Over the past few years, investigators in Brazil have been uncovering numerous corruption and money laundering schemes at all levels of government and in the country's largest corporations. It is estimated that between 2% and 5% of the global GDP is lost annually because of such practices, not only directly impacting public services and private sector development but also strengthening organized crime. However, most law enforcement agencies do not have the capability to carry out systematic corruption risk assessment leveraging on the availability of data related to public procurement. The currently prevailing approach employed by Brazilian law enforcement agencies to detect companies involved in potential cases of fraud consists in receiving circumstantial evidence or complaints from whistleblowers. As a result, a large number of companies involved in fraud remain undetected and unprosecuted. The decision support system (DSS) described in this work addresses these existing limitations by providing a tool for systematic analysis of public procurement. It allows the law enforcement agencies to establish priorities concerning the companies to be investigated. This DSS incorporates data mining algorithms for quantifying dozens of corruption risk patterns for all public contractors inside a specific jurisdiction, leading to improvements in the quality of public spending and to the identification of more cases of fraud. These algorithms combine operations research tools such as graph theory, clusterization, and regression analysis with advanced data science methods to allow the identification of the main risk patterns, such as collusion between bidders, conflicts of interest (e.g., a politician who owns a company contracted by the same government body where he or she was elected), and companies owned by a potentially straw person used for disguising its real owner (e.g., beneficiaries of cash conditional transfer programs). The DSS has already led to a detailed analysis of large public procurement datasets, which add up to more than 50 billion dollars. Moreover, the DSS provided strategic inputs to investigations conducted by federal and state agencies.

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2‐opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path‐relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best‐known solutions are made available for download and benchmarking purposes.

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Real-world networks are often extremely polarized because the communication between different groups of vertices can be weak and, most of the time, only vertices within the same group or sharing the same beliefs communicate to each other. In this work, we introduce the minimum-cardinality edge addition problem (MinCEAP) as a strategy for reducing polarization in real-world networks based on a principle of minimum external interventions. We present the problem formulation and discuss its complexity, showing that its decision version is NP-complete. We also propose three integer programming formulations for the problem and discuss computational results on artificially generated and real-life instances. Randomly generated instances with up to 1000 vertices are solved to optimality. On the real-life instances, we show that polarization can be reduced to the desired threshold with the addition of a few edges. The minimum intervention principle and the methods developed in this work are shown to constitute an effective strategy for tackling polarization issues in practice in social, interaction, and communication networks, which is a relevant problem in a world characterized by extreme political and ideological polarization.

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