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This paper aims at proposing a Constraint-based Learning Estimation of Distribution Algorithm (EDA) to solve the Multi-Mode Resource Constrained Project Scheduling Problem (MMRCPSP). This problem is considered a combinatorial optimization problem and consists of a set of tasks to be carried out in an ordered way, limited availability of resources, and an execution mode for each task. Generally, traditional EDAs handle the constraints of the problem using strategies such as penalty, Pareto dominance, or others, without taking into account these constraints during the learning process. These traditional approaches usually cause the generation of infeasible solutions in each iteration. In this paper, an approach based on the constraints handling during the learning process of the probabilistic model is proposed. To validate the performance of the algorithms, the new approach in two scenarios is compared. First, in the solution of a set of classical optimization problems, where different EDAs are compared in terms of efficiency and efficacy. The second group of experiments is performed on a set of instances of the PSPLIB database. In this case, the proposed algorithm is compared with a traditional EDA and with other results reported in the bibliography. The experimental results demonstrate that the proposal outperforms both the results of traditional EDA and other EDA reported in the literature. [ABSTRACT FROM AUTHOR]

One of the difficulties students from basic courses often show in learning probability and statistics at the university is understanding how the continuous normal probability distribution approximates the discrete binomial probability distribution. In this paper a didactic proposal is presented consisting in two algorithms, very easy to use, developed with software R which is completely free. These algorithms aim to introduce students in basic concepts of normal approximation to the binomial distribution by means of graphical representations and tables. They allow an active participation of student in the learning process. [ABSTRACT FROM AUTHOR]