scholarly journals Train-Scheduling Optimization Model for Railway Networks with Multiplatform Stations

2019 ◽  
Vol 12 (1) ◽  
pp. 257
Author(s):  
Gianmarco Garrisi ◽  
Cristina Cervelló-Pastor
Keyword(s):  
Mathematical Formulation ◽  
Computation Time ◽  
Mixed Integer ◽  
Initial Population ◽  
Mixed Integer Linear Program ◽  
Transit System ◽  
Train Scheduling ◽  
Railway Networks ◽  
Np Hard Problem ◽  
Problem Instances

This paper focuses on optimizing the schedule of trains on railway networks composed of busy complex stations. A mathematical formulation of this problem is provided as a Mixed Integer Linear Program (MILP). However, the creation of an optimal new timetable is an NP-hard problem; therefore, the MILP can be solved for easy cases, computation time being impractical for more complex examples. In these cases, a heuristic approach is provided that makes use of genetic algorithms to find a good solution jointly with heuristic techniques to generate an initial population. The algorithm was applied to a number of problem instances producing feasible, though not optimal, solutions in several seconds on a laptop, and compared to other proposals. Some improvements are suggested to obtain better results and further improve computation time. Rail transport is recognized as a sustainable and energy-efficient means of transport. Moreover, each freight train can take a large number of trucks off the roads, making them safer. Studies in this field can help to make railways more attractive to travelers by reducing operative cost, and increasing the number of services and their punctuality. To improve the transit system and service, it is necessary to build optimal train scheduling. There is an interest from the industry in automating the scheduling process. Fast computerized train scheduling, moreover, can be used to explore the effects of alternative draft timetables, operating policies, station layouts, and random delays or failures.

Train Planning on a Single Track Shared-Use Passenger and Freight Corridor With Demand Considerations

2014 ◽  
Author(s):  
Ahmadreza Talebian ◽  
Bo Zou
Keyword(s):  
Marginal Cost ◽  
Mathematical Formulation ◽  
Computation Time ◽  
Search Space ◽  
Computational Effort ◽  
Scheduling Problem ◽  
Sequential Approach ◽  
Train Scheduling ◽  
Passenger Train ◽  
Passenger Trains

While the train scheduling problem has been investigated for an extended period of time, shared passenger and freight corridor planning and capacity analysis have gained growing attention recently, due largely to the emergence of higher speed rail lines in the US. This study proposes an integrated, hypergraph-based approach that considers constraints from infrastructure supply as well as passenger demand in solving the train scheduling problem on a passenger-freight shared rail corridor. Two approaches are proposed to capture different policies which could be implemented in real world. The first, sequential approach considers passenger train priority in schedule planning, and then develop freight trains schedules given the fixed schedule of passenger trains. In the second approach, we minimize the total costs of freight and passenger trains simultaneously. Our results indicates that the marginal cost increase for freight railroad due to considering passenger train priority is larger than the associated marginal cost reduction for passengers. We also find that using high resolution time units in the mathematical formulation does not significantly improve the solution, meanwhile causing substantial increase in computation time. Therefore we suggest choosing coarser a time unit to first generate an approximate solution, which is subsequently used to reduce the search space for feasible train schedules using a finer-grained time unit. We show that this considerably saves computational effort.

scholarly journals A solution framework for linear PDE-constrained mixed-integer problems

2021 ◽  
Author(s):  
Fabian Gnegel ◽  
Armin Fügenschuh ◽  
Michael Hagel ◽  
Sven Leyffer ◽  
Marcus Stiemer
Keyword(s):  
Computation Time ◽  
Mixed Integer ◽  
Continuous Control ◽  
State Variables ◽  
Mixed Integer Linear Program ◽  
Numerical Solution Method ◽  
Linear Pde ◽  
Finite Set ◽  
Continuous Constraints ◽  
Naive Approach

AbstractWe present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

scholarly journals A Randomized Greedy Heuristic for Steerable Wireless Backhaul Reconfiguration

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 434
Author(s):  
Nina Skorin-Kapov ◽  
Ricardo Santos ◽  
Hakim Ghazzai ◽  
Andreas Kassler
Keyword(s):  
Packet Loss ◽  
Mixed Integer ◽  
Greedy Heuristic ◽  
Mixed Integer Linear Program ◽  
Wireless Backhaul ◽  
Online Planning ◽  
Backhaul Networks ◽  
Problem Instances ◽  
Reduced Time ◽  
Number Of Iterations

In this paper, we consider the reconfiguration of wireless backhaul networks with mechanically steerable antennas in the presence of changing traffic demands. Reconfiguration requires the scheduling and coordination of several operations, including antenna alignment and link establishment/removal, with minimal disruption to existing user traffic. Previously, we proposed a Mixed Integer Linear Program (MILP) to orchestrate such reconfiguration with minimal packet loss. While the MILP solves the problem optimally for a limited number of discrete reconfiguration time slots, it does not scale well. In this paper, we propose an iterative randomized greedy algorithm to obtain suboptimal solutions in reduced time. The algorithm schedules the reconfiguration of wireless links by ranking them according to a set of attributes with associated weights and selecting them according to a randomized greedy function. Results on six different network scenarios indicate that the proposed algorithm can achieve good quality solutions in significantly less time. Furthermore, by extending the reconfiguration time beyond the maximum number of time slots solvable by the MILP, the proposed heuristic can obtain superior solutions for some problem instances. The number of iterations of the algorithm can be tuned for its applicability in both offline and online planning scenarios.

