Frank Pettersson

An extended cutting plane method for solving convex MINLP problems

Abstract An extended version of Kelleys cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelleys cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP problems with a moderate degree of nonlinearity. The convergence properties of the method are given in the present paper and an example is provided to illustrate the numerical procedure.

A genetic algorithms based multi-objective neural net applied to noisy blast furnace data

A genetic algorithms based multi-objective optimization technique was utilized in the training process of a feed forward neural network, using noisy data from an industrial iron blast furnace. The number of nodes in the hidden layer, the architecture of the lower part of the network, as well as the weights used in them were kept as variables, and a Pareto front was effectively constructed by minimizing the training error along with the network size. A predator-prey algorithm efficiently performed the optimization task and several important trends were observed.

Hybrid ant colony optimization and visibility studies applied to a job-shop scheduling problem

A hybrid ant colony optimization (ACO) algorithm is applied to a well known job-shop scheduling problem: MT10 (Muth-Thompson). The ACO tries to preserve and improve existing solutions, and a postprocessing algorithm is applied to the tour of an ant upon its completion. Studies are performed to see what effect visibility has on the outcome with regards to the ACO part of the algorithm.

Analyzing Leaching Data for Low-Grade Manganese Ore Using Neural Nets and Multiobjective Genetic Algorithms

Existing acid leaching data for low-grade manganese ores are modeled using an evolving neural net. Three distinct cases of leaching in the presence of glucose, sucrose and lactose have been considered and the results compared with an existing analytical model. The neural models are then subjected to bi-objective optimization, using a predator–prey genetic algorithm, maximizing recovery in tandem with a minimization of the acid concentration. The resulting Pareto frontiers are analyzed and discussed.

Optimization of pump configurations as a MINLP problem

Abstract This paper introduces a method for solving optimal pump configurations as a MINLP (mixed integer non-linear programming) problem. The pump configurations considered consist of an arbitrary number of centrifugal pumps, of different sizes, coupled in series and/or parallel. Given the total required pressure rise and the required flow, the optimal pump configuration is sought. The pump configuration is optimized with respect to the minimum total cost including the investment and the running costs. The optimization problem consists of a non-linear objective function subject to linear and non-linear equality and inequality constraints including real, integer and binary variables. The MINLP problem is solved by a proposed ECP (extended cutting plane) method combined with a general (integer) branch and bound method, as well as by the DICOPT++ software in which an outer approximation method is used coupled with a zero-one branch and bound method. Simple linear transformations illustrate that integer problems are also efficiently solved by zero-one programming. Different problem formulations are also given to improve the solution by the methods. Results obtained by solving the optimization problem as a min-min problem are also given. Some problems arise from the fact that the objective function may have several local optima and is generally non-convex. Examples are given to illustrated the procedures.

Genetic Programming Evolved through Bi-Objective Genetic Algorithms Applied to a Blast Furnace

In this study, a new Bi-objective Genetic Programming (BioGP) technique was developed that initially attempts to minimize training error through a single objective procedure and subsequently switches to bi-objective evolution to work out a Pareto-tradeoff between model complexity and accuracy. For a set of highly noisy industrial data from an operational ironmaking blast furnace (BF) this method was pitted against an Evolutionary Neural Network (EvoNN) developed earlier by the authors. The BioGP procedure was found to produce very competitive results for this complex modeling problem and because of its generic nature, opens a new avenue for data-driven modeling in many other domains.

Genetic Algorithm-Based Multicriteria Optimization of Ironmaking in the Blast Furnace

A method has been developed for optimizing ironmaking in the blast furnace with the aim to minimize costs and CO2 emissions. These two goals are pursued by a genetic algorithm yielding states of operation on a Pareto-optimal front with nondominated solutions. The blast furnace process is described mathematically by a thermodynamic simulation model, where realistic operational constraints are imposed. The states on the Pareto-optimal fronts evolved are analyzed in more detail, considering the constraints of the process. The solutions are found to give rise to clearly different specific emissions but very similar specific costs as long as the production stays within the limits of the granted CO2 emissions allowances of the plant. However, this also implies that the costs of ironmaking may rise considerably along with increased prices of the allowances or reduced emission rights. The findings of the work are expected to be valuable in the strategic evaluation of future ironmaking options.

Synthesis of large-scale heat exchanger networks using a sequential match reduction approach

Abstract In this paper, a sequential approach is outlined which generates networks for industrial sized heat exchanger network synthesis (HENS) problems. The proposed match reduction approach solves a sequence of subproblems, posed as transportation problems, successively reducing the set of matches that are considered in the next stage. The terms involved in the objective function are included at each step with increasing accuracy, until a final design is obtained. One of the subproblems identifies subsets of matches that can be designed separately. Due to the sequential approach, the final design is an approximating solution. Two examples are presented to illustrate the potential of the proposed method. The results show that large HENS problems can be solved to good solutions with modest computational effort. The obtained solutions are in fact, better than the results reported earlier in the literature.

Method for the selection of inputs and structure of feedforward neural networks

Feedforward neural networks of multi-layer perceptron type can be used as nonlinear black-box models in data-mining tasks. Common problems encountered are how to select relevant inputs from a large set of variables that potentially affect the outputs to be modeled, as well as high levels of noise in the data sets. In order to avoid over-fitting of the resulting model, the input dimension and/or the number of hidden nodes have to be restricted. This paper presents a systematic method that can guide the selection of both input variables and a sparse connectivity of the lower layer of connections in feedforward neural networks of multi-layer perceptron type with one layer of hidden nonlinear units and a single linear output node. The algorithm is illustrated on three benchmark problems.

Evolving Nonlinear Time-Series Models of the Hot Metal Silicon Content in the Blast Furnace

Neural networks are versatile tools for nonlinear modeling, but in time-series modeling of complex industrial processes the choice of relevant inputs and time lags can be a major problem. A novel method for the simultaneous detection of relevant inputs and an appropriate structure of the lower part of the networks has been developed by evolving neural networks by a genetic algorithm, where the approximation error and the number of weights are minimized simultaneously by multiobjective optimization. The networks on the Pareto front are considered possible candidate models that are evaluated on an independent test set. In order to consider the problem of drift in the variables, which may cause parsimonious models to perform poorly on the test set, the weights in the upper layer of the networks are recursively estimated by a Kalman filter. The method is illustrated on a data set from ironmaking industry, where time-series models of the hot metal silicon content in a blast furnace are evolved. The technique is demonstrated to synthesize models with a choice of inputs in agreement with findings presented in the literature and process know-how.