| 1. |
- Andersson, Per-Åke, 1945-
(författare)
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Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- I avhandlingen studeras hur kostnadseffektiva underhålls- (uh-)planer för belagd väg kan genereras, på basis av information om aktuellt vägytetillstånd och funktionella modeller för kostnads- och tillståndsförändringar, delvis utvecklade i samarbete med svenska Vägverket (VV). Tilltänkt användning är på strategisk och programnivå, innan mer detaljerad objektinformation finns att tillgå. Till skillnad från hittills använda modeller, så genereras individuella uh-planer för varje vägsegment (en homogen vägsträcka vad gäller aktuellt beläggningstillstånd och beläggningshistorik), i kontinuerliga tillstånds- och åtgärdsrum. Genom användning av Lagrangerelaxerande optimeringsteknik, så kan de speciella nytto/kostnads-kvot-villkor som VV ålägger varje uh-objekt naturligen hanteras med dualpriser för budgetvillkoren. Antalet vägsegment som konkurrerar om budgetmedlen är vanligtvis stort. Data från VV:s Vägdatabank för Värmland har använts, omfattande ca 9000 vägsegment. Genom den stora datamängden har datorprogrammen implementerats för parallellbearbetning. Under avhandlingsarbetet har projektet beviljats tillgång till Monolith PCklustret vid NSC. För att kunna reducera optimeringskörtiderna har modell- och metodutveckling varit nödvändig. Genom att aggregera vägsegmenten till vägklasser har goda startvärden på dualpriserna erhållits. Genom utvecklingen av en speciell restvärdesrutin har den explicit behandlade tidsperioden kunnat reduceras. Vid lösandet av det duala subproblemet har speciell uppmärksamhet ägnats åt de diskretiseringseffekter som uppstår i metoden dynamisk programmering. En typ av tillämpning avser ett delvägnät, exempelvis en väg. Valideringsstudier har genomförts på väg 63 i Värmland – med lovande men inte tillfredsställande resultat (se nedan). En speciell modell för samordnat uh beaktar stordriftsfördelarna vid samtidig åtgärd på en hel vägsträcka. Den andra huvudtypen av studier gäller ett helt nätverk. Flera metodtyper har tillämpats, både för att lösa de relaxerade optimeringsproblemen och för att generera uhplaner som uppfyller budgetvillkoren. För en anständig diskretisering är körtiderna för hela Värmland mindre än 80 CPU-timmar. Genom en a posteriori primal heuristik reduceras kraven på parallellbearbetning till ett litet PC-kluster. Avhandlingen studerar vidare effekterna av omfördelade budgetmedel samt en övergång till en transparent, stokastisk modell – vilka båda visar små avvikelser från basmodellen.Optimeringsresultaten för Värmland indikerar att budgetnivåer på ca 40% av Värmlands verkliga uh-budget är tillräckliga. Dock saknas viktiga kostnadsdrivande faktorer i denna första modellomgång, exempelvis vissa funktionella prestanda (säkerhet), all miljöpåverkande prestanda (buller etc.) och strukturell prestanda (ex.vis bärighet, som enbart modelleras via ett åldersmått). För ökad tilltro till PMS i allmänhet och optimering i synnerhet, bör avvikelserna analyseras ytterligare och leda till förbättringar vad gäller tillståndsmätning, tillståndseffekt- & kostnadsmodellering samt matematisk modellering & implementering.
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| 2. |
- Lindberg, Sara, et al.
(författare)
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Expanded HILUS Trial: A Pooled Analysis of Risk Factors for Toxicity From Stereotactic Body Radiation Therapy of Central and Ultracentral Lung Tumors
- 2023
-
Ingår i: INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS. - 0360-3016 .- 1879-355X. ; 117:5, s. 1222-1231
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Tidskriftsartikel (refereegranskat)abstract
- Purpose: Stereotactic body radiation therapy for tumors near the central airways implies high-grade toxic effects, as concluded from the HILUS trial. However, the small sample size and relatively few events limited the statistical power of the study. We therefore pooled data from the prospective HILUS trial with retrospective data from patients in the Nordic countries treated outside the prospective study to evaluate toxicity and risk factors for high-grade toxic effects. Methods and Materials: All patients were treated with 56 Gy in 8 fractions. Tumors within 2 cm of the trachea, the mainstem bronchi, the intermediate bronchus, or the lobar bronchi were included. The primary endpoint was toxicity, and the secondary endpoints were local control and overall survival. Clinical and dosimetric risk factors were analyzed for treatment-related fatal toxicity in univariable and multivariable Cox regression analyses.Results: Of 230 patients evaluated, grade 5 toxicity developed in 30 patients (13%), of whom 20 patients had fatal bronchopul-monary bleeding. The multivariable analysis revealed tumor compression of the tracheobronchial tree and maximum dose to the mainstem or intermediate bronchus as significant risk factors for grade 5 bleeding and grade 5 toxicity. The 3-year local control and overall survival rates were 84% (95% CI, 80%-90%) and 40% (95% CI, 34%-47%), respectively.Conclusions: Tumor compression of the tracheobronchial tree and high maximum dose to the mainstem or intermediate bronchus increase the risk of fatal toxicity after stereotactic body radiation therapy in 8 fractions for central lung tumors. Simi-lar dose constraints should be applied to the intermediate bronchus as to the mainstem bronchi.
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| 3. |
- Ait Ali, Abderrahman, 1991-, et al.
