Tapio Westerlund

Tapio Westerlund
Åbo Akademi University · Faculty of Science and Engineering

Professor

About

165
Publications
33,506
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Introduction
Professor Emeritus of Process Design and Adjunct Professor in Mathematics at Åbo Akademi University as well as Adjunct Professor of Applied Mathematics at the University of Turku.

Publications

Publications (165)
Article
Full-text available
In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linea...
Article
Full-text available
In this paper we show that simple projections can improve the algorithmic performance of cutting plane-based optimization methods. Projected cutting planes can, for example, be used as alternatives to standard cutting planes or supporting hyperplanes in the extended cutting plane (ECP) method. In the paper we analyse the properties of such an algor...
Preprint
Full-text available
In this paper, a recently released open-source solver for convex mixed-integer nonlinear programming (MINLP) is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) solver combines a dual strategy based on polyhedral outer approximations (POA) with several primal heuristics. The outer approximation is achieved by expressing the nonlinea...
Chapter
In this chapter we review some deterministic solution methods for convex mixed integer nonsmooth optimization problems. The methods are branch and bound, outer approximation, extended cutting plane, extended supporting hyperplane and extended level bundle method. Nonsmoothness is taken into account by using Clarke subgradients as a substitute for t...
Article
Full-text available
Solution methods for convex mixed integer nonlinear programming (MINLP) problems have, usually, proven convergence properties if the functions involved are differentiable and convex. For other classes of convex MINLP problems fewer results have been given. Classical differential calculus can, though, be generalized to more general classes of functi...
Article
Full-text available
Several deterministic methods for convex mixed integer nonlinear programming generate a polyhedral approximation of the feasible region, and utilize this approximation to obtain trial solutions. Such methods are, e.g., outer approximation, the extended cutting plane method and the extended supporting hyperplane method. In order to obtain the optima...
Article
Here we present a center-cut algorithm for convex mixed-integer nonlinear programming (MINLP) that can either be used as a primal heuristic or as a deterministic solution technique. Like several other algorithms for convex MINLP, the center-cut algorithm constructs a linear approximation of the original problem. The main idea of the algorithm is to...
Article
In this paper, a framework for reformulating nonconvex mixed-integer nonlinear programming (MINLP) problems containing twice-differentiable (C²) functions to convex relaxed form is discussed. To provide flexibility and for utilizing more effective transformation strategies, the twice-differentiable functions can be partitioned into convex, signomia...
Article
Full-text available
In this paper, we generalize the extended supporting hyperplane algorithm for a convex continuously differentiable mixed-integer nonlinear programming problem to solve a wider class of nonsmooth problems. The generalization is made by using the subgradients of the Clarke subdifferential instead of gradients. Consequently, all the functions in the p...
Article
In this paper we derive and study a reformulation technique for general 0-1 quadratic programs (QP) that uses diagonal as well as non-diagonal perturbation of the objective function. The technique is an extension of the Quadratic Convex Reformulation (QCR) method developed by Billionnet and co-workers, adding non-diagonal perturbations whereas QCR...
Article
The reactions of soluble and reactive solids with components in the liquid phase are of high relevance in the field of chemical engineering. A mathematical model was recently developed applying an extended film theory, where the reactive solid material dissolves in the liquid phase and diffuses through a dynamic liquid film surrounding the particle...
Article
Stricter emission regulations require the improvement of SO2 scrubbing efficiency and energy usage. In this work, the dissolution of two very pure limestone samples under the effect of ultrasound (US) was compared to their dissolution in silent conditions. The aim of this work was to assess experimentally whether this method could be adopted as a p...
Chapter
In this paper a new open source solver for convex mixed-integer nonlinear programming (MINLP) implemented in Wolfram Mathematica is described. The Supporting Hyperplane Optimization Toolkit (SHOT) solver implements two methods for MINLP based on polyhedral outer approximations, namely the Extended Supporting Hyperplane (ESH) and Extended Cutting Pl...
Chapter
In this paper, we present a new algorithm for solving convex mixed-integer nonlinear programming problems. Similarly to other linearization-based methods, the algorithm generates a polyhedral approximation of the feasible region. The main idea behind the algorithm is to use a different approach for obtaining trial solutions. Here trial solutions ar...
Article
The reactivity of soluble solid particles with liquids was described with extended film theory: the solid material dissolves in the liquid phase and diffuses through the liquid film surrounding the particle. In both the liquid film and bulk liquid, chemical reactions take place. The solid particle shrinks due to the dissolution and consequent react...
