The vertex bisection problem (VBP) is an NP-hard combinatorial optimization problem with important practical applications in the context of network communications. The problem consists in finding a partition of the set of vertices of a generic undirected graph into two subsets (A and B) of approximately the same cardinality in such a way that the number of vertices in A with at least one adjacent vertex in B is minimized. In this article, we propose two new integer linear programming (ILP) formulations for VBP. Our first formulation (ILPVBP) is based on the redefinition of the objective function of VBP. The redefinition consists in computing the objective value from the vertices in B rather than from the vertices in A. As far as we are aware, this is the first time that this representation is used to solve VBP. The second formulation (MILP) reformulates ILPVBP in such a way that the number of variables and constraints is reduced. In order to assess the performance of our formulations, we conducted a computational experiment and compare the results with the best ILP formulation available in the literature (ILPLIT). The experimental results clearly indicate that our formulations outperform ILPLIT in (i) average objective value, (ii) average computing time and (iii) number of optimal solutions found. We statistically validate the results of the experiment through the well-known Wilcoxon rank sum test for a confidence level of 99.9%. Additionally, we provide 404 new optimal solutions and 73 new upper and lower bounds for 477 instances from 13 different groups of graphs.
The Vehicle Routing Problem (VRP) is a key to the efficient transportation management and supply-chain coordination. VRP research has often been too focused on idealized models with non-realistic assumptions for practical applications. Nowadays the evolution of methodologies allows that the classical problems could be used to solve VRP problems of real life. The evolution of methodologies allows the creation of variants of the VRP which were considered too difficult to handle by their variety of possible restrictions. A VRP problem that includes the addition of restrictions, which represent the variants in the problem, is called Rich VRP. This work presents an algorithm to optimize the transportation management. The authors are including a case of study which solves a real routing problem applied to the distribution of bottled products. The proposed algorithm shows a saving in quantity of vehicles and reduces the operation costs of the company.
Data mining is a complex process that involves the interaction of the application of human knowledge and skills and technology. This must be supported by clearly defined processes and procedures. This Chapter describes CRISP-DM (Cross-Industry Standard Process for Data Mining), a fully documented, freely available, robust, and non proprietary data mining model. The chapter analyzes the contents of the official Version 1.0 Document, and it is a guide through all the implementation process. The main purpose of data mining is the extraction of hidden and useful knowledge from large volumes of raw data. Data mining brings together different disciplines like software engineering, computer science, business intelligence, human-computer interaction, and analysis techniques. Phases of these disciplines must be combined for data mining project outcomes. CRISP-DM methodology defines its processes hierarchically at four levels of abstraction allowing a project to be structured modularly, being more maintainable, scalable and the most important, to reduce complexity. CRISP-DM describes the life cycle of a data mining project consisting of six phases: business understanding, data understanding, data preparation, modeling, evaluation, and deployment.
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