(författare)
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A disaggregate bundle method for train timetabling problems
- 2020
-
Ingår i: Journal of Rail Transport Planning & Management. - : Elsevier BV. - 2210-9706 .- 2210-9714. ; 16
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Tidskriftsartikel (refereegranskat)abstract
- The train timetabling problem (TTP) consists of finding a feasible timetable for a number of trains which minimises some objective function, e.g., sum of running times or deviations from ideal departure times. One solution approach is to solve the dual problem of the TTP using so-called bundle methods. This paper presents a new bundle method that uses disaggregate data, as opposed to the standard bundle method which in a certain sense relies on aggregate data. We compare the disaggregate and aggregate methods on realistic train timetabling scenarios from the Iron Ore line in Northern Sweden. Numerical results indicate that the proposed disaggregate method reaches better solutions faster than the standard aggregate approach.
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| 4. |
- Ait Ali, Abderrahman, 1991-, et al.
(författare)
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Disaggregation in Bundle Methods : Application to the Train Timetabling Problem
- 2017
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Konferensbidrag (refereegranskat)abstract
- Bundle methods are often used to solve dual problems that arise from Lagrangian relaxations of large scale optimization problems. An example of such problems is the train timetabling problem. This paper focuses on solving a dual problem that arises from Lagrangian relaxation of a train timetabling optimization program. The dual problem is solved using bundle methods. We formulate and compare the performances of two different bundle methods: the aggregate method, which is a standard method, and a new, disaggregate, method which is proposed here. The two methods were tested on realistic train timetabling scenarios from the Iron Ore railway line. The numerical results show that the new disaggregate approach generally yields faster convergence than the standard aggregate approach.
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| 5. |
- Bergström, Göran, 1964, et al.
(författare)
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Prevalence of Subclinical Coronary Artery Atherosclerosis in the General Population
- 2021
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Ingår i: Circulation. - Philadelphia : American Heart Association. - 0009-7322 .- 1524-4539. ; 144:12, s. 916-929
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Tidskriftsartikel (refereegranskat)abstract
- Background: Early detection of coronary atherosclerosis using coronary computed tomography angiography (CCTA), in addition to coronary artery calcification (CAC) scoring, may help inform prevention strategies. We used CCTA to determine the prevalence, severity, and characteristics of coronary atherosclerosis and its association with CAC scores in a general population.Methods: We recruited 30 154 randomly invited individuals age 50 to 64 years to SCAPIS (the Swedish Cardiopulmonary Bioimage Study). The study includes individuals without known coronary heart disease (ie, no previous myocardial infarctions or cardiac procedures) and with high-quality results from CCTA and CAC imaging performed using dedicated dual-source CT scanners. Noncontrast images were scored for CAC. CCTA images were visually read and scored for coronary atherosclerosis per segment (defined as no atherosclerosis, 1% to 49% stenosis, or ≥50% stenosis). External validity of prevalence estimates was evaluated using inverse probability for participation weighting and Swedish register data.Results: In total, 25 182 individuals without known coronary heart disease were included (50.6% women). Any CCTA-detected atherosclerosis was found in 42.1%; any significant stenosis (≥50%) in 5.2%; left main, proximal left anterior descending artery, or 3-vessel disease in 1.9%; and any noncalcified plaques in 8.3% of this population. Onset of atherosclerosis was delayed on average by 10 years in women. Atherosclerosis was more prevalent in older individuals and predominantly found in the proximal left anterior descending artery. Prevalence of CCTA-detected atherosclerosis increased with increasing CAC scores. Among those with a CAC score >400, all had atherosclerosis and 45.7% had significant stenosis. In those with 0 CAC, 5.5% had atherosclerosis and 0.4% had significant stenosis. In participants with 0 CAC and intermediate 10-year risk of atherosclerotic cardiovascular disease according to the pooled cohort equation, 9.2% had CCTA-verified atherosclerosis. Prevalence estimates had excellent external validity and changed marginally when adjusted to the age-matched Swedish background population.Conclusions: Using CCTA in a large, random sample of the general population without established disease, we showed that silent coronary atherosclerosis is common in this population. High CAC scores convey a significant probability of substantial stenosis, and 0 CAC does not exclude atherosclerosis, particularly in those at higher baseline risk.
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| 6. |
- Bergström, Göran, et al.
