Two-Stage Stochastic Programming for Transportation Network Design Problem

Hrabec, Dušan; Popela, Pavel; Roupec, Jan; Mazal, Jan; Stodola, Petr

doi:10.1007/978-3-319-19824-8_2

Cited by 5 publications

(2 citation statements)

References 10 publications

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“…In fact, many important engineering and scientific applications, such as those considered in wireless resource optimizations [1]- [3], transportation network design [4] and machine/deep learning [5]- [7], can be viewed as instances of the two-stage stochastic optimization problem P. Despite its wide applications, Problem P is very challenging and there only exist solutions for some specific applications. The existing two-stage stochastic optimization algorithms can be classified into the following four classes.…”

Section: Introductionmentioning

confidence: 99%

Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling

Liu,

Yang,

Quek

et al. 2021

Preprint

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We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic optimization plays a critical role in various engineering and scientific applications, there still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. To overcome the challenge caused by tightly coupled stochastic constraints, we first establish a two-stage primaldual decomposition (PDD) method to decompose the two-stage problem into a long-term problem and a family of short-term subproblems. Then we propose a PDD-based stochastic successive convex approximation (PDD-SSCA) algorithmic framework to find KKT solutions for two-stage stochastic optimization problems. At each iteration, PDD-SSCA first runs a short-term subalgorithm to find stationary points of the short-term subproblems associated with a mini-batch of the state samples. Then it constructs a convex surrogate for the long-term problem based on the deep unrolling of the short-term sub-algorithm and the back propagation method. Finally, the optimal solution of the convex surrogate problem is solved to generate the next iterate. We establish the almost sure convergence of PDD-SSCA and customize the algorithmic framework to solve two important application problems. Simulations show that PDD-SSCA can achieve superior performance over existing solutions.

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Section: Introductionmentioning

confidence: 99%

Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling

Liu,

Yang,

Quek

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…Two-stage optimization models have been used to model problems with sequential decisions, where decisions have to be made under some degree of uncertainty. Such an approach has been applied in many transportation and supply chain problems with sequential decisions (Brezina et al, 2010;Hrabec et al, 2015;Liu et al, 2018;Stewart & Ittmann, 1979). Problems are typically modelled to satisfy projected demand in the first stage, and upon realization of demand, the second-stage decision is made.…”

Section: Two-stage Optimization Problemmentioning

confidence: 99%

Data-driven integrated approach to airport demand management

Cheung¹

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The combination of air traffic growth and limitations in airport capacity result in significant congestion throughout the world's busiest airports. This imposes huge costs on airlines, passengers, and society. Without the option of capacity expansion, which is costly and has a long lead-time, the alleviation of air traffic congestion requires improvements in the utilization of capacity to enhance airport operation efficiency, and/or schedule adjustment to limit over-capacity scheduling. Motivated by the challenge of this important problem, this thesis comprising of three essays pertaining to one analytical capacity model and two variants of strategic demand management model are proposed to increase the utilization of capacity and efficient allocation of capacity.The first essay addresses the limitation of existing analytical capacity models which are not adequate in representing mixed mode operations that could take on any arbitrary sequence as they are unable to consider changes in the operation sequence.The proposed macroscopic analytical runway capacity model to quantify and forecast the maximum operational capacity of an airport provides an easy-to-use decisionsupport tool for airport operators and can accommodate practical constraints and parameters; model different modes of operations; be efficient in testing out various hypotheses; and provide sufficiently accurate capacity values. As quantifying airport capacity is a critical step towards determining the supply of slots available for allocation to airlines, the new capacity estimates will allow airport operators to design efficient schedules and operational strategies. Computations demonstrate the improvement in capacity estimates and enable quantifying capacity in mixed mode operations with an arbitrary aircraft sequence.The second essay considers the strategic demand management problem with the objective to minimize the number of flights displaced from its original schedule. The proposed model addresses peak traffic with a levelling effect through minor adjustment of the demand with respect to dynamic capacity derived from the earlier analytical capacity estimation model. The proposed approach also allows for exploration of runway configurations, arrival/departure priority, and operational modes (segregated/ mixed) to ensure that the higher levels of demand during the 33 Chapter 3: Sequence-specific analytical capacity modelIn this research, a macroscopic analytical runway capacity model to quantify and forecast the maximum operational capacity of an airport for an optimized flight sequence is proposed. This work extends the model proposed by Stamatopoulos et al. (2004). Current models do not estimate the capacity when arrival and departure operations are interspersed (without any pattern) within a flight sequence, but the proposed model can accurately reflect the improvement in airport capacity for any optimized aircraft sequence. The model provides an easy-to-use decision support tool for airport operators, which can accommodate practical constraints ...

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