Efficiently managing large deposits and warehouses is not an easy task. The amount of variables and processes involved from the moment a consumer purchases a single product until its receipt is quite considerable. There are two major problems involving warehouses processes: the order picking problem (OPP) and the order batching problem (OBP). The OPP aims to minimize the distance traveled by a picker while collecting a set of products (orders). The OBP seeks to assign orders to batches with a capacity limit in order to minimize the sum of distances traveled during the retrieving of products from all batches. When these two problems are approached together, they become the Joint Order Batching and Picking Routing Problem (JOBPRP). This work proposes a novel formulation for JOBPRP and develops a grouping genetic algorithm with controlled gene transmission. To assess our proposals, we executed computational experiments over literature datasets. The mathematical model was used within a mixed-integer programming solver (Gurobi) and tested on the smaller instances to evaluate the quality of the solutions of our metaheuristic approach. Our computational results evidence high stability for all tested instances and much lower objective value than the previously reported in the literature, while maintaining a reasonable computational time.

In this paper, we study the k-labeled spanning forest problem (kLSF). The input for this problem is an undirected graph with labeled edges and a positive integer k. The goal is to find a spanning forest of the graph with at most$k$different labels associated with the edges, minimizing the number of components. kLSF finds practical applications in different scenarios related to networks design and telecommunications. Solving it may help to reduce the negative impact of electromagnetic fields exposure on the population health or to increase profits of internet management companies, among others. The interest in kLSF is not only practical but also theoretical since the problem generalizes the best-known NP-hard minimum labeling spanning tree problem (MLST). To approach kLSF, we propose a fix-and-optimize matheuristic that was tested over several instances, achieving high-quality solutions in reasonable computational time. When compared to the best-known algorithms in the literature, our matheuristic outperformed the other proposals in most cases, finding better solutions in less computational time for the most challenging instances.

This work considers the Target Set Selection problem, which can be used to model the propagation and consumption of information, data, ideas and products through networks, with applications in marketing, medicine, sociology and bioinformatics. We propose a new version of the problem and prove it belongs to the NP-hard class. We also design an evolutionary algorithm that uses, in the crossover and mutation operators, exact solutions of sub-problems which were modeled by a new mathematical formulation. We test our approach over a benchmark of instances constructed from real-world data sets.