(författare)
-
Prevalence of Subclinical Coronary Artery Atherosclerosis in the General Population
- 2021
-
Ingår i: Circulation. - : Wolters Kluwer. - 0009-7322 .- 1524-4539. ; 144:12, s. 916-929
-
Tidskriftsartikel (refereegranskat)abstract
- Background: Early detection of coronary atherosclerosis using coronary computed tomography angiography (CCTA), in addition to coronary artery calcification (CAC) scoring, may help inform prevention strategies. We used CCTA to determine the prevalence, severity, and characteristics of coronary atherosclerosis and its association with CAC scores in a general population.Methods: We recruited 30 154 randomly invited individuals age 50 to 64 years to SCAPIS (the Swedish Cardiopulmonary Bioimage Study). The study includes individuals without known coronary heart disease (ie, no previous myocardial infarctions or cardiac procedures) and with high-quality results from CCTA and CAC imaging performed using dedicated dual-source CT scanners. Noncontrast images were scored for CAC. CCTA images were visually read and scored for coronary atherosclerosis per segment (defined as no atherosclerosis, 1% to 49% stenosis, or ≥50% stenosis). External validity of prevalence estimates was evaluated using inverse probability for participation weighting and Swedish register data.Results: In total, 25 182 individuals without known coronary heart disease were included (50.6% women). Any CCTA-detected atherosclerosis was found in 42.1%; any significant stenosis (≥50%) in 5.2%; left main, proximal left anterior descending artery, or 3-vessel disease in 1.9%; and any noncalcified plaques in 8.3% of this population. Onset of atherosclerosis was delayed on average by 10 years in women. Atherosclerosis was more prevalent in older individuals and predominantly found in the proximal left anterior descending artery. Prevalence of CCTA-detected atherosclerosis increased with increasing CAC scores. Among those with a CAC score >400, all had atherosclerosis and 45.7% had significant stenosis. In those with 0 CAC, 5.5% had atherosclerosis and 0.4% had significant stenosis. In participants with 0 CAC and intermediate 10-year risk of atherosclerotic cardiovascular disease according to the pooled cohort equation, 9.2% had CCTA-verified atherosclerosis. Prevalence estimates had excellent external validity and changed marginally when adjusted to the age-matched Swedish background population.Conclusions: Using CCTA in a large, random sample of the general population without established disease, we showed that silent coronary atherosclerosis is common in this population. High CAC scores convey a significant probability of substantial stenosis, and 0 CAC does not exclude atherosclerosis, particularly in those at higher baseline risk.
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| 7. |
- Björk, Kaj-Mikael, et al.
(författare)
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Some convexifications in global optimization of problems containing signomial terms
- 2003
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Ingår i: Computers and Chemical Engineering. - : Elsevier. - 0098-1354 .- 1873-4375. ; 27:5, s. 669-679
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Tidskriftsartikel (refereegranskat)abstract
- It is often possible to use different convexification techniques with different transformations in global optimization. In 'Optimization Eng. (submitted for publication)', a new global optimization technique based on convexifying signomial terms is presented. The technique is based on the solution of a sequence of convexified approximate subproblems. The choice of transformation functions is clearly essential. It is not enough to use convexifications that will result in convex and underestimating problems, if an effective optimization approach is wanted. The transformations should be such that they make the resulting problems convex but at the same time do not change the problem more than necessary. It will be shown in this article that for certain problems the choice of transformations has a clear influence on the efficiency of the proposed optimization approach. Using other transformations than what is proposed in 'Optimization Eng. (submitted for publication)' will, in some examples, give solution times that are shorter by an order of magnitude. The concept of power convex functions (Generalized Concavity Optimization Econ. (1981) 153) will be used as a measure of the quality of the transformations. In this paper, the new transformation functions are also shown to be very successful in a heat exchanger network synthesis application. © 2002 Elsevier Science Ltd. All rights reserved.
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| 8. |
- Blomvall, Jörgen, et al.
(författare)
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A Riccati-based primal interior point solver for multistage stochastic programming
- 2002
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Ingår i: European Journal of Operational Research. - Amsterdam, Netherlands : Elsevier. - 0377-2217 .- 1872-6860. ; 143:2, s. 452-461
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new method for certain multistage stochastic programs with linear or nonlinear objective function, combining a primal interior point approach with a linear-quadratic control problem over the scenario tree. The latter problem, which is the direction finding problem for the barrier subproblem is solved through dynamic programming using Riccati equations. In this way we combine the low iteration count of interior point methods with an efficient solver for the subproblems. The computational results are promising. We have solved a financial problem with 1,000,000 scenarios, 15,777,740 variables and 16,888,850 constraints in 20 hours on a moderate computer. © 2002 Elsevier Science B.V. All rights reserved.
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| 9. |
- Blomvall, Jörgen, et al.
(författare)
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A Riccati-based primal interior point solver for multistage stochastic programming - Extensions
- 2002
-
Ingår i: Optimization Methods and Software. - Oxfordshire, United Kingdom : Taylor & Francis. - 1055-6788 .- 1029-4937. ; 17:3, s. 383-407
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Tidskriftsartikel (refereegranskat)abstract
- We show that a Riccati-based Multistage Stochastic Programming solver for problems with separable convex linear/nonlinear objective developed in previous papers can be extended to solve more general Stochastic Programming problems. With a Lagrangean relaxation approach, also local and global equality constraints can be handled by the Riccati-based primal interior point solver. The efficiency of the approach is demonstrated on a 10 staged stochastic programming problem containing both local and global equality constraints. The problem has 1.9 million scenarios, 67 million variables and 119 million constraints, and was solved in 97 min on a 32 node PC cluster.
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| 10. |
- Blomvall, Jörgen, 1974-, et al.
(författare)
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Back-testing the performance of an actively managed option portfolio at the Swedish Stock Market, 1990–1999
- 2003
-
Ingår i: Journal of Economic Dynamics and Control. - Amsterdam, Netherlands : Elsevier. - 0165-1889 .- 1879-1743. ; 27:6, s. 1099-1112
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Tidskriftsartikel (refereegranskat)abstract
- We build an investment model based on Stochastic Programming. In the model we buy at the ask price and sell at the bid price. We apply the model to a case where we can invest in a Swedish stock index, call options on the index and the risk-free asset. By reoptimizing the portfolio on a daily basis over a ten-year period, it is shown that options can be used to create a portfolio that outperforms the index. With ex post analysis, it is furthermore shown that we can create a portfolio that dominates the index in terms of mean and variance, i.e. at given level of risk we could have achieved a higher return using options.