Article
Full-text available
BACKGROUND This study presents Supercritical Water Gasification (SCWG) as an alternative treatment process for black liquor: investigating the impacts of black liquor constituents, temperature and catalyst. The preliminary experiments include SCWG of sucrose and isoeugenol in stainless steel reactor, as model compounds of sugars and lignin. Then, t...
Article
Full-text available
Carbonate rocks are commonly utilized in Wet Flue Gas Desulfurization, WFGD, because of their capability to release calcium ions and precipitate as solid gypsum in an acidic environment. Studies on the reactivity of carbonate rocks and dissolution models can be employed for optimizing the WFGD process. The correct evaluation of limestone reactivity...
Chapter
Full-text available
Ji et al. (2012) introduced a new reformulation technique for general 0-1 quadratic programs. They did not name it so we call it Non-Diagonal Quadratic Convex Reformulation (NDQCR). The reformulation technique is based on the Quadratic Convex Reformulation method developed by Billionnet et al. (2009, 2012, 2013). In this paper we test the NDQCR met...
Article
Branch-and-bound in combination with convex underestimators constitute the basis for many algorithms in global nonconvex mixed-integer nonlinear programming (MINLP). Another option is to rely on reformulation-based techniques such as the α signomial global optimization (αSGO) algorithm, where power and exponential transformations for signomial or p...
Conference Paper
Biomass conversion in supercritical water represents one of the emerging areas of the reaction engineering. Additionally, Supercritical Water Gasification, SCWG, offers great possibilities for new ways of reactors design and operations. Reactive separation processes represent the future in this sense. In our studies experiments were done on SCWG of...
Article
Dissolution rates of two very pure limestone samples were measured experimentally by means of the pH-stat method under conditions where mechanical stirring did not affect the rates considerably. The experimental results were modeled mathematically by considering the surface areas of the particles changing dynamically through the reaction; moreover,...
Article
A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or qua...
Article
Background Stricter SO2 emission regulations for power plants and maritime transport encourage for a better understanding of the phenomena involved in wet flue gas desulfurization (WFGD) where limestone dissolution is regarded as one of the rate determining steps.ResultsThe dissolution kinetics of two limestone samples was studied in the industrial...
Article
Limestone dissolution has been widely studied because of its importance in different fields, a common assumption has been to consider that the roles of mass transport and chemical reaction change as a function of pH. Furthermore, a commonly accepted model for the kinetics has not been presented thus far for a wide pH range. A model which considers...
Article
Full-text available
The knowledge of the spatial solids distribution is important for predicting the performance of various processes carried out in mechanically stirred equipment. In this work, the solid suspension in a stirred tank equipped with PBT and Lightnin A310 impellers is investigated by electrical resistance tomography (ERT). The analysis concerns dense sol...
Article
Full-text available
Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $...
Article
This paper focuses on the formulation and solution of binary quadratic problems. A new metaheuristic approach is presented in order to acquire good solutions. Computational results show that the heuristic solver finds good solutions quite fast. One of the test problems is tai256c, a gray-scale pattern problem by Taillard (1995) found in the QAPLIB...
Article
In this paper we compare two recently described methods for convex underestimation. The first method is a variant of the nondiagonal αBB methods studied by the authors. The second method depends on algebraic characterizations of positive polynomials. Positive polynomials on a compact semi-algebraic set can be decomposed as polynomial terms containi...
Chapter
The signomial global optimization algorithm is a method for solving nonconvex mixed-integer signomial problems to global optimality. A convex underestimation is produced by replacing nonconvex signomial terms with convex underestimators obtained through single-variable power and exponential transformations in combination with linearization techniqu...
Article
Full-text available
In this article, a generalization of the ECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be...
Article
Full-text available
Sulfur dioxide (SO2) is one of the pollutant gases that result from energy conversion by coal and oil combustion. Limestone slurries are widely utilized in wet flue gas desulfurization (WFGD) processes. The evaluation of the reagent's reactivity is fundamental for process design and plant operation. The comparison of different limestone and dolomit...
Article
Full-text available
In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are u...
Article
Anthropogenic sulfur dioxide (SO2) is principally the product of energy conversion through combustion of fossil fuel sources. This pollutant causes acidic rain and can also be harmful for human health. Many means for controlling sulfur dioxide emission are available in the market and have been extensively applied. Among these techniques, wet flue g...
Article
Full-text available
Different environmental processes utilize calcium carbonate and sedimentary rocks, for instance sedimentary rocks are used for water purification as filters and utilized also for acid remediation of process waters before being discarded. Additionally sedimentary rocks are used in another very important environmental process, wet Flue Gas Desulfuriz...
