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  • 1.
    Bokrantz, Rasmus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.
    Fredriksson, Albin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. RaySearch Laboratories, Sweden.
    Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization2017In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 262, no 2, p. 682-692Article in journal (Refereed)
    Abstract [en]

    We provide necessary and sufficient conditions for robust efficiency (in the sense of Ehrgott et al., 2014) to multiobjective optimization problems that depend on uncertain parameters. These conditions state that a solution is robust efficient (under minimization) if it is optimal to a strongly increasing scalarizing function, and only if it is optimal to a strictly increasing scalarizing function. By counterexample, we show that the necessary condition cannot be strengthened to convex scalarizing functions, even for convex problems. We therefore define and characterize a subset of the robust efficient solutions for which an analogous necessary condition holds with respect to convex scalarizing functions. This result parallels the deterministic case where optimality to a convex and strictly increasing scalarizing function constitutes a necessary condition for efficiency. By a numerical example from the field of radiation therapy treatment plan optimization, we illustrate that the curvature of the scalarizing function influences the conservatism of an optimized solution in the uncertain case.

  • 2. Carlsson, Mats
    et al.
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Larson, Jeffrey
    Scheduling double round-robin tournaments with divisional play using constraint programming2017In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 259, no 3, p. 1180-1190Article in journal (Refereed)
    Abstract [en]

    We study a tournament format that extends a traditional double round-robin format with divisional single round-robin tournaments. Elitserien, the top Swedish handball league, uses such a format for its league schedule. We present a constraint programming model that characterizes the general double round-robin plus divisional single round-robin format. This integrated model allows scheduling to be performed in a single step, as opposed to common multistep approaches that decompose scheduling into smaller problems and possibly miss optimal solutions. In addition to general constraints, we introduce Elitserien-specific requirements for its tournament. These general and league-specific constraints allow us to identify implicit and symmetry-breaking properties that reduce the time to solution from hours to seconds. A scalability study of the number of teams shows that our approach is reasonably fast for even larger league sizes. The experimental evaluation of the integrated approach takes considerably less computational effort to schedule Elitserien than does the previous decomposed approach.

  • 3.
    Danielson, Mats
    et al.
    KTH, School of Information and Communication Technology (ICT), Computer and Systems Sciences, DSV.
    Ekenberg, Love
    KTH, School of Information and Communication Technology (ICT), Computer and Systems Sciences, DSV.
    Computing upper and lower bounds in interval decision trees2007In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 181, no 2, p. 808-816Article in journal (Refereed)
    Abstract [en]

    This article presents algorithms for computing optima in decision trees with imprecise probabilities and utilities. In tree models involving uncertainty expressed as intervals and/or relations, it is necessary for the evaluation to compute the upper and lower bounds of the expected values. Already in its simplest form, computing a maximum of expectancies leads to quadratic programming (QP) problems. Unfortunately, standard optimization methods based on QP (and BLP - bilinear programming) are too slow for the evaluation of decision trees in computer tools with interactive response times. Needless to say, the problems with computational complexity are even more emphasized in multi-linear programming (MLP) problems arising from multi-level decision trees. Since standard techniques are not particularly useful for these purposes, other, non-standard algorithms must be used. The algorithms presented here enable user interaction in decision tools and are equally applicable to all multi-linear programming problems sharing the same structure as a decision tree.

  • 4. Fampa, Marcia
    et al.
    Luke, Daniela
    Wang, Fei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wolkowicz, Henry
    Parametric Convex Quadratic Relaxation of the Quadratic Knapsack Problem2019In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 281, no 1, p. 36-49Article in journal (Refereed)
    Abstract [en]

    We consider a parametric convex quadratic programming (CQP) relaxation for the quadratic knapsack problem (QKP). This relaxation maintains partial quadratic information from the original QKP by perturbing the objective function to obtain a concave quadratic term. The nonconcave part generated by the perturbation is then linearized by a standard approach that lifts the problem to matrix space. We present a primal-dual interior point method to optimize the perturbation of the quadratic function, in a search for the tightest upper bound for the QKP. We prove that the same perturbation approach, when applied in the context of semidefinite programming (SDP) relaxations of the QKP, cannot improve the upper bound given by the corresponding linear SDP relaxation. The result also applies to more general integer quadratic problems. Finally, we propose new valid inequalities on the lifted matrix variable, derived from cover and knapsack inequalities for the QKP, and present separation problems to generate cuts for the current solution of the CQP relaxation. Our best bounds are obtained alternating between optimizing the parametric quadratic relaxation over the perturbation and applying cutting planes generated by the valid inequalities proposed.