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| 11. |
- Brännlund, Ulf, et al.
(författare)
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Railway Timetabling Using Lagrangian Relaxation
- 1998
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Ingår i: Transportation Science. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0041-1655 .- 1526-5447. ; 32:4, s. 358-369
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel optimization approach for the timetabling problem of a railway company, i.e., scheduling of a set of trains to obtain a profit maximizing timetable, while not violating track capacity constraints. The scheduling decisions are based on estimates of the value of running different types of service at specified times. We model the problem as a very large integer programming problem. The model is flexible in that if allows for general cost functions. We have used a Lagrangian relaxation solution approach, in which the track capacity constraints are relaxed and assigned prices, so that the problem separates into one dynamic program for each physical train. The number of dual variables is very large. However, it turns out that only a small fraction of these are nonzero, wh ich one may take advantage of in the dual updating schemes. The approach has been, tested on a realistic example suggested by the Swedish National Railway Administration. This example contains 18 passenger trains and 8 freight trains to be scheduled during a day on a stretch of single track, consisting of 17 stations. The computation times are rather modest and the obtained timetables are within a few percent of optimality.
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| 12. |
- Cerreia-Vioglio, Simone, et al.
(författare)
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A canon of probabilistic rationality
- 2021
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Ingår i: Journal of Economic Theory. - : Elsevier BV. - 0022-0531 .- 1095-7235. ; 196
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Tidskriftsartikel (refereegranskat)abstract
- We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and then random choice occurs according to a tie-breaking mechanism among such alternatives that satisfies Renyi's Conditioning Axiom. Our result shows that the Choice Axiom is, in a precise formal sense, a probabilistic version of the Weak Axiom. It thus supports Luce's view of his own axiom as a "canon of probabilistic rationality."
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| 13. |
- Daneva, Maria, et al.
(författare)
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A Conjugate Direction Frank-Wolfe Method for Nonconvex Problems
- 2003
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Rapport (refereegranskat)abstract
- In this paper we propose an algorithm for solving problems with nonconvex objective function and linear constraints. We extend the previously suggested Conjugate direction Frank–Wolfe algorithm to nonconvex problems. We apply our method to multi-class user equilibria under social marginal cost pricing. Results of numerical experiments on Sioux Falls and Winnipeg are reported.
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| 14. |
- Daneva, Maria, 1974-, et al.
(författare)
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A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem
- 2003
-
Ingår i: Operations Research Proceedings 2002: Selected Papers of the International Conference on Operations Research (SOR 2002), Klagenfurt, September 2-5, 2002". - : Springer. - 9783642555374 - 3540003878 ; , s. -550
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This proceedings volume contains a selection of papers presented at the International Conference on Operations Research (SOR 2002).The contributions cover the broad interdisciplinary spectrum of Operations Research and present recent advances in theory, development of methods, and applications in practice. Subjects covered are Production, Logistics and Supply Chain Production, Marketing and Data Analysis, Transportation and Traffic, Scheduling and Project Management, Telecommunication and Information Technology, Energy and Environment, Public Economy, Health, Agriculture, Education, Banking, Finance, Insurance, Risk Management, Continuous Optimization, Discrete and Combinatorial Optimization, Stochastic and Dynamic Programming, Simulation, Control Theory, Systems Dynamics, Dynamic Games, Game Theory, Auctioning and Bidding, Experimental Economics, Econometrics, Statistics and Mathematical Economics, Fuzzy Logic, Multicriteria Decision Making, Decision Theory.
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| 15. |
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| 16. |
- Engelson, Leonid, et al.
(författare)
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Congestion Pricing of Road Networks with Users Having Different Time Values
- 2006
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Ingår i: Mathematical and Computational Models for Congestion Charging. - : Springer Science+Business Media B.V.. ; , s. 81-104
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Bokkapitel (refereegranskat)abstract
- We study congestion pricing of road networks with users differing onlyin their time values. In particular, we analyze the marginal social cost (MSC) pricing,a tolling scheme that charges each user a penalty corresponding to the value of thedelays inflicted on other users, as well as its implementation through fixed tolls. Weshow that the variational inequalities characterizing the corresponding equilibria canbe stated in symmetric or nonsymmetric forms. The symmetric forms correspondto optimization problems, convex in the fixed-toll case and nonconvex in the MSCcase, which hence may have multiple equilibria. The objective of the latter problemis the total value of travel time, which thus is minimized at the global optima of thatproblem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibriawith possibly non-unique class specific flows, but with identical close-to-optimalvalues of the total value of travel time. Finally we give an adaptation, to the MSCsetting, of the Frank-Wolfe algorithm, which is further applied to some test cases,including Stockholm.
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| 17. |
- Engelson, Leonid, et al.
(författare)
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Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls
- 2004
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Ingår i: Operations Research Proceedings 2003. - Berlin, Heidelberg : Springer Berlin/Heidelberg. ; , s. 141-148
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In an earlier paper, we have demonstrated that traffic equilibria under social marginal cost tolls can be computedas a local optima of a nonconvex optimization problem. The nonconvexity of this problem implies in particular that linearizations, e.g. the Frank-Wolfe method, do not give underestimates of the optimal value. In this paper we derive the convex hull of nonconvex arc cost functions of BPR type. These convexifications can be used to get underestimates of the optimal value, or get better search directions in the initial phase of the Frank-Wolfe method. Computational results for the Sioux Falls and Stockholm networks are reported.
