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  • 1.
    Aas, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Limit points of the iterative scaling procedure2014In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 215, no 1, p. 15-23Article in journal (Refereed)
    Abstract [en]

    The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example if the initial matrix is strictly positive, the sequence is convergent. It is known that the sequence has at most two limit points. When these are distinct, convergence to these two points can be slow. We give an efficient algorithm which finds the limit points, invoking the ISP only on subproblems for which the procedure is convergent.

  • 2.
    Borst, Sem
    et al.
    Alcatel-Lucent Bell Labs.
    Hegde, Nidhi
    Orange Labs.
    Proutiere, Alexandre
    Interacting queues with server selection and coordinated scheduling - Application to cellular data networks2009In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 170, no 1, p. 59-78Article in journal (Refereed)
    Abstract [en]

    We consider a system of parallel servers handling users of various classes, whose service rates depend not only on user classes, but also on the set of active servers. We investigate the stability under two types of allocation strategies: (i) server assignment where the users are assigned to servers based on rates, load, and other considerations, and (ii) coordinated scheduling where the activity states of servers are coordinated. We show how the model may be applied to evaluate the downlink capacity of wireless data networks. Specifically, we examine the potential gains in wireless capacity from the two types of resource allocation strategies.

  • 3.
    Carlsson, Fredrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A conjugate-gradient based approach for approximate solutions of quadratic programsIn: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338Article in journal (Refereed)
    Abstract [en]

    This paper deals with numerical behaviour and convergence properties of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.

  • 4.
    Carlsson, Fredrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On column generation approaches for approximate solutions of quadratic programs in intensity-modulated radiation therapy2014In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 223, no 1, p. 471-481Article in journal (Refereed)
    Abstract [en]

    This paper deals with numerical behavior of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.

  • 5.
    Carlsson, Fredrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Rehbinder, Henrik
    RaySearch Labs.
    Eriksson, Kjell
    RaySearch Labs.
    Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem2006In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 148, no 1, p. 81-94Article in journal (Refereed)
    Abstract [en]

    Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included.

    The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition.

  • 6.
    Linusson, Svante
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ryd, Gustav
    Dynamic adjustment: An electoral method for relaxed double proportionality2014In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 215, no 1, p. 183-199Article in journal (Refereed)
    Abstract [en]

    We describe an electoral system for distributing seats in a parliament. It gives proportionality for the political parties and close to proportionality for constituencies. The system suggested here is a version of the system used in Sweden and other Nordic countries with permanent seats in each constituency and adjustment seats to give proportionality on the national level. In the national election of 2010 the current Swedish system failed to give proportionality between parties. We examine here one possible cure for this unwanted behavior. The main difference compared to the current Swedish system is that the number of adjustment seats is not fixed, but rather dynamically determined to be as low as possible and still insure proportionality between parties.

  • 7.
    Mattsson, Lars-Göran
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
    Residential location and school planning in a tightening urban economy1986In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 6, p. 181-200Article in journal (Refereed)
  • 8.
    Miettinen, Kaisa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ruiz, Francisco
    Luque, Mariano
    Improving the Computational Efficiency in a Global Formulation (GLIDE) for Interactive Multiobjective Optimization2012In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 197, no 1, p. 47-70Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a new general formulation for multiobjective optimization that can accommodate several interactive methods of different types (regarding various types of preference information required from the decision maker). This formulation provides a comfortable implementation framework for a general interactive system and allows the decision maker to conveniently apply several interactive methods in one solution process. In other words, the decision maker can at each iteration of the solution process choose how to give preference information to direct the interactive solution process, and the formulation enables changing the type of preferences, that is, the method used, whenever desired. The first general formulation, GLIDE, included eight interactive methods utilizing four types of preferences. Here we present an improved version where we pay special attention to the computational efficiency (especially significant for large and complex problems), by eliminating some constraints and parameters of the original formulation. To be more specific, we propose two new formulations, depending on whether the multiobjective optimization problem to be considered is differentiable or not. Some computational tests are reported showing improvements in all cases. The generality of the new improved formulations is supported by the fact that they can accommodate six interactive methods more, that is, a total of fourteen interactive methods, just by adjusting parameter values.

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