Searching a solution space using Stochastic Gradient Descent (SGD) depends on the examples picked at each iteration of the algorithm. Therefore, best practices suggest randomizing the order of training points to visit...
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ISBN:
(纸本)9781538678800
Searching a solution space using Stochastic Gradient Descent (SGD) depends on the examples picked at each iteration of the algorithm. Therefore, best practices suggest randomizing the order of training points to visit after every epoch. This random selection is typically implemented as a random shuffling of the order of the training vectors rather than a genuine random training point selection. The shuffling is usually performed after every epoch which results in an extremely low temporal locality of access to the training set. Indeed, each training point is used once, and not before all the other training points have been visited. This means that a cache layer in the memory hierarchy of a modern HPC computer system will have little benefit for the algorithm unless all the training points fit inside that cache.
Motion Planning and Control algorithms are often formulated as optimization problems as desired robot behaviors can be intuitively encoded in the form of cost and constraint functions. A fundamental challenge in robot...
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ISBN:
(纸本)9781450383073
Motion Planning and Control algorithms are often formulated as optimization problems as desired robot behaviors can be intuitively encoded in the form of cost and constraint functions. A fundamental challenge in robotics is to make optimization based motion planning reliable and real-time. This thesis aims to achieve this for motion planning and control problems encountered in a wide class of applications ranging from autonomous driving and object transportation to manipulation. In particular, we aim to develop optimization algorithms that identifies and leverages the underlying useful albeit limited convex structures in the problem through techniques like Alternating Direction Method of Multipliers and Bergman Iteration. During the first 1.5 years of the thesis, we have already obtained encouraging results that validated our core hypothesis and led to optimizer that surpasses the state of the art in many challenging problems.
Two simple yet powerful optimization algorithms, named the Best-Mean-Random (BMR) and Best-Worst-Random (BWR) algorithms, are developed and presented in this paper to handle both constrained and unconstrained optimiza...
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This paper discusses the different types of population-based optimization algorithms. It reviews several works done by a number of authors on these algorithms, highlighting their strengths and weaknesses. Specifically...
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ISBN:
(数字)9781728131269
ISBN:
(纸本)9781728131276
This paper discusses the different types of population-based optimization algorithms. It reviews several works done by a number of authors on these algorithms, highlighting their strengths and weaknesses. Specifically, this paper analyses the main components of a good optimization algorithms which are: Local Search, Global Search, and Randomness and it concludes, that to enjoy a good search, these components must be present in any good stochastic algorithm. Furthermore, the paper asserts that identification of the best solution in every iteration is a necessary criterion. The lack of any of these components, therefore, is the major of reason why some optimizations algorithms have not been as efficient and effective as envisaged at their design phases.
This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multiagent systems, particularly those subject to dis...
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Some autoregressive models exhibit in-context learning capabilities: being able to learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. The ...
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The aim of this work is to introduce an effective tool in order to help the EM designer to select the best optimization algorithm through an easy-to-manage classification of Evolutionary algorithms. In fact, choosing ...
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ISBN:
(纸本)9781479978076
The aim of this work is to introduce an effective tool in order to help the EM designer to select the best optimization algorithm through an easy-to-manage classification of Evolutionary algorithms. In fact, choosing the best tool for an application could be really difficult, especially for a user not aware of optimization theory. Here we propose a general analysis for EAs, highlighting their block-structure and classifying them through some objective (non-qualitative) parameters.
Applications of numerical optimization have appeared across a broad range of research fields, from finance and economics to the natural sciences and engineering. It is well known that the optimization techniques emplo...
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Applications of numerical optimization have appeared across a broad range of research fields, from finance and economics to the natural sciences and engineering. It is well known that the optimization techniques employed in each field are specialized to suit their problems. Recent advances in computing hardware and modeling software have given rise to new applications for numerical optimization. These new applications occasionally uncover bottlenecks in existing optimization algorithms and necessitate further specialization of the algorithms. However, such specialization requires expert knowledge of the underlying mathematical theory and the software implementation of existing algorithms. To address this challenge, we present modOpt, an open-source software framework that facilitates the construction of optimization algorithms from modules. The modular environment provided by modOpt enables developers to tailor an existing algorithm for a new application by only altering the relevant modules. modOpt is designed as a platform to support students and beginner developers in quickly learning and developing their own algorithms. With that aim, the entirety of the framework is written in Python, and it is well-documented, well-tested, and hosted open-source on GitHub. Several additional features are embedded into the framework to assist both beginner and advanced developers. In addition to providing stock modules, the framework also includes fully transparent implementations of pedagogical optimization algorithms in Python. To facilitate testing and benchmarking of new algorithms, the framework features built-in visualization and recording capabilities, interfaces to modeling frameworks such as OpenMDAO and CSDL, interfaces to general-purpose optimization algorithms such as SNOPT and SLSQP, an interface to the CUTEst test problem set, etc. In this paper, we present the underlying software architecture of modOpt, review its various features, discuss several educational and
We present three tailored algorithms for solving large-scale mixed-integer linear fractional programming (MILFP) problems. The first one combines Branch-and-Bound method with Charnes-Cooper transformation. The other t...
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ISBN:
(纸本)9781479917730
We present three tailored algorithms for solving large-scale mixed-integer linear fractional programming (MILFP) problems. The first one combines Branch-and-Bound method with Charnes-Cooper transformation. The other two tailored MILFP solution methods are the parametric algorithm and the reformulation-linearization algorithm. Extensive computational studies are performed to demonstrate the efficiency of these algorithms and to compare them with some general-purpose mixed-integer nonlinear programming methods. A performance profile is given based on the algorithm performance analysis and benchmarking methods. The applications of these algorithms are further illustrated through an application on water supply chain optimization for shale gas production. Computational results show that the parametric algorithm and the reformulation-linearization algorithm have the highest efficiency among all the tested solution methods.
Fejér monotonicity is a well-established property commonly observed in sequences generated by optimization algorithms. In this paper, we introduce an extension of this property, called Fejér* monotonicity, w...
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