Conference Paper
This paper presents an improved as well as a completely new version of a mixed integer linear programming (MILP) formulation for solving the quadratic assignment problem (QAP) to global optimum. Both formulations work especially well on instances where at least one of the matrices is sparse. Modification schemes, to decrease the number of unique el...
Conference Paper
The quadratic assignment problem is a well studied and notoriously difficult combinatorial problem. Recently, a discrete linear formulation of the quadratic assignment problem was presented that solved five previously unsolved instances from the quadratic assignment library, QAPLIB, to optimality. That formulation worked especially well on sparse i...
Conference Paper
The alpha-reformulation (alpha R) technique can be used to transform any nonconvex twice-differentiable mixed-integer nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestima...
Article
Full-text available
Significance It is shown that by reformulating the three-stage multiechelon inventory system with specific exact linearizations, larger problems can be solved directly with mixed-integer linear programming (MILP) without decomposition. The new formulation is significantly smaller in the number of continuous variables and constraints. An MILP undere...
Article
Full-text available
9 Different environmental processes utilize calcium carbonate and sedimentary rocks, for instance sedimentary 10 rocks are used for water purification as filters and utilized also for acid remediation of process waters before 11 being discarded. Additionally sedimentary rocks are used in another very important environmental process, wet 12 Flue Gas...
Article
Every year a significant amount of Sulfur Dioxide (SO 2) is discarded in the atmosphere. SO 2 can cause indirect ozone depletion, it leads to the formation of acidic rains and a large number of diseases are provoked by contact with sulfur dioxide. Limestone (CaCO 3) is widely utilized in Flue Gas Desulfurization (FGD) processes because of its abili...
Chapter
This paper focuses on the formulation and solution of certain quadratic assignment problem (QAP). A new mixed integer quadratic programming (MIQP) formulation of the QAP is presented that is especially well suited for solving instances where the flow or distance matrix is of rank-1. Computational experiments are conducted on some special generated...
Article
In this paper we describe a method for obtaining sets of transformations for reformulating a mixed integer nonlinear programming (MINLP) problem containing nonconvex twice- differentiable (C 2) functions to a convex MINLP problem in an extended variable space. The method for obtaining the transformations is based on solving a mixed integer linear p...
Chapter
We present a method to produce convex underestimators of smooth multivariate functions. The most immediate application for such underestimators is branch-and-bound algorithms in global optimization. The method is a generalization of the well-known αBB method. Classical αBB uses univariate quadratic perturbations, the new underestimators may also in...
Chapter
Described in this chapter, is a global optimization algorithm for mixedinteger nonlinear programming problems containing signomial functions. The method obtains a convex relaxation of the nonconvex problem through reformulations using single-variable transformations in combination with piecewise linear approximations of the inverse transformations....
Article
Full-text available
In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a global optimum. It is shown through a counterexampl...
Article
Full-text available
The classical αBB method determines univariate quadratic perturbations that convexify twice continuously differentiable functions. This paper generalizes αBB to additionally consider nondiagonal elements in the perturbation Hessian matrix. These correspond to bilinear terms in the underestimators, where previously all nonlinear terms were separable...
Article
Full-text available
The quadratic assignment problem (QAP) is a challenging combinatorial problem. The problem is NP-hard and in addition, it is considered practically intractable to solve large QAP instances, to proven optimality, within reasonable time limits. In this paper we present an attractive mixed integer linear programming (MILP) formulation of the QAP. We f...
Article
Full-text available
Sedimentary rocks, such as limestone, are widely utilized in flue gas desulfurization (FGD) processes because of their ability to form sulfur compounds. The most common system adopted for FGD is the wet scrubbing process, in which the dissolution rate of sedimentary rocks represents one of the most important factors. Evaluation of the dissolution a...
Article
Sulfur is present in coal and oil and during combustion it is oxidized to sulfur dioxide (SO 2). Limestone, constituted mainly by calcium carbonate, is widely utilized in Flue Gas Desulfurization (FGD) processes because of the ability to capture the sulfur as sulfate salts. The evaluation of limestone reactivity is therefore a key aspect for FGD pr...
Article
Full-text available
In this paper we model and solve a large linear equality constrained 0–1 quadratic programming (QP) problem arising in theoretical physics, more precisely in the study of lightly doped semiconductors: finding the ground state of a Coulomb glass. Semidefinite programming is used for relaxation and then for reformulation. The relaxation gives a lower...
