Mixed Integer Linear Programming and Heuristic Methods for Feature Selection in Clustering

This paper studies the problem of selecting relevant features in clustering problems, out of a data set in which many features are useless, or masking. The data set comprises a set U of units, a set V of features, a set R of (tentative) cluster centres and distances dijk for every i ∈ U, k ∈ R, j ∈ V . The feature selection problem consists of finding a subset of features Q ⊆ V such that the total sum of the distances from the units to the closest centre is minimized. This is a combinatorial optimization problem that we show to be NP-complete, and we propose two mixed integer linear programming formulations to calculate the solution. Some computational experiments show that if clusters are well separated and the relevant features are easy to detect, then both formulations can solve problems with many integer variables. Conversely, if clusters overlap and relevant features are ambiguous, then even small problems are unsolved. To overcome this difficulty, we propose two heuristic methods to find that, most of the time, one of them, called q-vars, calculates the optimal solution quickly. Then, the q-vars heuristic is combined with the k-means algorithm to cluster some simulated data. We conclude that this approach outperforms other methods for clustering with variable selection that were proposed in the literature.Ministerio de Economía y CompetitividadFundación SénecaMinistero dell’Istruzione, dell’Universitá e della Ricerc

A Literature Survey on Reverse Logistics of End of Life Vehicles

Today, recycling of used products and materials has become an increasingly important sector. Mankind, who uses the natural resources unconsciously, has found ways to improve recycling techniques when they realized that resources are becoming increasingly depleted. In the automotive sector, which is one of the largest sectors in the world, natural resources are being used to a great extent. According to the statistics, in 2009, approximately 9 million end-of-life vehicles (ELV) in Europe were withdrawn from traffic. Undoubtedly, this figure shows the necessity and importance of designing reverse logistics network optimized for ELVs. This research aims to determine the gaps in the literature by examining the studies made from the past to the present day in the field of reverse logistic network design for vehicles that have completed their life cycle. In this article, the studies in the fieldare analyzed based on objective functions, decision variables, constraint handling metod, optimization methods used. Considered studies in this work are clustered using a special artificial neural network tool, Self-Organizing Maps (SOM), and the frequencies of the characteristics are shown in the study. This study, which includes a review of the literature and a clustering of studies, aims to guidethe researchers working on the design of rreverse logistics networks for ELVs

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

ASlib: A Benchmark Library for Algorithm Selection

The task of algorithm selection involves choosing an algorithm from a set of algorithms on a per-instance basis in order to exploit the varying performance of algorithms over a set of instances. The algorithm selection problem is attracting increasing attention from researchers and practitioners in AI. Years of fruitful applications in a number of domains have resulted in a large amount of data, but the community lacks a standard format or repository for this data. This situation makes it difficult to share and compare different approaches effectively, as is done in other, more established fields. It also unnecessarily hinders new researchers who want to work in this area. To address this problem, we introduce a standardized format for representing algorithm selection scenarios and a repository that contains a growing number of data sets from the literature. Our format has been designed to be able to express a wide variety of different scenarios. Demonstrating the breadth and power of our platform, we describe a set of example experiments that build and evaluate algorithm selection models through a common interface. The results display the potential of algorithm selection to achieve significant performance improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa

On Solving Selected Nonlinear Integer Programming Problems in Data Mining, Computational Biology, and Sustainability

This thesis consists of three essays concerning the use of optimization techniques to solve four problems in the fields of data mining, computational biology, and sustainable energy devices. To the best of our knowledge, the particular problems we discuss have not been previously addressed using optimization, which is a specific contribution of this dissertation. In particular, we analyze each of the problems to capture their underlying essence, subsequently demonstrating that each problem can be modeled as a nonlinear (mixed) integer program. We then discuss the design and implementation of solution techniques to locate optimal solutions to the aforementioned problems. Running throughout this dissertation is the theme of using mixed-integer programming techniques in conjunction with context-dependent algorithms to identify optimal and previously undiscovered underlying structure