Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Goal Programming (GP) is an important analytical approach devised to solve many realworld problems. The first GP model is known as Weighted Goal Programming (WGP). However, Multi-Choice Aspirations Level (MCAL) problems cannot be solved by current GP techniques. In this paper, we propose a Multi-Choice Mixed Integer Goal Programming model (MCMI-GP) for the aggregate production planning of a Brazilian sugar and ethanol milling company. The MC-MIGP model was based on traditional selection and process methods for the design of lots, representing the production system of sugar, alcohol, molasses and derivatives. The research covers decisions on the agricultural and cutting stages, sugarcane loading and transportation by suppliers and, especially, energy cogeneration decisions; that is, the choice of production process, including storage stages and distribution. The MCMIGP allows decision-makers to set multiple aspiration levels for their problems in which the more/higher, the better and the less/lower, the better in the aspiration levels are addressed. An application of the proposed model for real problems in a Brazilian sugar and ethanol mill was conducted; producing interesting results that are herein reported and commented upon. Also, it was made a comparison between MCMI GP and WGP models using these real cases. © 2013 Elsevier Inc.

A mixed-integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems

This paper presents a mixed-integer linear programming model to solve the problem of allocating voltage regulators and fixed or switched capacitors (VRCs) in radial distribution systems. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The results of one test system and one real distribution system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. An heuristic to obtain the Pareto front for the multiobjective VRCs allocation problem is also presented. © 2012 Elsevier Ltd. All rights reserved.

Bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works. © The Institution of Engineering and Technology 2013.

On the regularization of mixed complementarity problems

A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable inexact solutions of the strictly monotone MCP's is bounded and every accumulation point is a solution. Under an additional condition on the precision used for solving each subproblem, the sequence converges to the minimum norm solution of the MCP. Copyright © 2000 by Marcel Dekker, Inc.

On the solution of bounded and unbounded mixed complementarity problems

A reformulation of the bounded mixed complementarity problem is introduced. It is proved that the level sets of the objective function are bounded and, under reasonable assumptions, stationary points coincide with solutions of the original variational inequality problem. Therefore, standard minimization algorithms applied to the new reformulation must succeed. This result is applied to the compactification of unbounded mixed complementarity problems. © 2001 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint, a member of the Taylor & Francis Group.

Optimal conductor size selection and reconductoring in radial distribution systems using a mixed-integer LP approach

This paper presents a mixed-integer linear programming model to solve the conductor size selection and reconductoring problem in radial distribution systems. In the proposed model, the steady-state operation of the radial distribution system is modeled through linear expressions. The use of a mixed-integer linear model guarantees convergence to optimality using existing optimization software. The proposed model and a heuristic are used to obtain the Pareto front of the conductor size selection and reconductoring problem considering two different objective functions. The results of one test system and two real distribution systems are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. © 1969-2012 IEEE.

A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation

The problem of reconfiguration of distribution systems considering the presence of distributed generation is modeled as a mixed-integer linear programming (MILP) problem in this paper. The demands of the electric distribution system are modeled through linear approximations in terms of real and imaginary parts of the voltage, taking into account typical operating conditions of the electric distribution system. The use of an MILP formulation has the following benefits: (a) a robust mathematical model that is equivalent to the mixed-integer non-linear programming model; (b) an efficient computational behavior with exiting MILP solvers; and (c) guarantees convergence to optimality using classical optimization techniques. Results from one test system and two real systems show the excellent performance of the proposed methodology compared with conventional methods. © 2012 Published by Elsevier B.V. All rights reserved.

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 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.

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mixed-integer convex model for VAr expansion planning

This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning solution, in the proposed approach the taps settings of under-load tap-changing of transformers are modeled as a mixed-integer linear set equations. Are also considered the continuous and discrete variables for the existing and new capacitive and reactive power sources. The problem is solved for three significant demand scenarios (low demand, average demand and peak demand). Numerical results are presented for the CIGRE-32 electric power system.

Estatégias para incorporação das deçisões de sequenciamento em um problema integrado de produção de bebidas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Imposing Radiality Constraints in Distribution System Optimization Problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.