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| 18. |
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| 19. |
- Engelson, Leonid, et al.
(författare)
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Multi-Class User Equilibria under Social Marginal Cost Pricing
- 2002
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Ingår i: Operations Research 2002. - 9783540003878 ; , s. 174-179
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In the congested cities of today, congestion pricing is a tempting alternative. With a single user class, already Beckmann et al. showed that ``system optimal'' traffic flows can be achieved by social marginal cost (SMC) pricing where users have to pay for the delays the incur on others. However different user classes can have widly differing time values. Hence, when introducing tolls, one should consider multi-class user equilibria, where the classes have different time values. In the single class case, the equilibrium conditions can be viewn as optimality conditions of an equivalent optimization problem. In the multi-class case, however, netter claims that this is not possible. We show that, depending on the formulation, the multi-class SMC-pricing equilibrium problem (with different time values) can be stated either as an asymmetric or as a symmetric equilibrium problem. In the latter case, the corresponding optimization problems is in general non-convex. For this non-convex problem, we devise descent methods of Frank-Wolfe type. We apply the methods and study a synthetic case based on Sioux Falls.
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| 20. |
- Engström, Gunnar, et al.
(författare)
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Pulmonary function and atherosclerosis in the general population : causal associations and clinical implications
- 2024
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Ingår i: European Journal of Epidemiology. - : Springer Nature. - 0393-2990 .- 1573-7284. ; 39:1, s. 35-49
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Tidskriftsartikel (refereegranskat)abstract
- Reduced lung function is associated with cardiovascular mortality, but the relationships with atherosclerosis are unclear. The population-based Swedish CArdioPulmonary BioImage study measured lung function, emphysema, coronary CT angiography, coronary calcium, carotid plaques and ankle-brachial index in 29,593 men and women aged 50–64 years. The results were confirmed using 2-sample Mendelian randomization. Lower lung function and emphysema were associated with more atherosclerosis, but these relationships were attenuated after adjustment for cardiovascular risk factors. Lung function was not associated with coronary atherosclerosis in 14,524 never-smokers. No potentially causal effect of lung function on atherosclerosis, or vice versa, was found in the 2-sample Mendelian randomization analysis. Here we show that reduced lung function and atherosclerosis are correlated in the population, but probably not causally related. Assessing lung function in addition to conventional cardiovascular risk factors to gauge risk of subclinical atherosclerosis is probably not meaningful, but low lung function found by chance should alert for atherosclerosis.
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| 21. |
- Fosgerau, M., et al.
(författare)
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A note on the invariance of the distribution of the maximum
- 2018
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Ingår i: Journal of Mathematical Economics. - : Elsevier. - 0304-4068 .- 1873-1538. ; 74, s. 56-61
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Tidskriftsartikel (refereegranskat)abstract
- Many models in economics involve discrete choices where a decision-maker selects the best alternative from a finite set. Viewing the array of values of the alternatives as a random vector, the decision-maker draws a realization and chooses the alternative with the highest value. The analyst is then interested in the choice probabilities and in the value of the best alternative. The random vector has the invariance property if the distribution of the value of a specific alternative, conditional on that alternative being chosen, is the same, regardless of which alternative is considered. This note shows that the invariance property holds if and only if the marginal distributions of the random components are positive powers of each other, even when allowing for quite general statistical dependence among the random components. We illustrate the analytical power of the invariance property by way of examples.
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| 22. |
- Fosgerau, Mogens, et al.
(författare)
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Invariance of the distribution of the maximum
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Many models in economics involve probabilistic choices where each decision-maker selects the best alternative from a finite set. Viewing the value of each alternative as a random variable, the analyst is then interested in the choice probabilities, that is, the probability for an alternative to give the maximum value. Much analytical power can be gained, both for positive and normative analysis, if the maximum value is statistically independent of which alternative obtains the highest value. This note synthesizes and generalizes previous results on this invariance property. We provide characterizations of this property within a wide class of distributions that comprises the McFadden GEV class, show implications in several directions, and establish connections with copulas. We illustrate the usefulness of the invariance property by way of a few examples.
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| 23. |
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| 24. |
- Holmberg, Anders, et al.
(författare)
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Towards 10-nm Soft X-Ray Zone Plate Fabrication
- 2011
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Konferensbidrag (refereegranskat)abstract
- In this paper the latest efforts to improve our nanofabrication process for soft x‐ray zone plates is presented. The resolving power, which is proportional to the smallest outermost zone width of the zone plate, is increased by introducing cold development of the electron beam resist that is used for the patterning. With this process we have fabricated Ni zone plates with 13‐nm outermost zone and shown potential for making 11‐nm half‐pitch lines in the electron beam resist. Maintaining the diffraction efficiency of the zone plate is a great concern when the outermost zone width is decreased. To resolve this problem we have developed the so‐called Ni‐Ge zone plate in which the zone plate is build up by Ni and Ge, resulting in an increase of the diffraction efficiency. In a proof‐of‐principle experiment with 25‐nm Ni‐Ge zone plates, we have shown a doubling of the diffraction efficiency. When combined with cold development, the Ni‐Ge process has been shown to work down to 16‐nm half‐pitch. It is plausible that further refinement of the process will make it possible to go to 10‐nm outermost zone widths.
