Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants

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

Solution approaches for the soft drink integrated production lot sizing and scheduling problem

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

Analog nonderivative optimizers

Analog networks for solving convex nonlinear unconstrained programming problems without using gradient information of the objective function are proposed. The one-dimensional net can be used as a building block in multi-dimensional networks for optimizing objective functions of several variables.

Projeto E análise de uma rede neural para resolver problemas de programação dinâmica

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems. This paper presents a novel approach for solving dynamic programming problems using artificial neural networks. 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 which represent solutions (not necessarily optimal) for the dynamic programming problem. Simulated examples are presented and compared with other neural networks. The results demonstrate that proposed method gives a significant improvement.

Planejamento de Fontes Reativas em Sistemas de Energia Elétrica utilizando a técnica de Decomposição de Benders e o algoritmo de Branch-and-Bound

This paper presents the Benders decomposition technique and Branch and Bound algorithm used in the reactive power planning in electric energy systems. The Benders decomposition separates the planning problem into two subproblems: an investment subproblem (master) and the operation subproblem (slave), which are solved alternately. The operation subproblem is solved using a successive linear programming (SLP) algorithm while the investment subproblem, which is an integer linear programming (ILP) problem with discrete variables, is resolved using a Branch and Bound algorithm especially developed to resolve this type of problem.

Planning of secondary distribution circuits through evolutionary algorithms

In this work, the planning of secondary distribution circuits is approached as a mixed integer nonlinear programming problem (MINLP). In order to solve this problem, a dedicated evolutionary algorithm (EA) is proposed. This algorithm uses a codification scheme, genetic operators, and control parameters, projected and managed to consider the specific characteristics of the secondary network planning. The codification scheme maps the possible solutions that satisfy the requirements in order to obtain an effective and low-cost projected system-the conductors' adequate dimensioning, load balancing among phases, and the transformer placed at the center of the secondary system loads. An effective algorithm for three-phase power flow is used as an auxiliary methodology of the EA for the calculation of the fitness function proposed for solutions of each topology. Results for two secondary distribution circuits are presented, whereas one presents radial topology and the other a weakly meshed topology. © 2005 IEEE.

GPS ambiguity resolution and validation under multipath effects: Improvements using wavelets

Integer carrier phase ambiguity resolution is the key to rapid and high-precision global navigation satellite system (GNSS) positioning and navigation. As important as the integer ambiguity estimation, it is the validation of the solution, because, even when one uses an optimal, or close to optimal, integer ambiguity estimator, unacceptable integer solution can still be obtained. This can happen, for example, when the data are degraded by multipath effects, which affect the real-valued float ambiguity solution, conducting to an incorrect integer (fixed) ambiguity solution. Thus, it is important to use a statistic test that has a correct theoretical and probabilistic base, which has became possible by using the Ratio Test Integer Aperture (RTIA) estimator. The properties and underlying concept of this statistic test are shortly described. An experiment was performed using data with and without multipath. Reflector objects were placed surrounding the receiver antenna aiming to cause multipath. A method based on multiresolution analysis by wavelet transform is used to reduce the multipath of the GPS double difference (DDs) observations. So, the objective of this paper is to compare the ambiguity resolution and validation using data from these two situations: data with multipath and with multipath reduced by wavelets. Additionally, the accuracy of the estimated coordinates is also assessed by comparing with the ground truth coordinates, which were estimated using data without multipath effects. The success and fail probabilities of the RTIA were, in general, coherent and showed the efficiency and the reliability of this statistic test. After multipath mitigation, ambiguity resolution becomes more reliable and the coordinates more precise. © Springer-Verlag Berlin Heidelberg 2007.

