Abstract
This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures (IPLS) in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch (ED) problem studied in the field of power systems analysis. The theory of the method is examined for quadratic programming problems and involves the analysis of iterative schemes, computational implementation, and issues concerning the adaptation of the proposed algorithm to solve ED problems. Numerical results are presented, which demonstrate improvements and the efficiency of the IPLS method when compared to several other methods described in the literature. Finally, postoptimization analyses are performed for the solution of ED problems.
Highlights
Since its introduction in 1984, the projective transformation algorithm proposed by Karmarkar in 1 has proved to be a notable interior point method for solving linear programming problems LPPs
This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures IPLS in both the predictor and corrector steps
From the results presented in this table, it is clear that the dispatches calculated by all the types of genetic algorithms cannot reach the global optimum dispatch attained by the interior point methods PCPD and IPLS
Summary
Since its introduction in 1984, the projective transformation algorithm proposed by Karmarkar in 1 has proved to be a notable interior point method for solving linear programming problems LPPs. The purpose of this procedure is to solve the problem pointed out by Megiddo, that is, to prevent an interior solution from becoming “trapped” at the border of the problem possibly a vertex. The polynomial time complexity theory was successfully demonstrated by Kojima et al in 20 and Monteiro et al in 19 based on Megiddo’s work, which provided a theoretical analysis for the logarithmic barrier method and proposed the primal-dual approach. The point previously obtained in the predictor step was “centralized” to exploit the potential function related to the logarithmic barrier function This procedure significantly improved the performance of the primal-dual interior point methods.
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