A Review on Multicommodity Urban Evacuation Problem

Urban evacuation regards as a critical course of action that helps to re-locate the maximum number of people and property from the disaster zone of the urban area to the safe zone within the shortest possible time. Multi-commodity urban evacuation problem (MCUEP) explores and identifies the re-construction of the traffic routes to be followed in evacuation with the mobility of two or more types of the vehicles allowing two way streets. The idea of the paper is to introduce a multi-commodity urban evacuation traffic routing modeling with the bus commodity and the vehicle commodity in the street segment and intersection segment where the crossing and merging cannot be prohibited. The evacuation is made effective by sending and re-sending the buses (if necessary) and using the personal vehicles for once. The paper will give a review of MCUEP as the state of the art basically designed as a mixed integer model functioning as the remedy of the shortcomings of one-way evacuation model and put forwards a brief discussion of the solution approaches.Journal of Institute of Science and TechnologyVolume 21, Issue 1, August 2016, page: 19-27

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Exact Methods for the Traveling Salesman Problem with Drone

Transportation Science ◽

10.1287/trsc.2020.1017 ◽

2021 ◽

Vol 55 (2) ◽

pp. 315-335

Author(s):

Roberto Roberti ◽

Mario Ruthmair

Keyword(s):

Dynamic Programming ◽

Traveling Salesman Problem ◽

State Of The Art ◽

The State ◽

Set Partitioning ◽

Traveling Salesman ◽

Mixed Integer ◽

Branch And Price ◽

Last Mile ◽

The Traveling Salesman Problem

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

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Mixed-integer nonlinear optimization

Acta Numerica ◽

10.1017/s0962492913000032 ◽

2013 ◽

Vol 22 ◽

pp. 1-131 ◽

Cited By ~ 254

Author(s):

Pietro Belotti ◽

Christian Kirches ◽

Sven Leyffer ◽

Jeff Linderoth ◽

James Luedtke ◽

...

Keyword(s):

Branch And Bound ◽

Convex Functions ◽

State Of The Art ◽

Small Sample ◽

The State ◽

Decision Problems ◽

Mixed Integer ◽

Feasible Region ◽

Convex Relaxations ◽

Single Tree

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. We review models and applications of MINLP, and survey the state of the art in methods for solving this challenging class of problems.Most solution methods for MINLP apply some form of tree search. We distinguish two broad classes of methods: single-tree and multitree methods. We discuss these two classes of methods first in the case where the underlying problem functions are convex. Classical single-tree methods include nonlinear branch-and-bound and branch-and-cut methods, while classical multitree methods include outer approximation and Benders decomposition. The most efficient class of methods for convex MINLP are hybrid methods that combine the strengths of both classes of classical techniques.Non-convex MINLPs pose additional challenges, because they contain non-convex functions in the objective function or the constraints; hence even when the integer variables are relaxed to be continuous, the feasible region is generally non-convex, resulting in many local minima. We discuss a range of approaches for tackling this challenging class of problems, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non-convex structures to obtain improved convex relaxations.We finish our survey with a brief discussion of three important aspects of MINLP. First, we review heuristic techniques that can obtain good feasible solution in situations where the search-tree has grown too large or we require real-time solutions. Second, we describe an emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP. Third, we survey the state of the art in software for MINLP.

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Practical Picture Processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051700 ◽

1974 ◽

Vol 32 ◽

pp. 338-339

Author(s):

T. A. Welton

Keyword(s):

Radiation Damage ◽

Coherence Length ◽

Spatial Information ◽

State Of The Art ◽

Coherent Radiation ◽

The State ◽

Energy Spread ◽

Electron Micrograph ◽

Picture Processing ◽

Molecular Skeleton

Various authors have emphasized the spatial information resident in an electron micrograph taken with adequately coherent radiation. In view of the completion of at least one such instrument, this opportunity is taken to summarize the state of the art of processing such micrographs. We use the usual symbols for the aberration coefficients, and supplement these with £ and 6 for the transverse coherence length and the fractional energy spread respectively. He also assume a weak, biologically interesting sample, with principal interest lying in the molecular skeleton remaining after obvious hydrogen loss and other radiation damage has occurred.

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