Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

A Fuzzy Goal Programming model for solving aggregate production-planning problems under uncertainty: A case study in a Brazilian sugar mill

This paper proposes a Fuzzy Goal Programming model (FGP) for a real aggregate production-planning problem. To do so, an application was made in a Brazilian Sugar and Ethanol Milling Company. The FGP Model depicts the comprehensive production process of sugar, ethanol, molasses and derivatives, and considers the uncertainties involved in ethanol and sugar production. Decision-makings, related to the agricultural and logistics phases, were considered on a weekly-basis planning horizon to include the whole harvesting season and the periods between harvests. The research has provided interesting results about decisions in the agricultural stages of cutting, loading and transportation to sugarcane suppliers and, especially, in milling decisions, whose choice of production process includes storage and logistics distribution. (C)2014 Elsevier B.V. All rights reserved.

A mixed-integer quadratically-constrained programming model for the distribution system expansion planning

This paper presents a mixed-integer quadratically-constrained programming (MIQCP) model to solve the distribution system expansion planning (DSEP) problem. The DSEP model considers the construction/reinforcement of substations, the construction/reconductoring of circuits, the allocation of fixed capacitors banks and the radial topology modification. As the DSEP problem is a very complex mixed-integer non-linear programming problem, it is convenient to reformulate it like a MIQCP problem; it is demonstrated that the proposed formulation represents the steady-state operation of a radial distribution system. The proposed MIQCP model is a convex formulation, which allows to find the optimal solution using optimization solvers. Test systems of 23 and 54 nodes and one real distribution system of 136 nodes were used to show the efficiency of the proposed model in comparison with other DSEP models available in the specialized literature. (C) 2014 Elsevier Ltd. All rights reserved.

Design and analysis of an efficient neural network model for solving nonlinear optimization problems

This paper presents an efficient approach based on a recurrent neural network for solving constrained nonlinear optimization. More specifically, a modified Hopfield network is developed, and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it handles optimization and constraint terms in different stages with no interference from each other. Moreover, the proposed approach does not require specification for penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyse its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.

Interior point algorithm for linear programming used in transmission network synthesis

This article presents a well-known interior point method (IPM) used to solve problems of linear programming that appear as sub-problems in the solution of the long-term transmission network expansion planning problem. The linear programming problem appears when the transportation model is used, and when there is the intention to solve the planning problem using a constructive heuristic algorithm (CHA), ora branch-and-bound algorithm. This paper shows the application of the IPM in a CHA. A good performance of the IPM was obtained, and then it can be used as tool inside algorithm, used to solve the planning problem. Illustrative tests are shown, using electrical systems known in the specialized literature. (C) 2005 Elsevier B.V. All rights reserved.

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Bilevel Approach to Transmission Expansion Planning Within a Market Environment

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

KT-invexity in optimal control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

A class of multiobjective control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Towards an intelligent graphical interface for linear programming modelling

The increase of computing power of the microcomputers has stimulated the building of direct manipulation interfaces that allow graphical representation of Linear Programming (LP) models. This work discusses the components of such a graphical interface as the basis for a system to assist users in the process of formulating LP problems. In essence, this work proposes a methodology which considers the modelling task as divided into three stages which are specification of the Data Model, the Conceptual Model and the LP Model. The necessity for using Artificial Intelligence techniques in the problem conceptualisation and to help the model formulation task is illustrated.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.