| 11. |
- Karlsson, Carl-Joar, 1995
(författare)
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Game theory and applications
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Individual-level interactions and decisions spread though populations and change the collective-level dynamics in an intricate way. Nevertheless, game theory is well suited for the unification of these viewpoints. This thesis introduces the works The strength of diversity and Decisions and disease: a mechanism for the evolution of cooperation, which show that games have broad applications in population dynamics modeling. In The strength of diversity we calculate the equilibrium strategies of the so-called game of teams. The game of teams is an individual-level competition between teams, and a team's strategy in this context is a distribution of strength over the team members. It turns out that the equilibrium strategies are flat distributions or 'alternating' flat distributions whenever there exists equilibrium strategies. In Decisions and disease: a mechanism for the evolution of cooperation we combine the classic SIR and SIS models from epidemiology with the prisoner's dilemma game. The transmission rate is computed as the average over defecting and cooperating individuals, and the individuals are subjected to a replicator equation that takes into account the portion of infectious members of the population. We compute the steady state solutions and interpret the results.
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| 12. |
- Andersson, Fredrik K., et al.
(författare)
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The mathematics of internet search engines
- 2008
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 13. |
- Laksman, Efraim, 1983, et al.
(författare)
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The stochastic opportunistic replacement problem, part III: improved bounding procedures
- 2020
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
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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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| 14. |
- Britz, Thomas, et al.
(författare)
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Demi-matroids from codes over finite Frobenius rings
- 2015
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 75:1, s. 97-107
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Tidskriftsartikel (refereegranskat)abstract
- We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.
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| 15. |
- Arnlind, Joakim, et al.
(författare)
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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
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Tidskriftsartikel (refereegranskat)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 16. |
- Dhamal, Swapnil Vilas, 1988, et al.
(författare)
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Resource Allocation Polytope Games: Uniqueness of Equilibrium, Price of Stability, and Price of Anarchy
- 2018
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Ingår i: AAAI 2018 - Proceedings of the 32nd AAAI Conference on Artificial Intelligence. ; , s. 997-1006
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Konferensbidrag (refereegranskat)abstract
- We consider a two-player resource allocation polytope game, in which the strategy of a player is restricted by the strategy of the other player, with common coupled constraints. With respect to such a game, we formally introduce the notions of independent optimal strategy profile, which is the profile when players play optimally in the absence of the other player; and common contiguous set, which is the set of top nodes in the preference orderings of both the players that are exhaustively invested on in the independent optimal strategy profile. We show that for the game to have a unique PSNE, it is a necessary and sufficient condition that the independent optimal strategies of the players do not conflict, and either the common contiguous set consists of at most one node or all the nodes in the common contiguous set are invested on by only one player in the independent optimal strategy profile. We further derive a socially optimal strategy profile, and show that the price of anarchy cannot be bound by a common universal constant. We hence present an efficient algorithm to compute the price of anarchy and the price of stability, given an instance of the game. Under reasonable conditions, we show that the price of stability is 1. We encounter a paradox in this game that higher budgets may lead to worse outcomes.
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| 17. |
- 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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| 18. |
- 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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| 19. |
- Willsch, Dennis, et al.
(författare)
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Benchmarking Advantage and D-Wave 2000Q quantum annealers with exact cover problems
- 2022
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Ingår i: Quantum Information Processing. - : Springer Science and Business Media LLC. - 1570-0755 .- 1573-1332. ; 21:4
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Tidskriftsartikel (refereegranskat)abstract
- We benchmark the quantum processing units of the largest quantum annealers to date, the 5000 + qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance.
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| 20. |
- 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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