Per Olov Lindberg

Railway Timetabling Using Lagrangian Relaxation

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 it 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 sm all fraction of these are nonzero, which 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.

Central dopamine receptor agonist and antagonist actions of the enantiomers of 3-PPP

The two enantiomers of the putative centrally acting dopamine (DA) autoreceptor agonist 3-(3-hydroxyphenyl)-N-n-propylpiperidine, 3-PPP (Hjorth et al. 1981), were pharmacologically evaluated. An extensive series of biochemical and behavioural experiments unexpectedly revealed that both (+)- and (-)-3-PPP showed clear, but differential, effects on the DA receptors. Thus, (+)-3-PPP is a DA agonist with autoreceptor as well as postsynaptic receptor stimulatory properties. In contrast, although (-)-3-PPP similarly activates DA autoreceptors it acts concomitantly as an antagonist at postsynaptic DA receptors. Moreover, both behavioural and biochemical data on motor activity and DA synthesis and turnover suggest a preferential limbic action for the (-)-enantiomer. These results are discussed in terms of the dual antidopaminergic action of (-)-3-PPP coupled with anatomical differences in the feedback organisation in central (viz, limbic vs striatal) DA systems. It is suggested that compounds like (-)-3-PPP may be of potential clinical utility in the treatment of psychotic disorders, whilst lacking the seriously incapacitating motor dysfunctions produced by current neuroleptic therapy.

Measurement of Contrast Transmission Characteristics in Optical Image Formation

A method of testing the performance of lenses is worked out, based upon the fact that the light distribution in the image of any one-dimensional test pattern can be determined from the light distri...

A Riccati-based primal interior point solver for multistage stochastic programming

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 ov ...

Additively decomposed quasiconvex funtions

AbstractIn a recently published paper with the same title, Debreu and Koopmans have studied conditions which imply the quasiconvexity of the function

Congestion Pricing of Road Networks with Users Having Different Time Values

f(x) = \mathop \sum \limits_{i = 1}^n f_i (x_i ),x_i \in X_i ,

On Traffic Equilibrium Models with a Nonlinear Time/Money Relation

wherex = (x1,x2,⋯,xn) and, fori = 1, 2,⋯, n,X1 is a finite-dimensional open convex set andfi a real-valued nonconstant function onX1 These conditions involve the convexity indices of functionsfi, a concept introduced in the Debreu and Koopmans paper. First, we give a new definition of the convexity index equivalent to that of Debreu and Koopmans. Then, by means of this definition, we can simplify the proofs given by Debreu and Koopmans and extend some of their results.

The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment*

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.