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| 25. |
- Holmgren, Johan, et al.
(författare)
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Upright Stiff : subproblem updating in the FW method for traffic assignment
- 2013
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Ingår i: EURO Journal on Transportation and Logistics. - : Springer Berlin/Heidelberg. - 2192-4376 .- 2192-4384.
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Tidskriftsartikel (refereegranskat)abstract
- We present improvements of the Frank–Wolfe (FW) method for static vehicular traffic and telecom routing. The FW method has been the dominating method for these problem types, but due to its slow asymptotic convergence it has been considered dead by methods oriented researchers. However, the recent introduction of conjugate FW methods has shown that it is still viable, and in fact the winner on multi-core computers. In this paper, we show how to speed up the FW iterations, by updating the subproblems in the FW method, instead of solving them from scratch. The subproblem updating is achieved by viewing the subproblems as network flow problems with a threaded representation of the shortest path trees. In addition, we introduce a new technique, thread following, implying that a single traversal of the thread is enough to find a new shortest path tree. Our computational tests show that very few nodes in practice are visited more than once when searching for improving arcs. Moreover, we update also the all-or-nothing solutions of the subproblems, resulting in significantly reduced loading times. For a set of standard test problems, we observe speedups in the region of 25–50 % for the subproblem updating FW method, compared to the traditional non-updating version. We typically achieve higher speedups for more difficult problems and converged solutions.
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| 26. |
- Hägglöf, Kristoffer, et al.
(författare)
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A dual algorithm for the convex multicommodity flow problem
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper introduces a new dual ascent algorithm for solving the convex multicommodity flow problem, CMFP for short. CMFPs arize in many different routing problems such as the design of packet switched computer networks and the computation of traffic network equilibria. The algorithm utilizes the structure of the dual convex multicommodity flow problem, DCMFP for short. The dual objective is a sum of a concave differentiable function and a piecewise linear concave function. The algorithm exploits the local structure of the dual objective in an ascent scheme. In this paper a thorough explanation of the CMFPs and DCMFPs are given along with an outline of the dual ascent algorithm proposed. The method are applied to CMFPs arizing in the traffic assignment setting.
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| 27. |
- Hägglöf, Kristoffer, et al.
(författare)
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Verified feasibility of structured multicommodity flow solutions
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- This paper introduces a new approach for verifying feasibility for multicommodity flow problems, MFP:s for short. This feasibility problem priginates in a new solution method for the convex MFP based on the solution of the dual convex MFP, where optimality is demonstrated by showing that a given solution to the dual convex MFP is feasible for the convex MFP and hence optimal. In this paper a brief description of the MFP and the structure of its solutions are given. Furthermore, a distance minimizing method, based on simplicial decomposition, is described and used to efficiently verify feasibility and hence demonstrate optimality. The method is applied to convex MFP:s arizing in a traffic assignment setting.
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| 28. |
- Kiwiel, Krzysztof C, et al.
(författare)
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Bregman proximal relaxation of large-scale 0-1 problems
- 2000
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Ingår i: Computational optimization and applications. - 0926-6003 .- 1573-2894. ; 15:1, s. 33-44
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Tidskriftsartikel (refereegranskat)abstract
- We apply a recent extension of the Bregman proximal method for convex programming to LP relaxations of 0-1 problems. We allow inexact subproblem solutions obtained via dual ascent, increasing their accuracy successively to retain global convergence. Our framework is applied to relaxations of large-scale set covering problems that arise in airline crew scheduling. Approximate relaxed solutions are used to construct primal feasible solutions via a randomized heuristic. Encouraging preliminary experience is reported.
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| 29. |
- Kiwiel, Krzysztof C., et al.
(författare)
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Lagrangian relaxation via ballstep subgradient methods
- 2007
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Ingår i: Mathematics of Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0364-765X .- 1526-5471. ; 32:3, s. 669-686
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Tidskriftsartikel (refereegranskat)abstract
- We exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value. Augmented with simple averaging schemes, they asymptotically find objective and constraint subgradients involved in optimality conditions. When applied to Lagrangian relaxation of convex programs, they find both primal and dual solutions, and have practicable stopping criteria. Up until now, similar results have only been known for proximal bundle methods, and for subgradient methods with divergent series stepsizes, whose convergence can be slow. Encouraging numerical results are presented for large-scale nonlinear multicommodity network flow problems. ©2007 INFORMS.
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| 30. |
- Lindberg, Per Olov, et al.
(författare)
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A note on a recent paper by Dagsvik on IIA and random utilities
- 2017
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Ingår i: Theory and Decision. - : SPRINGER. - 0040-5833 .- 1573-7187. ; 82:2, s. 305-307
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper in this journal, Dagsvik derives the class of independent random utility representations that are "equivalent" to the independence-from-irrelevant-alternatives (IIA) assumption by Luce (Individual choice behavior: a theoretical analysis. Wiley, New York, 1959). In this short note, we clarify the relations between this paper by Dagsvik, and a paper in Lindberg's 2012 thesis.
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| 31. |
- Lindberg, Per Olov
(författare)
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A Note on Power Invariance in Random Utility Models
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Invariance in Random Utility (RU) Models is the property that the distribution of achievedutility is invariant across the alternatives chosen. In this note we study a generalization termedPower Invariance (PI). It generalizes the property, showed by Mattsson and Weibull, thatinvariance holds for an independent RU Model, where the cdf’s of the random terms arepositive powers of a given base cdf . The power invariant copulas turn out to be the copulasof Multivariate Extreme Value distributions. We further show that, under natural regularityconditions, the copulas of the marginal distributions of a PI copula are power invariant.
