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1.
  • Ivanenko, Yevhen, et al. (författare)
  • Quasi-Herglotz functions and convex optimization
  • 2020
  • Ingår i: Royal Society Open Science. - : The Royal Society Publishing. - 2054-5703. ; 7:1, s. 1-15
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.
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2.
  • Fotedar, Sunney, 1989 (författare)
  • Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops
  • 2023
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item , multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory. In Paper I , we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II , we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III , we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV , using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap .
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3.
  • Laksman, Efraim, 1983, et al. (författare)
  • The stochastic opportunistic replacement problem, part III: improved bounding procedures
  • 2020
  • Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.
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4.
  • Pereira, Mike, 1992, et al. (författare)
  • Parameter and density estimation from real-world traffic data: A kinetic compartmental approach
  • 2022
  • Ingår i: Transportation Research Part B: Methodological. - : Elsevier BV. - 0191-2615. ; 155, s. 210-239
  • Tidskriftsartikel (refereegranskat)abstract
    • The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is proposed aiming at reproducing the evolution in time of the density of vehicles along a road, as observed in the measurements. This system is formulated as a chemical reaction network where road cells are interpreted as compartments, the transfer of vehicles from one cell to the other is seen as a chemical reaction between adjacent compartment and the density of vehicles is seen as a concentration of reactant. Several degrees of flexibility on the parameters of this system, which basically consist of the reaction rates between the compartments, can be considered: a constant value or a function depending on time and/or space. Density measurements coming from trajectory data are then interpreted as observations of the states of this system at consecutive times. Optimal reaction rates for the system are then obtained by minimizing the discrepancy between the output of the system and the state measurements. This approach was tested both on simulated and real data, proved successful in recreating the complexity of traffic flows despite the assumptions on the flux-density relation.
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5.
  • Nedic, Mitja, et al. (författare)
  • Herglotz functions and applications in electromagnetics
  • 2020
  • Ingår i: Advances in Mathematical Methods for Electromagnetics. - : Institution of Engineering and Technology. - 9781785613845 - 9781785613852 ; , s. 491-514
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
    • Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.
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6.
  • Y Banaem, Hossein, et al. (författare)
  • Brain tumor modeling : glioma growth and interaction with chemotherapy
  • 2011
  • Ingår i: International Conference on Graphic and Image Processing (ICGIP 2011). - : SPIE. ; 8285
  • Konferensbidrag (refereegranskat)abstract
    • In last decade increasingly mathematical models of tumor growths have been studied, particularly on solid tumors which growth mainly caused by cellular proliferation. In this paper we propose a modified model to simulate the growth of gliomas in different stages. Glioma growth is modeled by a reaction-advection-diffusion. We begin with a model of untreated gliomas and continue with models of polyclonal glioma following chemotherapy. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter. Tumor growth is characterized by a dangerous change in the control mechanisms, which normally maintain a balance between the rate of proliferation and the rate of apoptosis (controlled cell death). Result shows that this model closes to clinical finding and can simulate brain tumor behavior properly.
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7.
  • Foda, O., et al. (författare)
  • Overlaps of partial Neel states and Bethe states
  • 2016
  • Ingår i: Journal of Statistical Mechanics. - : IOP Publishing. - 1742-5468 .- 1742-5468.
  • Tidskriftsartikel (refereegranskat)abstract
    • Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.
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8.
  • Ljunggren Söderman, Maria, 1967, et al. (författare)
  • Integrated Economic and Environmental Assessment of Waste Policy Instruments
  • 2016
  • Ingår i: Sustainability. - : MDPI AG. - 2071-1050. ; 8:5
  • Tidskriftsartikel (refereegranskat)abstract
    • The need for new policy instruments supporting the on-going transition from end-of-pipe waste treatment to resource management has been recognized in European policy. Instruments need to be carefully assessed before implementation to promote the desired changes and avoid problem shifting. Mathematical models may assist policy makers in such assessments. This paper presents a set of soft-linked models for assessing the economic and environmental impacts of policy instruments for both the prevention and management of waste and discusses its strengths and limitations. Consisting of (1) a macro-economic model, (2) a systems engineering model for waste management and (3) a life cycle assessment model for waste management, the set is primarily suited to assessing market-based instruments and environmental regulations. Considerable resources were needed for developing and using the set, and there are clear limits as to what can be addressed. However, if only one of the models had been used, neither the range of instruments nor the scope of impacts would have been possible to cover. Furthermore, soft-linked models allow many disciplines to contribute within one harmonized framework. Such integrated assessments may become increasingly useful for continuing the implementation of policy for sustainable governance of society's material resources.
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9.
  • Berbyuk, Viktor, 1953 (författare)
  • Dynamics and optimal control of biotechnical systems "Man-Prosthesis"
  • 1997
  • Ingår i: IUTAM Symposium on Interaction Between Dynamics and Control in Advanced Mechanical Systems, Ed. D. van Campen, Kluwer Academic Publishers, 1997. - Dordrecht : Springer Netherlands. ; , s. 35-42
  • Konferensbidrag (refereegranskat)abstract
    • In the paper, a mathematical model is proposed for investigating the controlled motion of human locomotion system (HLS) with an above-knee prosthesis. To provide insight into the interaction between dynamics and control in biotechnical system Man-Prosthesis the energy­ optimal control problem of the HLS wearing a lower limb prosthesis has been con­sidered. The algorithm is based on special conversion of the optimal control problem for a nonlinear dynamical system which models HLS into a standard nonlinear programming problem. A number of energy-optimal control problems of hu­man locomotion with an artificial leg, and optimization problems for the constructive parameters of the prostheses under different boundary conditions and constraints have been solved. The numerical results obtained were compared with experimental data for normal human locomotion. The energy-optimal elastic and viscoelastic characteristics of the ankle and knee joints of the prostheses have been determined.
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10.
  • Fotedar, Sunney, 1989, et al. (författare)
  • Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
  • 2019
  • Ingår i: Proceedings of the 10th Aerospace Technology Congress. - : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789175190068 ; , s. 183-188
  • Konferensbidrag (refereegranskat)abstract
    • In the aerospace industry, with low volumes and many products, there is a critical need to efficiently use available manufacturing resources. Currently, at GKN Aerospace, resource allocation decisions that in many cases will last for several years are to some extent made with a short-term focus so as to minimize machining time, which results in a too high load on the most capable machines, and too low load on the less capable ones. This creates an imbalance in capacity utilization that leads to unnecessary queuing at some machines, resulting in long lead times and in an increase in tied-up capital. Tactical resource allocation on the medium to long-range planning horizon (six months to several years) aims to address this issue by allocating resources to meet the predicted future demand as effectively as possible, in order to ensure long range profitability. Our intent is to use mathematical optimization to find the best possible allocations.
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