Implementação paralela escalável e eficiente do algoritmo simplex padrão em arquitetura multicore

This work presents a scalable and efficient parallel implementation of the Standard Simplex algorithm in the multicore architecture to solve large scale linear programming problems. We present a general scheme explaining how each step of the standard Simplex algorithm was parallelized, indicating some important points of the parallel implementation. Performance analysis were conducted by comparing the sequential time using the Simplex tableau and the Simplex of the CPLEXR IBM. The experiments were executed on a shared memory machine with 24 cores. The scalability analysis was performed with problems of different dimensions, finding evidence that our parallel standard Simplex algorithm has a better parallel efficiency for problems with more variables than constraints. In comparison with CPLEXR , the proposed parallel algorithm achieved a efficiency of up to 16 times better

Formulações e algoritmos para o problema das p-medianas heterogêneo livre de penalidade

This work presents a new model for the Heterogeneous p-median Problem (HPM), proposed to recover the hidden category structures present in the data provided by a sorting task procedure, a popular approach to understand heterogeneous individual’s perception of products and brands. This new model is named as the Penalty-free Heterogeneous p-median Problem (PFHPM), a single-objective version of the original problem, the HPM. The main parameter in the HPM is also eliminated, the penalty factor. It is responsible for the weighting of the objective function terms. The adjusting of this parameter controls the way that the model recovers the hidden category structures present in data, and depends on a broad knowledge of the problem. Additionally, two complementary formulations for the PFHPM are shown, both mixed integer linear programming problems. From these additional formulations lower-bounds were obtained for the PFHPM. These values were used to validate a specialized Variable Neighborhood Search (VNS) algorithm, proposed to solve the PFHPM. This algorithm provided good quality solutions for the PFHPM, solving artificial generated instances from a Monte Carlo Simulation and real data instances, even with limited computational resources. Statistical analyses presented in this work suggest that the new algorithm and model, the PFHPM, can recover more accurately the original category structures related to heterogeneous individual’s perceptions than the original model and algorithm, the HPM. Finally, an illustrative application of the PFHPM is presented, as well as some insights about some new possibilities for it, extending the new model to fuzzy environments