scholarly journals Multiperiod hydrothermal economic dispatch by an interior point method

2002 ◽  
Vol 8 (1) ◽  
pp. 33-42 ◽  
Author(s):  
L. M. Kimball ◽  
K. A. Clements ◽  
P. W. Davis ◽  
I. Nejdawi
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Large Scale ◽  
Necessary Conditions ◽  
Economic Dispatch ◽  
Optimization Methods ◽  
Interior Point Algorithm ◽  
Peak Shaving ◽  
Network Characteristics ◽  
First Order

This paper presents an interior point algorithm to solve the multiperiod hydrothermal economic dispatch (HTED). The multiperiod HTED is a large scale nonlinear programming problem. Various optimization methods have been applied to the multiperiod HTED, but most neglect important network characteristics or require decomposition into thermal and hydro subproblems. The algorithm described here exploits the special bordered block diagonal structure and sparsity of the Newton system for the first order necessary conditions to result in a fast efficient algorithm that can account for all network aspects. Applying this new algorithm challenges a conventional method for the use of available hydro resources known as the peak shaving heuristic.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

scholarly journals Heat transfer from convecting-radiating fin through optimized Chebyshev polynomials with interior point algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 102-110
Author(s):  
Elyas Shivanian ◽  
Mahdi Keshtkar ◽  
Hamidreza Navidi
Keyword(s):  
Heat Transfer ◽  
Chebyshev Polynomials ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Interior Point Algorithm ◽  
Equivalent Problem ◽  
One Dimensional ◽  
Fin Efficiency

AbstractIn this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.

Hybrid Harmony Search Algorithm and Interior Point Method for Economic Dispatch with Valve-Point Effect

2014 ◽  
Vol 15 (3) ◽  
pp. 253-261 ◽  
Author(s):  
S. Sivasubramani ◽  
Md. Samar Ahmad
Keyword(s):  
Convex Optimization ◽  
Hybrid Method ◽  
Interior Point ◽  
Interior Point Method ◽  
Economic Dispatch ◽  
Harmony Search ◽  
Point Method ◽  
Local Optimum ◽  
Local Minima ◽  
Valve Point Effect

Abstract This paper proposes a new hybrid algorithm combining harmony search (HS) algorithm and interior point method (IPM) for economic dispatch (ED) problem with valve-point effect. ED problem with valve-point effect is modeled as a non-linear, constrained and non-convex optimization problem having several local minima. IPM is a best non-linear optimization method for convex optimization problems. Since ED problem with valve-point effect has multiple local minima, IPM results in a local optimum solution. In order to avoid IPM getting trapped in a local optimum, a new evolutionary algorithm HS, which is good in global exploration, has been combined. In the hybrid method, HS is used for global search and IPM for local search. The hybrid method has been tested on three different test systems to prove its effectiveness. Finally, the simulation results are also compared with other methods reported in the literature.

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION BASED ON AN EXPONENTIAL KERNEL FUNCTION

2014 ◽  
Vol 07 (01) ◽  
pp. 1450018
Author(s):  
Behrouz Kheirfam ◽  
Fariba Hasani
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Polynomial Complexity ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Math Model ◽  
Newton Step ◽  
Infeasible Interior Point Method ◽  
Full Newton Step

This paper deals with an infeasible interior-point algorithm with full-Newton step for linear optimization based on a kernel function, which is an extension of the work of the first author and coworkers (J. Math. Model Algorithms (2013); DOI 10.1007/s10852-013-9227-7). The main iteration of the algorithm consists of a feasibility step and several centrality steps. The centrality step is based on Darvay's direction, while we used a kernel function in the algorithm to induce the feasibility step. For the kernel function, the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods.

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