2,201 research outputs found
Enabling the “Easy Button” for Broad, Parallel Optimization of Functions Evaluated by Simulation
Java Optimization by Simulation (JOBS) is presented: an open-source, object-oriented Java library designed to enable the study, research, and use of optimization for models evaluated by simulation. JOBS includes several novel design features that make it easy for a simulation modeler, without extensive expertise in optimization or parallel computation, to define an optimization model with deterministic and/or stochastic constraints, choose one or more metaheuristics to solve it and run, using massively parallel function evaluation to reduce wall-clock times.
JOBS is supported by a new language independent, application programming interface (API) for remote simulation model evaluation and a serverless computing environment to provide massively parallel function evaluation, on demand. Dynamic loop scheduling methods are evaluated in the serverless environment with the opportunity for significant resource contention for master node computing power and network bandwidth.
JOBS implements several population-based and single-solution improvement metaheuristics (solvers) for real, discrete, and mixed problems. The object-oriented design is extendible with classes that drastically reduce the amount of code required to implement a new solver and encourage re-use of solvers as building blocks for creating new multi-stage solvers or memetic algorithms
Accuracy of Numerical Solution to Dynamic Programming Models
Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.Research Methods/ Statistical Methods,
Algorithms for Nonconvex Optimization Problems in Machine Learning and Statistics
The purpose of this thesis is the design of algorithms that can be used to determine optimal solutions to nonconvex data approximation problems.
In Part I of this thesis, we consider a very general class of nonconvex and large-scale data approximation problems and devise an algorithm that efficiently computes locally optimal solutions to these problems. As a type of trust-region Newton-CG method, the algorithm can make use of directions of negative curvature to escape saddle points, which otherwise might slow down the optimization process when solving nonconvex problems. We present results of numerical experiments on convex and nonconvex problems which support our claim that our algorithm has significant advantages compared to methods like stochastic gradient descent and its variance-reduced versions.
In Part II we consider the univariate least-squares spline approximation problem with free knots, which is known to possess a large number of locally minimal points far from the globally optimal solution. Since in typical applications, neither the dimension of the decision variable nor the number of data points is particularly large, it is possible to make use of the specific problem structure in order to devise algorithmic approaches to approximate the globally optimal solution of problem instances of relevant sizes. We propose to approximate the continuous original problem with a combinatorial optimization problem, and investigate two algorithmic approaches for the computation of the optimal solution of the latter
A Hierarchal Planning Framework for AUV Mission Management in a Spatio-Temporal Varying Ocean
The purpose of this paper is to provide a hierarchical dynamic mission
planning framework for a single autonomous underwater vehicle (AUV) to
accomplish task-assign process in a limited time interval while operating in an
uncertain undersea environment, where spatio-temporal variability of the
operating field is taken into account. To this end, a high level reactive
mission planner and a low level motion planning system are constructed. The
high level system is responsible for task priority assignment and guiding the
vehicle toward a target of interest considering on-time termination of the
mission. The lower layer is in charge of generating optimal trajectories based
on sequence of tasks and dynamicity of operating terrain. The mission planner
is able to reactively re-arrange the tasks based on mission/terrain updates
while the low level planner is capable of coping unexpected changes of the
terrain by correcting the old path and re-generating a new trajectory. As a
result, the vehicle is able to undertake the maximum number of tasks with
certain degree of maneuverability having situational awareness of the operating
field. The computational engine of the mentioned framework is based on the
biogeography based optimization (BBO) algorithm that is capable of providing
efficient solutions. To evaluate the performance of the proposed framework,
firstly, a realistic model of undersea environment is provided based on
realistic map data, and then several scenarios, treated as real experiments,
are designed through the simulation study. Additionally, to show the robustness
and reliability of the framework, Monte-Carlo simulation is carried out and
statistical analysis is performed. The results of simulations indicate the
significant potential of the two-level hierarchical mission planning system in
mission success and its applicability for real-time implementation
Upravljanje putanjama vazduhoplova u kontroli letenja na pre-taktičkom i taktičkom nivou
Global air traffic demand is continuously increasing, and it is predicted
to be tripled by 2050. The need for increasing air traffic capacity motivates a
shift of ATM towards Trajectory Based Operations (TBOs). This implies the
possibility to design efficient congestion-free aircraft trajectories more in
advance (pre-tactical, strategic level) reducing controller’s workload on tactical
level. As consequence, controllers will be able to manage more flights.