  • 5. Lahdelma, Risto
    et al.
    Miettinen, Kaisa
    Helsinki School of Economics.
    Salminen, Pekka
    School of Business and Economics, University of Jyväskylä.
    Reference Point Approach for Multiple Decision Makers2005In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 164, no 3, p. 785-791Article in journal (Refereed)
    Abstract [en]

    We consider multiple criteria decision-making problems where a group of decision-makers wants to find the most preferred solution from a discrete set of alternatives. We develop a method that uses achievement functions for charting subsets of reference points that would support a certain alternative to be the most preferred one. The resulting descriptive information is provided to the decision-makers in the form of reference acceptability indices and central reference points for each decision alternative. Then, the decision-makers can compare this information with their own preferences. We demonstrate the use of the method using a strategic multiple criteria decision model for an electricity retailer.

  • 6.
    Lundqvist, L.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
    Mattsson, Lars-Göran
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
    Transportation systems and residential location1983In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 12, p. 279-294Article in journal (Refereed)
  • 7.
    Mazidi, Peyman
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power and Energy Systems. Research Institute for Technology (IIT), Comillas Pontifical University, Madrid 28015, Spain.
    Tohidi, Yaser
    KTH, School of Electrical Engineering (EES), Electric Power and Energy Systems.
    Ramos, Andres
    Sanz-Bobi, Miguel A.
    Profit-maximization generation maintenance scheduling through bi-level programming2018In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 264, no 3, p. 1045-1057Article in journal (Refereed)
    Abstract [en]

    This paper addresses the generation maintenance scheduling (GMS) dilemma in a deregulated power system. At first, under a centralized cost minimization framework, a GMS is formulated and set as the benchmark (cost-minimization GMS). Then, the cost-minimization is changed into a profit-maximization problem of generation companies (GENCOs) and the GMS is developed as a bi-level optimization. Karush-Kuhn-Tucker conditions are applied to transform the bi-level into a single-level mixed-integer linear problem and subsequently, Nash equilibrium is obtained as the final solution for the GMS under a deregulated market (profit-maximization GMS). Moreover, to incorporate reliability and economic regulatory constraints, two rescheduling signals (incentive and penalty) are considered as coordination processes among GENCOs and independent system operators. These signals are based on energy-not-supplied and operation cost, and ensure that the result of profit-maximization GMS is in the given reliability and social cost limits, respectively. These limits are obtained from the cost-minimization GMS. Lastly, the model is evaluated on a test system. The results demonstrate applicability and challenges in GMS problems. 

  • 8.
    Miettinen, Kaisa
    et al.
    University of Jyväskylä.
    Molina, Julián
    University of Málaga, Málaga, Spain.
    González, Mercedes
    University of Málaga, Málaga, Spain.
    Hernández-Díaz, Alfredo
    Pablo de Olavide University, Seville, Spain.
    Caballero, Rafael
    University of Málaga, Málaga, Spain.
    Using Box Indices in Supporting Comparison in Multiobjective Optimization2009In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 197, no 1, p. 17-24Article in journal (Refereed)
    Abstract [en]

    Because of the conflicting nature of criteria or objectives, solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question. Due to the difficulties of dealing with multiple objectives, the way information is presented plays a very important role. Questions posed to the decision maker must be simple enough and information shown must be easy to understand. For this purpose, visualization and graphical representations can be useful and constitute one of the main tools used in the literature. In this paper, we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives. Box indices are an intelligible and easy to handle way to represent data. They are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way.