Article
Introduction Mathematical Programming as a Tool for Production Optimization Metsä Tissue Mänttä Mill The MISPT Tool The Mixed-Time MILP Model Illustrative Case Examples Discussion
Conference Paper
By means of supercritical water gasification (SCWG) different types of wet biomass can be gasified resulting in a hydrogen-rich product gas. The product gas can be used as such or be further refined into for example renewable traffic fuels or chemicals. The dry matter content of the feed is preferably 1-20 wt%. In pulp and paper production several...
Article
Full-text available
Supercritical water gasification (SCWG) is a method by which biomass can be converted into a hydrogen-rich gas product. Wet industrial waste streams, which contain both organic and inorganic material, are well suited for treatment by SCWG. In this study, the gasification of two streams of biomass resulting from the pulp and paper industry, black li...
Article
Full-text available
We introduce a new formulation for a cutting stock problem in the stainless steel industry. The formulation extends some previous models developed for the paper industry. In this formulation, mother coils are assumed to have finite lengths, and the widths and lengths of the mother coils are considered variables as well as the lengths of the product...
Article
Full-text available
The well-known αBB method solves very general smooth nonconvex optimization problems. The algorithm works by replacing nonconvex functions with convex underestimators. The approximations are improved by branching and bounding until global optimality is achieved. Applications are abundant in engineering and science. We present a convex formulation i...
Conference Paper
Convex relaxations play an important role in many areas, especially in optimization and particularly in global optimization. In this paper we will consider some special, but fundamental, issues related to convex relaxation techniques in constrained nonconvex optimization. We will especially consider optimization problems including nonconvex inequal...
Conference Paper
In this paper the problem to identify modularity in a complex network is studied. The ability to identify modularity can be vital for a clear understanding of how a complex network is constructed and the interaction in the network. The aim in this study is to compare different solving strategies and find the most appropriate ones to solve this type...
Article
Full-text available
In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for...
Conference Paper
In supercritical water gasification (SCWG) complete gasification of biomass can be achieved resulting in a valuable hydrogen product gas. Potential raw material sources for this process are wet organic waste streams containing more than 80 wt-% water. The large variety of industrial biomass is challenging and needs to be further investigated for fu...
Article
Carbonates are widely used in flue gas desulfurization (FGD) processes because of their ability to form sulfur-carbonate compounds [1]. It is well established that particle size and shape substantially influence the bulk properties of powdered materials, although these characteristics are closely interrelated [2]. In order to evaluate accurately th...
Article
Sedimentary rocks, such as limestone, are widely utilized in Flue Gas Desulfurization (FGD) processes. The study of the dissolution for solid particles involved in FGD is therefore significant for process design and plant operation. The rate of dissolution affects the cost of makeup and waste disposal. For this reason a method to test different qua...
Chapter
In this paper, a method for determining an optimized set of transformations for sig-nomial functions in a nonconvex mixed integer nonlinear programming (MINLP) problem is described. Through the proposed mixed integer linear programming (MILP) problem formulation, a set of single-variable transformations is obtained. By varying the parameters in the...
Conference Paper
In this paper, an implementation of a global optimization framework for Mixed Integer Nonlinear Programming (MINLP) problems containing signomial functions is described. In the implementation, the global optimal solution to a MINLP problem is found by solving a sequence of convex relaxed subproblems overestimating the original problem. The describe...
Article
Large scale scheduling problems are often difficult Mixed Integer Linear Programming (MILP) problems. The large amount of binary variables in a scheduling problem with multiple production lines sets a limit on the problem size which is solvable in a reasonable time. In this paper an efficient continuous time job precedence MILP formulation for a sc...
Article
Full-text available
Different types of underestimation strategies are used in deterministic global optimization. In this paper, convexification and underestimation techniques applicable to problems containing signomial functions are studied. Especially, power transformation and exponential transformation (ET) will be considered in greater detail and some new theoretic...
Article
Full-text available
The development of methods to solve mixed-integer nonlinear programming (MINLP) problems has given rise to new solvers and improved the current ones. In this Article, the focus is set on the MINLP solvers in the General Algebraic Modeling System (GAMS) and especially GAMS/AlphaECP. In this Article, a comprehensive comparison of the MINLP solvers is...
Article
Full-text available
In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, ofte...
Article
Full-text available
Global optimization of mixed integer nonlinear programming (MINLP) problems containing signomial terms is in many cases a difficult task, and many different approaches to solve these problems have been devised. In Westerlund (2005) a method where a relaxed convex relaxation of the original problem is obtained by approximating single-variable transf...