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| 2. |
- Fotedar, Sunney, 1989
(författare)
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Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops
- 2023
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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. |
- Gourevitch, D., et al.
(författare)
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EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
- 2021
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Ingår i: Representation Theory. - : American Mathematical Society (AMS). - 1088-4165. ; 25, s. 481-507
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Tidskriftsartikel (refereegranskat)abstract
- We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
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| 4. |
- Yun, Yixiao, 1987, et al.
(författare)
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Maximum-Likelihood Object Tracking from Multi-View Video by Combining Homography and Epipolar Constraints
- 2012
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Ingår i: 6th ACM/IEEE Int'l Conf on Distributed Smart Cameras (ICDSC 12), Oct 30 - Nov.2, 2012, Hong Kong. - 9781450317726 ; , s. 6 pages-
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Konferensbidrag (refereegranskat)abstract
- This paper addresses problem of object tracking in occlusion scenarios, where multiple uncalibrated cameras with overlapping fields of view are used. We propose a novel method where tracking is first done independently for each view and then tracking results are mapped between each pair of views to improve the tracking in individual views, under the assumptions that objects are not occluded in all views and move uprightly on a planar ground which may induce a homography relation between each pair of views. The tracking results are mapped by jointly exploiting the geometric constraints of homography, epipolar and vertical vanishing point. Main contributions of this paper include: (a) formulate a reference model of multi-view object appearance using region covariance for each view; (b) define a likelihood measure based on geodesics on a Riemannian manifold that is consistent with the destination view by mapping both the estimated positions and appearances of tracked object from other views; (c) locate object in each individual view based on maximum likelihood criterion from multi-view estimations of object position. Experiments have been conducted on videos from multiple uncalibrated cameras, where targets experience long-term partial or full occlusions. Comparison with two existing methods and performance evaluations are also made. Test results have shown effectiveness of the proposed method in terms of robustness against tracking drifts caused by occlusions.
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| 5. |
- Fridenfalk, Mikael, 1971-
(författare)
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Cellular Automata in Modular Space : Rigid Systems – Volume I – Number I
- 2015. - 1
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book series presents a new type of cellular automata for 2D pattern generation, characterized by a high reproduction rate, in combination with the application of a small-sized 2D modular square lattice. The presented patterns are in the spirit of mathematical minimalism, generated from rudimentary kernels and a minimal set of rules. In similarity with fractals, this new concept could provide for the generation of patterns and geometries with applications in areas such as, visual arts, logo design, architecture, and game design.
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| 6. |
- Grezet, Matthias, et al.
(författare)
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Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes
- 2019
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Ingår i: IEEE Transactions on Information Theory. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9448 .- 1557-9654. ; 65:10, s. 6089-6100
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Tidskriftsartikel (refereegranskat)abstract
- Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been carried out to understand the optimal rate-distance tradeoff, but only recently the size of the alphabet has been taken into account. In this paper, a novel definition of locality is proposed to keep track of the precise number of nodes required for a local repair when the repair sets do not yield MDS codes. Then, a new alphabet-dependent bound is derived, which applies both to the new definition and the initial definition of locality. The new bound is based on consecutive residual codes and intrinsically uses the Griesmer bound. A special case of the bound yields both the extension of the Cadambe-Mazumdar bound and the Singleton-type bound for codes with locality (r, delta), implying that the new bound is at least as good as these bounds. Furthermore, an upper bound on the asymptotic rate-distance tradeoff of LRCs is derived, and yields the tightest known upper bound for large relative minimum distances. Achievability results are also provided by deriving the locality of the family of Simplex codes together with a few examples of optimal codes.
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| 7. |
- Fotedar, Sunney, 1989, et al.
(författare)
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Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
- 2019
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Ingår i: Proceedings of the 10th Aerospace Technology Congress. - : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789175190068 ; , s. 183-188
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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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| 8. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Simultaneous scheduling of replacement and repair of common components in operating systems A multi-objective mathematical optimization model
- 2022
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 0254-5330 .- 1572-9338. ; 322, s. 147-65
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Tidskriftsartikel (refereegranskat)abstract
- In order for a system to stay operational, its components need maintenance. We consider two stakeholders-a system operator and a maintenance workshop-and a contract governing their joint activities. Components in the operating systems that are to be maintained are sent to the maintenance workshop, which should perform all maintenance activities on time in order to satisfy the contract. The maintained components are then sent back to be used in the operating systems. Our modeling of this system-of-systems includes stocks of damaged and repaired components, the workshop scheduling, and the planning of preventive maintenance for the operating systems. Our modeling is based on a mixed-binary linear optimization (MBLP) model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We generalize and extend this model with the flow of components through the workshop, including the stocks of spare components. The resulting scheduling model-a mixed-integer optimization (MILP) model-is then utilized to optimize the main contract in a bi-objective setting: maximizing the availability of repaired (or new) components and minimizing the costs of maintaining the operating systems over the time horizon. We analyze the main contract and briefly discuss a turn-around time contract. Our results concern the effect of our modeling on the levels of the stocks of components over time, in particular minimizing the risk for lack of spare components.
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| 9. |
- Åblad, Edvin, 1991, et al.
(författare)
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Exact makespan minimization of unrelated parallel machines
- 2021
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Ingår i: Open Journal of Mathematical Optimization. - : Cellule MathDoc/CEDRAM. - 2777-5860. ; 2
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Tidskriftsartikel (refereegranskat)abstract
- We study methods for the exact solution of the unrelated parallel machine problem with makespan minimization, generally denoted as R||Cmax. Our original application arises from the automotive assembly process where tasks needs to be distributed among several robots. This involves the solutions of several R||Cmax instances, which proved hard for a MILP solver since the makespan objective induces weak LP relaxation bounds. To improve these bounds and to enable the solution of larger instances, we propose a branch–and–bound method based on a Lagrangian relaxation of the assignment constraints. For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. Our computational studies indicate that the proposed algorithm is competitive with state-of-the-art methods on different types of instances. Moreover, the impact of each proposed feature is analysed.
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