  • 9.
    Miettinen, Kaisa
    et al.
    Helsinki School of Economics.
    Mäkelä, Marko M.
    Department of Mathematical Information Technology, University of Jyväskylä.
    Synchronous approach in interactive multiobjective optimization2006In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 170, no 3, p. 909-922Article in journal (Refereed)
    Abstract [en]

    We introduce a new approach in the methodology development for interactive multiobjective optimization. The presentation is given in the context of the interactive NIMBUS method, where the solution process is based on the classification of objective functions. The idea is to formulate several scalarizing functions, all using the same preference information of the decision maker. Thus, opposed to fixing one scalarizing function (as is done in most methods), we utilize several scalarizing functions in a synchronous way. This means that we as method developers do not make the choice between different scalarizing functions but calculate the results of different scalarizing functions and leave the final decision to the expert, the decision maker. Simultaneously, (s)he obtains a better view of the solutions corresponding to her/his preferences expressed once during each iteration.

    In this paper, we describe a synchronous variant of the NIMBUS method. In addition, we introduce a new version of its implementation WWW-NIMBUS operating on the Internet. WWW-NIMBUS is a software system capable of solving even computationally demanding nonlinear problems. The new version of WWW-NIMBUS can handle versatile types of multiobjective optimization problems and includes new desirable features increasing its user-friendliness.

  • 10.
    Miettinen, Kaisa
    et al.
    Helsinki School of Economics.
    Mäkelä, Marko M.
    Department of Mathematical Information Technology, University of Jyväskylä.
    Kaario, Katja
    Department of Mathematical Information Technology, University of Jyväskylä.
    Experiments with classification-based scalarizing functions in interactive multiobjective optimization2006In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 175, no 2, p. 931-947Article in journal (Refereed)
    Abstract [en]

    In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this respect. We also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons.

  • 11.
    Miettinen, Kaisa
    et al.
    Dept. of Mathematical Information Technology, University of Jyväskylä.
    Ruiz, Francisco
    University of Malaga.
    Luque, Mariano
    University of Malaga.
    Eskelinen, Petri
    NAUTILUS Method: An Interactive Technique in Multiobjective Optimization based on the Nadir Point2010In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 206, no 2, p. 426-434Article in journal (Refereed)
    Abstract [en]

    Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates.

  • 12.
    Moiseeva, Ekaterina
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power and Energy Systems.
    Wogrin, Sonja
    Universidad Pontificia Comillas.
    Hesamzadeh, Mohammad Reza
    KTH, School of Electrical Engineering (EES), Electric Power and Energy Systems.
    Generation Flexibility in Ramp Rates: Strategic Behavior and Lessons for Electricity Market Design2017In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 261, no 2, p. 755-771Article in journal (Refereed)
    Abstract [en]

    A ramp rate usually defines the speed at which an electric power producer can decrease or increase its production in limited time. The availability of fast-ramping generators significantly affects the economic dispatch, especially in the systems with high penetration of intermittent energy sources, e.g. wind power, since the fluctuations in supply are common and sometimes unpredictable. One of the regulatory practices of how to impel generators to provide their true ramp rates is to separate the stages of submitting the bids on ramp rate and production. In this paper we distinguish two types of market structures: one-stage – when electric power producers are deciding their production and ramp rate at the same time, or two-stage – when generators decide their ramp rate first, and choose their production levels at the second stage. We employ one-stage and two-stage equilibrium models respectively to represent these market setups and use a conjectured price response parameter ranging from perfect competition to the Cournot oligopoly to investigate the effect of the market competition structure on the strategic decisions of the generators. We compare these two market setups in a symmetric duopoly case with two time periods and prove that in the two-stage market setup the level of ramp rate is independent of the strategic behavior in the spot market and generally lower than the one offered in the one-stage setup. We also show that the ramp-rate levels in one- and two-stage models coincide at the Cournot oligopoly. We extend the model to asymmetry, several load periods, portfolio bidding, and uncertainty, and show that withholding the ramp rate still occurs in both models. Our findings prove that market regulators cannot rely on only separating the decision stages as an effective measure to mitigate market power and in certain cases it may lead to an adverse effect.

  • 13. Skorin-Kapov, Nina
    et al.
    Furdek, Marija
    Aparicio Pardo, Ramon
    Pavon Marino, Pablo
    Wavelength assignment for reducing in-band crosstalk attack propagation in optical networks: ILP formulations and heuristic algorithms2012In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 222, no 3, p. 418-429Article in journal (Refereed)
1 - 13 of 13
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