Current flow management practices in air traffic management (ATM)
system shows that under the present system settings there are only timid
demand management actions taken prior to the day of operation such as: slot
allocation and strategic flow rerouting. But the choice of air route for a
particular flight is seen as a commercial decision to be taken by airlines, given
air traffic control constraints. This thesis investigates the potential of robust
trajectory planning (considered as an additional demand management action)
at pre-tactical level as a mean to alleviate the en-route congestion in airspace.
Robust trajectory planning (RTP) involves generation of congestion-free
trajectories with minimum operating cost taking into account uncertainty of
trajectory prediction and unforeseen event. Although planned cost could be
higher than of conventional models, adding robustness to schedules might
reduce cost of disruptions and hopefully lead to reductions in operating cost.
The most of existing trajectory planning models consider finding of conflict-free
trajectories without taking into account uncertainty of trajectory prediction. It is
shown in the thesis that in the case of traffic disturbances, it is better to have a
robust solution otherwise newly generated congestion problems would be hard
and costly to solve.
This thesis introduces a novel approach for route generation (3D
trajectory) based on homotopic feature of continuous functions. It is shown that
this approach is capable of generating a large number of route shapes with a
reasonable number of decision variables. Those shapes are then coupled with
time dimension in order to create trajectories (4D)...Globalna potražnja za vazdušnim saobraćajem u stalnom je porastu i
prognozira se da će broj letova biti utrostručen do 2050 godine. Potreba za
povećanjem kapaciteta sistema vazdušnog saobraćaja motivisala je promene u
sistemu upravljanja saobraćajnim tokovima u kome će u budućnosti centralnu
ulogu imati putanje vazduhoplova tzv. “trajectory-based” koncept. Takav
sistem omogućiće planiranje putanja vazduhoplova koje ne stvaraju zagušenja
u sistemu na pre-taktičkom nivou i time smanjiti radno opterećenje kontrolora
na taktičkom nivou. Kao posledica, kontrolor će moći da upravlja više letova
nego u današnjem sistemu.
Današnja praksa upravljanja saobraćajnim tokovima pokazuje da se mali
broj upravljačkih akcija primenjuje pre dana obavljanja letova npr.: alokacija
slotova poletanja i strateško upravljanje saobraćajnim tokovima. Međutim izbor
putanje kojom će se odviti let posmatra se kao komercijalna odluka aviokompanije
(uz poštovanje postavljenih ograničenja od strane kontrole letenja) i
stoga je ostavljen na izbor avio-kompaniji. Većina, do danas razvijenih, modela
upravljanja putanjama vazduhoplova ima za cilj generisanje bez-konfliktnih
putanja, ne uzimajući u obzir neizvesnost u poziciji vazduhoplova. U ovoj
doktorskoj disertaciji ispitivano je planiranje robustnih putanja vazduhoplova
(RTP) na pre-taktičkom nivou kao sredstvo ublažavanja zagušenja u
vazdušnom prostoru . Robustno upravljanje putanjama vazduhoplova
podrazumeva izbor putanja vazduhoplova sa minimalnim operativnim
troškovima koje ne izazivaju zagušenja u vazdušnom prostoru u uslovima
neizvesnosti buduđe pozicije vazduhoplova i nepredviđenih događaja. Iako
predviđeni (planirani) operativni troškovi robustnih putanja mogu u startu biti
veći od operativnih troškova bez-konfliktnih putanja, robusnost može uticati na
smanjenje troškove poremećaja putanja jer ne zahteva dodatnu promenu
putanja vazduhplova radi izbegavanja konfliktnih situacija na taktičkom nivou.
To na kraju može dovesti i do smanjenja stvarnih operativnih troškova. U tezi je
pokazano, da je u slučaju poremećaja saobraćaja bolje imati robustno rešenje
(putanje), jer novo-nastali problem zagušenosti vazdušnog prostora je teško i
skupo rešiti..
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