set of representational items (e.g., products, brands) and sort them into piles such that the items in each pile “go together.” The sorting task is flexible in accommodating different instructions and has been used for decades in exploratory marketing research in brand positioning and categorization. However, no general analytic procedures yet exist for analyzing sorting task data without performing arbitrary transformations to the data that influence the results and insights obtained. This manuscript introduces a flexible framework for analyzing sorting task data, as well as a new optimization approach to identify summary piles, which provide an easy way to explore associations consumers make among a set of items. Using two Monte Carlo simulations and an empirical application of single-serving snacks from a local retailer, the authors demonstrate that the resulting procedure is scalable, can provide additional insights beyond those offered by existing procedures, and requires mere minutes of computational time.