scholarly journals Learning-‘N-Flying: A Learning-Based, Decentralized Mission-Aware UAS Collision Avoidance Scheme

2021 ◽  
Vol 5 (4) ◽  
pp. 1-26
Author(s):  
Alëna Rodionova ◽  
Yash Vardhan Pant ◽  
Connor Kurtz ◽  
Kuk Jang ◽  
Houssam Abbas ◽  
...  
Keyword(s):  
Collision Avoidance ◽  
Computation Time ◽  
Unmanned Aircraft ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Online Computation ◽  
Multiple Case ◽  
Aircraft System ◽  
The City

Urban Air Mobility, the scenario where hundreds of manned and Unmanned Aircraft Systems (UASs) carry out a wide variety of missions (e.g., moving humans and goods within the city), is gaining acceptance as a transportation solution of the future. One of the key requirements for this to happen is safely managing the air traffic in these urban airspaces. Due to the expected density of the airspace, this requires fast autonomous solutions that can be deployed online. We propose Learning-‘N-Flying (LNF), a multi-UAS Collision Avoidance (CA) framework. It is decentralized, works on the fly, and allows autonomous Unmanned Aircraft System (UAS)s managed by different operators to safely carry out complex missions, represented using Signal Temporal Logic, in a shared airspace. We initially formulate the problem of predictive collision avoidance for two UASs as a mixed-integer linear program, and show that it is intractable to solve online. Instead, we first develop Learning-to-Fly (L2F) by combining (1) learning-based decision-making and (2) decentralized convex optimization-based control. LNF extends L2F to cases where there are more than two UASs on a collision path. Through extensive simulations, we show that our method can run online (computation time in the order of milliseconds) and under certain assumptions has failure rates of less than 1% in the worst case, improving to near 0% in more relaxed operations. We show the applicability of our scheme to a wide variety of settings through multiple case studies.

scholarly journals Optimal Coordinated Bidding of a Profit Maximizing, Risk-Averse EV Aggregator in Three-Settlement Markets Under Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1755 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Real Time ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Computation Time ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Mixed Integer Linear Program ◽  
Market Prices

This paper develops a two-stage stochastic and dynamically updated multi-period mixed integer linear program (SD-MILP) for optimal coordinated bidding of an electric vehicle (EV) aggregator to maximize its profit from participating in competitive day-ahead, intra-day and real-time markets. The hourly conditional value at risk (T-CVaR) is applied to model the risk of trading in different markets. The objective of two-stage SD-MILP is modeled as a convex combination of the expected profit and the T-CVaR hourly risk measure. When day-ahead, intra-day and real-time market prices and fleet mobility are uncertain, the proposed two-stage SD-MILP model yields optimal EV charging/discharging plans for day-ahead, intra-day and real-time markets at per device level. The degradation costs of EV batteries are precisely modeled. To reflect the continuous clearing nature of the intra-day and real-time markets, rolling planning is applied, which allows re-forecasting and re-dispatching. The proposed two-stage SD-MILP is used to derive a bidding curve of an aggregator managing 1000 EVs. Furthermore, the model statistics and computation time are recorded while simulating the developed algorithm with 5000 EVs.

Using a genetic algorithm to solve the troops-to-tasks problem in military operations planning

2017 ◽  
Vol 14 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Maria Fleischer Fauske
Keyword(s):  
Genetic Algorithm ◽  
Time Frame ◽  
Optimization Techniques ◽  
Operational Planning ◽  
Mixed Integer ◽  
Data Sets ◽  
Military Operations ◽  
Mixed Integer Linear Program ◽  
Problem Instances ◽  
Feasible Solutions

The troops-to-tasks analysis in military operational planning is the process where the military staff investigates who should do what, where, and when in the operation. In this paper, we describe a genetic algorithm for solving troops-to-tasks problems, which are typically solved manually. The study was motivated by a request from Norwegian military staff, who acknowledged the potential for solving the troops-to-tasks analysis more effectively by using optimization techniques. Also, NATO’s operational planning tool, TOPFAS, lacks an optimization module for the troops-to-tasks analysis. The troops-to-tasks problem generalizes the well-known resource-constrained project scheduling problem, and thus it is very difficult to solve. As the troops-to-tasks problem is particularly complex, the main purpose of our study was to develop an algorithm capable of solving real-sized problem instances. We developed a genetic algorithm with new features, which were crucial to finding good solutions. We tested the algorithm on two different data sets representing high-intensity military operations. We compared the performance of the algorithm to that of a mixed integer linear program solved by CPLEX. In contrast to CPLEX, the algorithm found feasible solutions within an acceptable time frame for all instances.

