## Welcome to THE OSE GROUP

The Optimization and Systems Engineering (OSE) group at Åbo Akademi University is an interdisciplinary research group focusing on theory, methods and algorithms in systems engineering, optimization and statistics, and their applications in science and engineering.

OSE bridges the systems engineering, systems theory and mathematical disciplines at ÅAU, and the OSE group represents the kernel of expertise in this field at the University.

The group was appointed a Center of Excellence within research at the university for the time-period 2010-2014.

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## ONGOING RESEARCH

I´m working on global optimization of MINLP problems containing signomial functions. This is an important class of problems since they are quite general, and appear in many different types of applications. However, since signomial functions are generally nonconvex, these problems are difficult to solve.

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My research pertains to creating and improving algorithms that find the undirected graphical model which best represents the dependence structure of a multidimensional probability distribution. Such representations combine probability theory and graph theory. The research also aims to improve algorithms for data clustering, and for each data cluster find the graphical model that best represents the dependence structure within the given cluster.

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One of the research areas in the OSE group is to apply optimization methods on large scale industrial production planning problems. The goal is to create accurate and effective optimization models for various industries in order to improve productivity and minimize costs throughout the supply chain.

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The Coulomb glass is a model for a disordered material, where the conduction electrons are localized to impurity sites and the electrons strongly interact with each other [1,2]. Given n possible sites where the k electrons can be localized, the problem is to find the electron configuration that minimizes the total energy of the system. A certain configuration of electrons in a material gives rise to a specific total energy of the system.

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I study infinite-dimensional linear systems from an input/output free perspective, mainly using the general but still well-structured class of passive state/signal systems. My main interests are the basic properties, realization theory and (rather general) interconnection theory of continuous-time state/signal systems. On a longer term, I am also interested in extending the state/signal theory to non-linear systems where this is feasible.

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My work focuses on global optimization in nonconvex mathematical programming (NLPs, MINLPs). Algorithms for such problems usually include an element of branch-and-bound. I study various convex relaxations and the quality of the lower bounds they generate. I am particularly interested in twice differentiable constraint functions. The first and second order derivatives (gradient and Hessian) give enough information to construct convex underestimators of such expressions.

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In research and industry the need to solve complex problems is evident and the use of optimization often provides a solution. A researcher might gain insights by solving a problem while an industry might find more efficient operational solutions. Therefore, it is important that the development in the optimization field is made accessible to its practitioners. The advances in optimization consist of theoretical findings that improve methods and models, as well as, the increase in computing power. Optimization platforms like AIMMS, AMPL and GAMS provide the interface to the optimization methods.

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Many real world problems can be formulated as quadratic assignment problems. These problems arise in economics, archeology, electronics, facility layout and many more different fields of research. Some real-life examples:

-Backboard Wiring. Minimize the total wiring between components on a backboard.

-Hospital Design. Determine where to place the different wards in a hospital to minimize moving of the patients.

-Gate Assignment. Minimize the total amount passengers have to walk between gates.

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My research focuses on using support vector machines for identification of a dynamical system from experimental data, which forms an important problem in various control and signal processing tasks. Support vector Regression is a promising linear and nonlinear modeling method that has been found to perform very well in many fields, and has a powerful potential to be applied in system identification.
An important part of my research consists of developing identification methods for hybrid and switching systems, for which efficient general identification methods are largely lacking, especially for nonlinear systems.

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My research focuses on designing nonlinear optimization tools and vector-valued time series algorithms on parallel computers. The computational resources can be linked as support libraries to the Genetic Hybrid Algorithm (GHA). I have been developing GHA since the beginning of 2000. I have shown that the complexity of binary mixed-integer-nonlinear problems can be significantly reduced on parallel processors using asynchronic mesh interrupts and binary coding of local box constraints.

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I am generalizing the ECP method and it's variants to cover nonsmooth problems. The work consists of creating appropriate modifications to the algorithm and proving convergence of the resulting algorithm.

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My research focuses on solving binary quadratic optimization problems. Binary quadratic problems arise for example in theoretical physics when looking into disordered materials. The Coulomb glass is a model for a disordered material, where the electrons are localized to impurity sites and the electrons strongly interact with each other. We try to find the ground state of these materials, that is the electron configuration with the lowest total energy.

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My research interests are in the area of approximation theory in the complex unit disk. For example, finite Blaschke products in connection with constructive methods for rational Chebyshev approximation, and various types of rational interpolation problems, so-called Nevanlinna-Pick interpolation, in the unit disk. Applications of such methods can be found in H^{∞}-optimization and control theory (model reduction, model matching theory etc.).

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One problem from my field of physics can be formulated as an optimization problem - finding the ground state of a Coulomb glass. The Coulomb glass ground state can then be studied with methods from the field of global optimization

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My research pertains to developing the theory and designing inference algorithms for a class of probabilistic models called context specific graphical models.

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I study modeling and identification of periodically time-varying dynamical systems. Such systems exhibit a significantly more complicated dynamic behaviour than non-periodic systems.

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Cylinder balancing is one important application of intelligent control for internal combustion engines, where advances have been made lately. Apart from reducing emissions, cylinder balancing serves the purpose of minimizing torsional vibrations that propagate through the engine crankshaft.

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