Heuristic algorithm to solve the short term transmission network expansion planning

In this paper, a method for solving the short term transmission network expansion planning problem is presented. This is a very complex mixed integer nonlinear programming problem that presents a combinatorial explosion in the search space. In order to And a solution of excellent quality for this problem, a constructive heuristic algorithm is presented in this paper. In each step of the algorithm, a sensitivity index is used to add a circuit (transmission line or transformer) or a capacitor bank (fixed or variable) to the system. This sensitivity index is obtained solving the problem considering the numbers of circuits and capacitors banks to be added (relaxed problem), as continuous variables. The relaxed problem is a large and complex nonlinear programming and was solved through a higher order interior point method. The paper shows results of several tests that were performed using three well-known electric energy systems in order to show the possibility and the advantages of using the AC model. ©2007 IEEE.

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice. © 2006 Elsevier Ltd. All rights reserved.

Specialized genetic algorithm for transmission network expansion planning considering reliability

This paper presents a methodology to solve the transmission network expansion planning problem (TNEP) considering reliability and uncertainty in the demand. The proposed methodology provides an optimal expansion plan that allows the power system to operate adequately with an acceptable level of reliability and in an enviroment with uncertainness. The reliability criterion limits the expected value of the reliability index (LOLE - Loss Of Load Expectation) of the expanded system. The reliability is evaluated for the transmission system using an analytical technique based in enumeration. The mathematical model is solved, in a efficient way, using a specialized genetic algorithm of Chu-Beasley modified. Detailed results from an illustrative example are presented and discussed. © 2009 IEEE.

Reformulação para um problema integrado de dimensionamento e sequenciamento de lotes

In this paper, some new constraints and an extended formulation are presented for a Lot Sizing and Scheduling Model proposed in the literature. In the production process considered a key material is prepared and is transformed into different final items. The sequencing decisions are related to the order in which the materials are processed and the lot sizing decisions are related to the final items production. The mathematical formulation considers sequence-dependent setup costs and times. Results of the computational tests executed using the software Cplex 10.0 showed that the performance of the branch-and-cut method can be improved by the proposed a priori reformulation.

Optimal switch allocation for automatic load transfer in distribution substations

This work proposes a methodology for optimized allocation of switches for automatic load transfer in distribution systems in order to improve the reliability indexes by restoring such systems which present voltage classes of 23 to 35 kV and radial topology. The automatic switches must be allocated on the system in order to transfer load remotely among the sources at the substations. The problem of switch allocation is formulated as nonlinear constrained mixed integer programming model subject to a set of economical and physical constraints. A dedicated Tabu Search (TS) algorithm is proposed to solve this model. The proposed methodology is tested for a large real-life distribution system. © 2011 IEEE.

Optimal allocation of capacitors in radial distribution systems with distributed generation

This paper presents a mixed-integer linear programming approach to solving the optimal fixed/switched capacitors allocation (OCA) problem in radial distribution systems with distributed generation. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. 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. © 2011 IEEE.

An enhanced genetic algorithm to solve the static and multistage transmission network expansion planning

An enhanced genetic algorithm (EGA) is applied to solve the long-term transmission expansion planning (LTTEP) problem. The following characteristics of the proposed EGA to solve the static and multistage LTTEP problem are presented, (1) generation of an initial population using fast, efficient heuristic algorithms, (2) better implementation of the local improvement phase and (3) efficient solution of linear programming problems (LPs). Critical comparative analysis is made between the proposed genetic algorithm and traditional genetic algorithms. Results using some known systems show that the proposed EGA presented higher efficiency in solving the static and multistage LTTEP problem, solving a smaller number of linear programming problems to find the optimal solutions and thus finding a better solution to the multistage LTTEP problem. Copyright © 2012 Luis A. Gallego et al.

Product mix: The approach of throughput per day

Defining product mix is very important for organisations because it determines how productive resources are allocated among various operations. However, it is often defined subjectively. The methods commonly used for this definition are Integer Linear Programming and heuristics based in Theory of Constraints, which use maximum throughput as a performance measure. Although this measure provides maximum throughput to specific problem, it does not consider aspects of time, as days, utilised to make the throughput. Taking this into account, the aim of this paper is to present a throughput per day approach to define product mix, as well as to propose a constructive heuristic to help in this process. The results show that the proposed heuristic obtained satisfactory approximation when compared to the optimum values obtained by enumeration. © 2013 Copyright Taylor and Francis Group, LLC.