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- Connors, R., et al.
(författare)
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Sensitivity analysis of welfare, equity, and acceptability level of transport policies
- 2015
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. - 9783319185668 - 9783319185675 ; 130, s. 39-65
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Konferensbidrag (refereegranskat)abstract
- Transport planners face a major challenge to devise policies to meet multiple expectations and objectives. While we know that transport networks are complex, multi-modal, and spatially distributed systems, there is now a long history of mathematical tools which assist planners in understanding travel movements. However, the objectives that they are asked to achieve do not always admit such a quantification, and so there is a potential mismatch between seemingly qualitatively driven objectives and quantitatively expressed models of the transport system. In the present chapter we address this mismatch, by focusing on three objectives that we believe represent the typical interests of a planner. These are namely: is the policy economically justifiable (efficient), is it “fair” (equitable), and is it justifiable to a democratic society (acceptable)? We provide mathematical representations of these three objectives and link them to mathematical theory of transport networks, in which we may explore the sensitivity of travel behaviour (and hence the objectives) to various multi-modal transport policies. The detailed steps for representing the policy objectives and sensitivities in the network are set out, and the results of a case study reported in which road tolls, road capacities, and bus fares are the policy variables. Overall, the chapter sets out a systematic method for planners to choose between multi-modal policies based on these three objectives.
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| 2. |
- Daneva (Mitradjieva), Maria, et al.
(författare)
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A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
- 2010
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Ingår i: Computational optimization and applications. - : Springer Science and Business Media LLC. - 0926-6003 .- 1573-2894. ; 46:3, s. 451-466
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Tidskriftsartikel (refereegranskat)abstract
- The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.
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| 3. |
- Mitradjieva-Daneva, Maria, 1974-
(författare)
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Feasible Direction Methods for Constrained Nonlinear Optimization : Suggestions for Improvements
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps.The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one.The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed.We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space.
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