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The aim of this paper is to propose a procedure to create escape vectors specifically developed to perform an orthogonal projection from an Ax≤b type polyhedron's edge to its interior. The proposed procedure can be implemented in interior-point methods for solving linear programming problems since in these methods various strategies are used to avoid reaching the borders of the polyhedron. A projection procedure was developed to the polyhedron's interior starting from three scenarios and it was used on a context case demonstrating its applicability. The results show that the projection carried out in the iteration in which the escape is done not only allows abandoning from a suboptimal solution but it also kept the same objective function value. Therefore, it can be concluded that interior-point methods do not need to avoid the frontier or to adjust values, as it occurs in other applications. [ABSTRACT FROM AUTHOR]

This paper presents a study done to find an interior point in the feasible region of linear programming problems is an aspect that should be solved in the initial stage of the implementation of the interior point algorithms used to optimize them. Consequently, it is proposed a methodology that starts with a formulation that does not require adding surplus or slack variables. It only includes an additional variable to generate a polyhedron in a new expanded space and with simple projections finds an interior point in the same polyhedron. It is demonstrated that the optimal solution of the extended linear programming problem allows obtaining a feasible point of the original problem or concluding that it has no feasible solutions. [ABSTRACT FROM AUTHOR]

This paper presents an optimal budget assignment model for improving quality service in distribution systems. The model consists on a multi objective problem which aims at minimizing maintenance costs in distribution systems while maximizing the reduction of faults rate. This last objective is measured through the SAIFI indicator (System Average Interruption Frequency Index). To solve the proposed model two algorithms were implemented: NSGAII (Non-Dominated Sorting Genetic Algorithm II) and a Memetic Algorithm. Several tests were performed with two real electrical systems of 100 and 200 nodes in the Department of Antioquia in Colombia, showing the applicability of the proposed approach. The optimal Pareto fronts obtained in the problem solution show a set of available options that represent a trade-off between both objectives and provides the system operator with an estimate of how much to invest in maintenance to achieve a desired value of the SAIFI indicator. [ABSTRACT FROM AUTHOR]