Kaj-Mikael Björk

Global optimization of heat exchanger network synthesis problems with and without the isothermal mixing assumption

In this paper, a new global optimization approach for the synthesis of heat exchanger networks is presented. The Synheat model by [Comp. Chem. Eng. 1 (1990) 1165] uses a promising superstructure that includes the most common heat exchanger structures, and optimizes utility costs, the number of units and heat exchanger areas simultaneously. With some minor modifications of the model, it is possible to apply a new global optimization strategy to the problem. The heart of the strategy is to convexify signomial terms, and create approximate convexified subproblems. If the Synheat model is extended in an appropriate way, the isothermal mixing assumption can be removed. Applying the new global optimization strategy to the model allowing non-isothermal mixing makes it possible to find truly optimal network configurations for the case of constant heat-capacity flow rates and heat transfer coefficients. Some examples to illustrate the global optimization strategy and to illustrate that the Synheat model can exclude optimal configurations due to the isothermal mixing assumption are also given in this paper.

High-Performance Extreme Learning Machines: A Complete Toolbox for Big Data Applications

This paper presents a complete approach to a successful utilization of a high-performance extreme learning machines (ELMs) Toolbox for Big Data. It summarizes recent advantages in algorithmic performance; gives a fresh view on the ELM solution in relation to the traditional linear algebraic performance; and reaps the latest software and hardware performance achievements. The results are applicable to a wide range of machine learning problems and thus provide a solid ground for tackling numerous Big Data challenges. The included toolbox is targeted at enabling the full potential of ELMs to the widest range of users.

An analytical solution to a fuzzy economic order quantity problem

This paper contributes to the set of models capturing the economic order quantity with backorders. In real life situations, both the demand and the lead times are uncertain. These uncertainties are handled with fuzzy numbers and the analytical solution to the optimization problem, where both the demand and the lead times are formulated as a triangular fuzzy numbers, is obtained. Finally the solution from the new approach is compared to earlier work and through an example, it is shown that the uncertainties result in increased order quantities.

Global solution of optimization problems with signomial parts

In this paper a new approach for the global solution of nonconvex MINLP (Mixed Integer NonLinear Programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applying different variable transformation techniques and a discretization scheme a lower bounding convex MINLP problem can be derived. The convexified MINLP problem can be solved with standard methods. The key element in this approach is that all transformations are applied termwise. In this way all convex parts of the problem are left unaffected by the transformations. The method is illustrated by four example problems.

Extreme learning machine for missing data using multiple imputations

In the paper, we examine the general regression problem under the missing data scenario. In order to provide reliable estimates for the regression function (approximation), a novel methodology based on Gaussian Mixture Model and Extreme Learning Machine is developed. Gaussian Mixture Model is used to model the data distribution which is adapted to handle missing values, while Extreme Learning Machine enables to devise a multiple imputation strategy for final estimation. With multiple imputation and ensemble approach over many Extreme Learning Machines, final estimation is improved over the mean imputation performed only once to complete the data. The proposed methodology has longer running times compared to simple methods, but the overall increase in accuracy justifies this trade-off.

Arbitrary Category Classification of Websites Based on Image Content

This paper presents a comprehensive methodology for general large-scale image-based classification tasks. It addresses the Big Data challenge in arbitrary image classification and more specifically, filtering of millions of websites with abstract target classes and high levels of label noise. Our approach uses local image features and their color descriptors to build image representations with the help of a modified k-NN algorithm. Image representations are refined into image and website class predictions by a two-stage classifier method suitable for a very large-scale real dataset. A modification of an Extreme Learning Machine is found to be a suitable classifier technique. The methodology is robust to noise and can learn abstract target categories; website classification accuracy surpasses 97% for the most important categories considered in this study.

Manifold learning in local tangent space via extreme learning machine

In this paper, we propose a fast manifold learning strategy to estimate the underlying geometrical distribution and develop the relevant mathematical criterion on the basis of the extreme learning machine (ELM) in the high-dimensional space. The local tangent space alignment (LTSA) method has been used to perform the manifold production and the single hidden layer feedforward network (SLFN) is established via ELM to simulate the low-dimensional representation process. The scheme of the ELM ensemble then combines the individual SLFN for the model selection, where the manifold regularization mechanism has been brought into ELM to preserve the local geometrical structure of LTSA. Some developments have been done to evaluate the inherent representation embedding in the ELM learning. The simulation results have shown the excellent performance in the accuracy and efficiency of the developed approach.

SOM-ELM-Self-Organized Clustering using ELM

This paper presents two new clustering techniques based on Extreme Learning Machine (ELM). These clustering techniques can incorporate a priori knowledge (of an expert) to define the optimal structure for the clusters, i.e. the number of points in each cluster. Using ELM, the first proposed clustering problem formulation can be rewritten as a Traveling Salesman Problem and solved by a heuristic optimization method. The second proposed clustering problem formulation includes both a priori knowledge and a self-organization based on a predefined map (or string). The clustering methods are successfully tested on 5 toy examples and 2 real datasets.

The Economic Production Quantity Problem with a Finite Production Rate and Fuzzy Cycle Time

Managing the inventories along with carrying out the production program is essential for many companies in the producing industry. In this paper, a fuzzy EPQ (Economic Production Quantity) model is developed to address this specific problem as a theoretical study. However, this problem derives from some real world applications, in which the producing company in a supply chain had to decide the size of the production batches under uncertainty. The uncertainty will be handled with fuzzy numbers and we will find an analytical solution to the optimization problem. The paper concludes with a small example to illustrate the analytical results.

ELMVIS+: Fast nonlinear visualization technique based on cosine distance and extreme learning machines

Abstract This paper presents a fast algorithm and an accelerated toolbox 1 for data visualization. The visualization is stated as an assignment problem between data samples and the same number of given visualization points. The mapping function is approximated by an Extreme Learning Machine, which provides an error for a current assignment. This work presents a new mathematical formulation of the error function based on cosine similarity. It provides a closed form equation for a change of error for exchanging assignments between two random samples (called a swap), and an extreme speed-up over the original method even for a very large corpus like the MNIST Handwritten Digits dataset. The method starts from random assignment, and continues in a greedy optimization algorithm by randomly swapping pairs of samples, keeping the swaps that reduce the error. The toolbox speed reaches a million of swaps per second, and thousands of model updates per second for successful swaps in GPU implementation, even for very large dataset like MNIST Handwritten Digits.