Managing Navigation Channel Traffic and Anchorage Area Utilization of a Container Port

2019 ◽  
Vol 53 (3) ◽  
pp. 728-745 ◽  
Author(s):  
Shuai Jia ◽  
Chung-Lun Li ◽  
Zhou Xu
Keyword(s):  
Lagrangian Relaxation ◽  
Computation Time ◽  
Mixed Integer ◽  
Container Port ◽  
Online Appendix ◽  
Computational Performance ◽  
Navigation Channel ◽  
Data Files ◽  
Problem Instances ◽  
Operational Data

Navigation channels are fairways for vessels to travel in and out of the terminal basin of a container port. The capacity of a navigation channel is restricted by the number of traffic lanes and safety clearance of vessels, and the availability of a navigation channel is usually affected by tides. The limited capacity and availability of a navigation channel could lead to congestion in the terminal basin. When the navigation channels run out of capacity, the anchorage areas in the terminal basin could serve as a buffer. This paper aims to develop a mathematical model that simultaneously optimizes the navigation channel traffic and anchorage area utilization. We provide a mixed integer programming formulation of the problem, analyze its complexity, and propose a Lagrangian relaxation heuristic in which the relaxed problem is decomposed into two asymmetric assignment problems. Computational performance of the Lagrangian relaxation heuristic is tested on problem instances generated based on the operational data of a port in Shanghai. Computational results show that the proposed heuristic is able to achieve satisfactory performance within a reasonable computation time. Data files and the online appendix are available at https://doi.org/10.1287/trsc.2018.0879 .

Development of a Multimodal Microsimulation-Based Evacuation Model

2019 ◽  
Vol 2673 (10) ◽  
pp. 477-488
Author(s):  
Jahedul Alam ◽  
Muhammad Ahsanul Habib ◽  
Uday Venkatadri
Keyword(s):  
Dynamic Traffic Assignment ◽  
Route Choice ◽  
Computation Time ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Modeling Framework ◽  
Transit System ◽  
Microsimulation Modeling ◽  
Transit Route ◽  
Transit Routes

This study presents a multimodal evacuation microsimulation modeling framework. The paper first determines optimum marshal point locations and transit routes, then examines network conditions through traffic microsimulation of a mass evacuation of the Halifax Peninsula, Canada. The proposed optimization modeling approach identifies marshal point locations based on transit demand obtained from a Halifax Regional Transport network model. A mixed integer linear programming (MILP) technique is used to formulate the marshal point location and transit route choice problem. The study proposes a novel approach to solving the MILP problem, using the “branch and cut” algorithm, which demonstrates superiority in computation time and production of quality solutions. The optimization model determines 135 marshal points and 12 transit routes to evacuate approximately 8,400 transit-dependent individuals. Transit demand and marshal point locations are found to be concentrated at the core of the peninsula. The microsimulation modeling takes a dynamic traffic assignment-based approach. The simulation model predicts that it takes 22 h to evacuate all auto users but just 7 h for the transit-dependent population. The study reveals that the transit system has excess capacity to assist evacuees who switch from auto and other modes. Local traffic congestion prolongs the evacuation of a few densely-populated zones in the downtown core of the peninsula. The findings of this research help policy-makers understand the impacts of marshal point locations and transit route choice decisions on multimodal evacuation performance, and provide insights into emergency planning of multimodal evacuations under "mode switch" and transit-based evacuation scenarios.

scholarly journals Investment Incentives in Competitive Electricity Markets

2018 ◽  
Vol 8 (10) ◽  
pp. 1978 ◽  
Author(s):  
Jaber Valinejad ◽  
Taghi Barforoshi ◽  
Mousa Marzband ◽  
Edris Pouresmaeil ◽  
Radu Godina ◽  
...  
Keyword(s):  
Electricity Markets ◽  
Electricity Market ◽  
Planning Horizon ◽  
Optimization Method ◽  
Design Criterion ◽  
Mixed Integer ◽  
Investment Incentives ◽  
Mixed Integer Linear Program ◽  
Interconnected Power System ◽  
The Impact

This paper presents the analysis of a novel framework of study and the impact of different market design criterion for the generation expansion planning (GEP) in competitive electricity market incentives, under variable uncertainties in a single year horizon. As investment incentives conventionally consist of firm contracts and capacity payments, in this study, the electricity generation investment problem is considered from a strategic generation company (GENCO) ′ s perspective, modelled as a bi-level optimization method. The first-level includes decision steps related to investment incentives to maximize the total profit in the planning horizon. The second-level includes optimization steps focusing on maximizing social welfare when the electricity market is regulated for the current horizon. In addition, variable uncertainties, on offering and investment, are modelled using set of different scenarios. The bi-level optimization problem is then converted to a single-level problem and then represented as a mixed integer linear program (MILP) after linearization. The efficiency of the proposed framework is assessed on the MAZANDARAN regional electric company (MREC) transmission network, integral to IRAN interconnected power system for both elastic and inelastic demands. Simulations show the significance of optimizing the firm contract and the capacity payment that encourages the generation investment for peak technology and improves long-term stability of electricity markets.

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