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| 32. |
- Lindberg, Per Olov
(författare)
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A Note on Two Papers by Dial
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This note discusses some shortcomings of two papers by Dial. In these insightful but somewhat confused papers Dial studies the problem of determining “optimal” congestion tolls. The papers have several flaws, as well as outright errors. Moreover the presentation often is not very clear, often leaving the reader in doubt of what is proved about what. In this note we try to pinpoint the main flaws of the papers.
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| 33. |
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| 34. |
- Lindberg, Per Olov
(författare)
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A simple derivation of the Williams-Daly-Zachery theorem
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this note we give a simple elementary proof of the Williams-Daly-Zachery theorem for additive random utility (ARU) models. This theorem says that the choice probabilities in an ARU model are the partial derivatives of the expected achieved utility. This is proved under the condition that the choice probabilities are continuous. We further prove that the choice probabilities are continuous exactly when the probability of ties is zero. Finally we prove that the probability of ties is zero if the cdf of the random term (of the ARU model) is differentiable with locally bounded gradient.
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| 35. |
- Lindberg, Per Olov, 1942-
(författare)
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Aspects of Static Multi-Class Traffic equilibria under Congestion Pricing
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Congestion charging is a now accepted means of influencing traffic to behave in a more socio-economic optimal way, like e.g. in the Stockholm project. Already early work, in the 1920’s, showed that road use can be inefficient due externalities, i.e. that users don’t experience their own (negative) effect on other users: an extra car on a traffic link causes delays for other cars, but the driver himself does not experience this cost.In the 1950’s it was further shown - for a congested road network with homogeneous users – that if each user is charged a toll equal to the total value of time loss incurred on other users of the network, then -if we have fixed travel demand - this will induce an equilibrium that is system optimal in the sense that the total cost of network usage is minimal (assuming that all users have fixed and identical time values). But toll charges need to be levied in monetary units, and different travelers have different values of time. Therefore, to account for the effects of tolls, and to be able to compute equilibria, one needs to introduce different user classes, differing in their time values.In this thesis, consisting of four papers, we study congestion pricing of road networks with users differing only in their time values. In particular, we analyze marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls.Paper III contains the main theoretical work of the thesis. In that paper we show that the variational inequalities characterizing the equilibria in question can be stated in symmetric or non-symmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and non-convex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.Paper I is an early application using Frank-Wolfe, after having realized the possibility to symmetrize the problem.Paper II gives a convexification of non-convex equilibrium problem for MSC tolls. We have used these convexifications to compute lower bounds when computing equilibria.Paper IV is a short note commenting some flaws in two papers by Dial on MSC tolls.
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| 36. |
- Lindberg, Per Olov
(författare)
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Choice Probabilities in Random Utility Models : Necessary and Sufficient Conditions for a Much Used Formula, andImplications for the Conditional Distributions of Achieved Utility
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Random Utility (RU) Models have reached a wide applicability in many areas of applied Economics. In all application areas, the formulas for the choice probabilities play a central role. For the formulas to be useful, the probabilities further need to sum up to 1. In this note, we give necessary and sufficient conditions for the validity of the classical choice probability formula (i.e. that the choice probabilities are the integrals of the partial derivatives of the cdf of the random term along the diagonal), and that the probabilities sum up to 1. Further, it is proved sufficient that the gradient of said cdf is continuous and piecewise differentiable with locally bounded gradient, along the diagonal. Along the way we prove many intermediate results relating different derivatives of the cdf. Finally the results are applied to derive formulas for the distribution of achieved utility conditioned on a given alternative being chosen.
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| 37. |
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| 38. |
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| 39. |
- Lindberg, Per Olov, et al.
(författare)
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Homothetic functions revisited
- 2002
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Ingår i: Economic Theory. ; 19:2, s. 417-427
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Tidskriftsartikel (refereegranskat)
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| 40. |
- Lindberg, Per Olov, et al.
(författare)
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Homothetic functions revisited
- 2002
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Ingår i: Economic Theory. - 0938-2259 .- 1432-0479. ; 19:2, s. 417-427
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Tidskriftsartikel (refereegranskat)abstract
- This paper examines the proposition that homotheticity is equivalent to the property that (e.g., in the context of a production function) the marginal rate of substitution is constant along any ray from the origin. This claim is made in many places, but hitherto the prerequisites have not been stated explicitly. In the present contribution it is demonstrated that an additional condition is required for the claim to hold. We present a theorem that achieves equivalence by also assuming 'nowhere ray constancy'. It turns out that this condition is implied by assumptions often made, e.g., in production theory. Further, a complete characterization is given of the class of functions that satisfy ray constant marginal rates of substitution or, somewhat more generally, a condition of ray parallel gradients. In addition to homothetic functions this class contains functions homogeneous of degree 0 (i.e., ray constant) and functions which are homothetic in disjoint regions separated by regions of ray constancy.
