| 1. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
-
Expedited analytical hierarchical process for multicriteria decision making
- 2022
-
Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2
-
Tidskriftsartikel (refereegranskat)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
|
|
| 2. |
- Berndtsson, Bo, 1950
(författare)
-
Probability measures associated to geodesics in the space of kähler metrics
- 2018
-
Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 395-419
-
Konferensbidrag (refereegranskat)abstract
- We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H0(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second order moments implies a recent result of Chen and Sun on geodesic distances in the respective spaces, while the convergence of first order moments gives convergence of Donaldson’s Z-functional to the Aubin–Yau energy. We also include a result on approximation of infinite dimensional geodesics by Bergman kernels which generalizes work of Phong and Sturm.
|
|
| 3. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
-
Performance of the decision-making trial and evaluation laboratory
- 2023
-
Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
-
Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
|
|
| 4. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
-
Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
-
Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
|
|
| 5. |
- Fotedar, Sunney, 1989, et al.
(författare)
-
A criterion space decomposition approach to generalized tri-objective tactical resource allocation
- 2023
-
Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20, s. 1-28
-
Tidskriftsartikel (refereegranskat)abstract
- We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the generalized tactical resource allocation problem (GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the quadrant shrinking method (QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances.
|
|
| 6. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
-
Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model
- 2024
-
Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101
-
Tidskriftsartikel (refereegranskat)abstract
- Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
|
|
| 7. |
- Brandes, Julia, et al.
(författare)
-
On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- 2021
-
Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
-
Tidskriftsartikel (refereegranskat)abstract
- We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
|
|
| 8. |
- Ericsson, Niklas, 1968
(författare)
-
A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain
- 2021
-
Ingår i: Computational Methods in Applied Mathematics. - : Walter de Gruyter GmbH. - 1609-4840 .- 1609-9389. ; 21:4
-
Tidskriftsartikel (refereegranskat)abstract
- We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems. © 2021 Ericsson, published by De Gruyter 2021.
|
|
| 9. |
- Wang, Siyang, et al.
(författare)
-
CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
-
Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
-
Tidskriftsartikel (refereegranskat)abstract
- When using a finite difference method to solve an initial-boundary-value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
|
|
| 10. |
- Zhao, D., et al.
(författare)
-
Low Phase-Rank Approximation
- 2022
-
Ingår i: Linear Algebra and Its Applications. - : Elsevier BV. - 0024-3795. ; 639, s. 177-204
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose and solve low phase-rank approximation problems, which serve as a counterpart to the well-known low-rank approximation problem and the Schmidt-Mirsky theorem. It is well known that a nonzero complex number can be specified by its gain and phase, and while it is generally accepted that the gains of a matrix may be defined by its singular values, there is no widely accepted definition for its phases. In this work, we consider sectorial matrices, whose numerical ranges do not contain the origin, and adopt the canonical angles of such matrices as their phases. Similarly to the rank of a matrix being defined as the number of its nonzero singular values, we define the phase-rank of a sectorial matrix as the number of its nonzero phases. While a low-rank approximation problem is associated with the matrix arithmetic mean, it turns out that a natural parallel for the low phase-rank approximation problem is to use the matrix geometric mean to measure the approximation error. Importantly, we derive a majorization inequality between the phases of the geometric mean and the arithmetic mean of the phases, similarly to the Ky-Fan inequality for eigenvalues of Hermitian matrices. A characterization of the solutions to the proposed problem, with the same flavor as the Schmidt-Mirsky theorem, is then obtained in the case where both the objective matrix and the approximant are restricted to be positive-imaginary. In addition, we provide an alternative formulation of the low phase-rank approximation problem using geodesic distances between sectorial matrices. The two formulations give rise to the exact same set of solutions when the involved matrices are additionally assumed to be unitary. © 2022 Elsevier Inc.
|
|