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| 41. |
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| 42. |
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| 43. |
- Lindberg, Per Olov
(författare)
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Random Utility Models, IIA, Mattsson-Weibull-Li Distributionsand a Conjecture by Luce and Suppes
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In recent papers, Mattsson and Weibull, and independently Li, have introduced a class of independent distributions, where the individual cdf’s are powers of each other. For this class they have showed that the choice probabilities are of “Luce form”, i.e. the form following from the Independence from Irrelevant Alternatives (IIA) assumption. We show a converse to this result. For a class of “independent” Random Utility (RU) Models, allowing non-uniform expansion, and where the cdf’s in question are well-behaved in a certain sense, the only possibility is that the cdf’s are of the above mentioned Mattsson-Weibull-Li (MWL) type. This result resolves an old conjecture by Luce and Suppes. The result demands unbounded choice sets. For finite models, we show on the contrary, that any finite independent RU model with Luce form choice probabilities, there is a version with random terms that are not MWL-distributed
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| 44. |
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| 45. |
- Lindberg, Per Olov
(författare)
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The Choice Axiom Revisited
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The famous Choice Axiom by Luce is now more than half a century old. We investigate the consequences of going back to Luce’s original formulation of the axiom, which had a more succinct formulation. Using this, what we term Strong Choice Axiom, we prove a sort of “lexicographic” version of the “Luce form” choice probabilities. Further, we study whether these extended choice probabilities are representable by Random Utility models.
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| 46. |
- Lindberg, Per Olov, 1942-, et al.
(författare)
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The Stiff is Moving - Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment
- 2012
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Ingår i: Transportation Science. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0041-1655 .- 1526-5447. ; 47:2, s. 280-293
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Tidskriftsartikel (refereegranskat)abstract
- We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, Conjugate direction Frank-Wolfe (CFW), Bi-conjugate Frank-Wolfe (BFW) and ”PARTANized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to Bar-Gera’s origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements suggested by Boyce et al. We further show that CFW is globally convergent. We moreover point at independent studies by other researchers that show that our methods compare favourably with recent bush-based and gradient projection algorithms on computers with several cores.
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| 47. |
- Lindberg, Per Olov, et al.
(författare)
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Tolled multi-class traffic equilibria and toll sensitivities
- 2015
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Ingår i: EURO Journal on Transportation and Logistics. - : Elsevier BV. - 2192-4376 .- 2192-4384. ; 4:2, s. 197-222
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Tidskriftsartikel (refereegranskat)abstract
- We review properties of tolled equilibria in road networks, with users differing in their time values, and study corresponding sensitivities of equilibrium link flows w.r.t. tolls. Possible applications include modeling of individual travellers that have different trip purposes (e.g. work, business, leisure, etc.) and therefore perceive the relation between travel time and monetary cost in dissimilar ways. The typical objective is to reduce the total value of travel time (TVT) over all users. For first best congestion pricing, where all links in the network can be tolled, the solution can be internalized through marginal social cost (MSC) pricing. The MSC equilibrium typically has to be implemented through fixed tolls. The MSC as well as the fixed-toll equilibrium problems can be stated as optimization problems, which in general are convex in the fixed-toll case and non-convex in the MSC case. Thus, there may be several MSC equilibria. Second-best congestion pricing, where one only tolls a subset of the links, is much more complex, and equilibrium flows, times and TVT are not in general differentiable w.r.t. tolls in sub-routes used by several classes. For generic tolls, where the sets of shortest paths are stable, we show how to compute Jacobians (w.r.t positive tolls) of link flows and times as well as of the TVT. This can be used in descent schemes to find tolls that minimize the TVT at least locally. We further show that a condition of independent equilibrium cycles, together with a natural extension of the single class regularity condition of strict complementarity, leads to genericity, and hence existence of said Jacobians.
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| 48. |
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| 49. |
- Mattsson, Lars-Göran, et al.
(författare)
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Extreme values, invariance and choice probabilities
- 2011
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Konferensbidrag (refereegranskat)abstract
- Consider a finite set of alternatives, and an associatedcollection of random variables representing some given relevant property of eachalternative, such as its utility, cost or reliability. Suppose that there is a processthat selects exactly one of these alternatives, an alternative with an extreme(maximal or minimal) value. In economics, discrete-choice analysis based onrandom utility theory is the most well-known modelling approach to such aprocess. Among practitioners, it is widely believed that in order to analyze suchsituations, one needs to resort to particular parametric forms of the underlyingprobability distributions of the random variables. We show that this is notso. Indeed, parametric forms impose unnecessary theoretical and empiricalconstraints and may hide more general properties. For the special case ofstatistical independence, we further provide a characterization of the invarianceproperty that all random variables, representing the relevant property of thealternatives, have the same distribution, conditional upon being chosen.
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| 50. |
- Mattsson, Lars-Göran, et al.
(författare)
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Extreme values, invariance and choice probabilities
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Since the pioneering work of McFadden (1974), discretechoice random-utility models have become work horses in many areas in economics.In these models, the random variables enter additively or multiplicatively, and the noise distributions take a particular parametric form. We show that the same qualitative results, with closed-form choice probabilities, can be obtained for a wide class of distributions without such specifications. This class generalizes the statistically independent distributions where any two c.d.f.:s are powers of each others to a class that allows for statistical dependence, in a way analogous to how GEV distributions generalize Gumbel distributions. We show that this generalization is sufficient, and under statistical independence also necessary, for the following invariance property: all conditional random variables, when conditioning upon a certain alternative having been chosen, are identically distributed. In our general framework, proofs become simpler, more direct and transparent, well-known results are obtained as special cases, and one can characterize the Gumbel, Fréchet and Weibull distributions.
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