361 research outputs found
Study of distributed Lagrangian heuristics for self-adaptive publish/subscribe network design problems
The Internet of Things (IoT) has revolutionized information collection and processing through the interconnection of smart objects that can transmit data for analysis. However, IoT devices typically send data to cloud servers, which can lead to connectivity and data transfer issues. Edge computing-based solutions are being studied as a solution, which involves processing data directly at the source to enable more efficient and effective services. However, current IoT infrastructures are not yet ready for this transition. One solution being explored is the use of multiple distributed MQTT brokers on different interconnected machines to improve system reliability and scalability. A fully-distributed optimization solution based on a Lagrangian relaxation approach is being considered to ensure optimal load balancing and reliability for the entire system. The objective is to evaluate the effectiveness of distributed Lagrangian heuristic algorithms in the field of communication network management, which allows network nodes to act autonomously based on information about themselves and neighboring nodes they can communicate with, without centralized management
Optimization of low-cost integration of wind and solar power in multi-node electricity systems: Mathematical modelling and dual solution approaches
The global production of electricity contributes significantly to the release of CO2 emissions. Therefore, a transformation of the electricity system is of vital importance in order to restrict global warming. This thesis concerns modelling and methodology of electricity systems which contain a large share of variable renewable electricity generation (i.e. wind and solar power).The two models developed in this thesis concern optimization of long-term investments in the electricity system. They aim at minimizing investment and production costs under electricity production constraints, using different spatial resolutions and technical detail, while meeting the electricity demand. These models are very large in nature due to the 1) high temporal resolution needed to capture the wind and solar variations while maintaining chronology in time, and 2) need to cover a large geographical scope in order to represent strategies to manage these variations (e.g.\ electricity trade). Thus, different decomposition methods are applied to reduce computation times. We develop three different decomposition methods: Lagrangian relaxation combined with variable splitting solved using either i) a subgradient algorithm or ii) an ADMM algorithm, and iii) a heuristic decomposition using a consensus algorithm. In all three cases, the decomposition is done with respect to the temporal resolution by dividing the year into 2-week periods. The decomposition methods are tested and evaluated for cases involving regions with different energy mixes and conditions for wind and solar power. Numerical results show faster computation times compared to the non-decomposed models and capacity investment options similar to the optimal solutions given by the latter models. However, the reduction in computation time may not be sufficient to motivate the increase in complexity and uncertainty of the decomposed models
Covering problem with minimum radius enclosing circle
This study extends the classical smallest enclosing circle problem in location science to optimize healthcare communication hubs. Given a set of demand points and potential groups, we identify the optimal number of subgroups to cover all points and the circle enclosing them with minimum radius. The center of this circle serves as the communication hub location, minimizing the distance between demand points and facilities subject to customer demand. We develop a nonconvex-nonlinear optimization model and propose a quadratic programming-based approximation algorithm to solve it. Tested on various hypothetical and real scenarios, our model effectively reduces the facility setup cost and identifies the optimal communication hub location
Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization
Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes
Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the
problem of decomposing a corrupted data matrix into a sparse matrix of
perturbations plus a low-rank matrix containing the ground truth. SLR is a
fundamental problem in Operations Research and Machine Learning which arises in
various applications, including data compression, latent semantic indexing,
collaborative filtering, and medical imaging. We introduce a novel formulation
for SLR that directly models its underlying discreteness. For this formulation,
we develop an alternating minimization heuristic that computes high-quality
solutions and a novel semidefinite relaxation that provides meaningful bounds
for the solutions returned by our heuristic. We also develop a custom
branch-and-bound algorithm that leverages our heuristic and convex relaxations
to solve small instances of SLR to certifiable (near) optimality. Given an
input -by- matrix, our heuristic scales to solve instances where
in minutes, our relaxation scales to instances where in
hours, and our branch-and-bound algorithm scales to instances where in
minutes. Our numerical results demonstrate that our approach outperforms
existing state-of-the-art approaches in terms of rank, sparsity, and
mean-square error while maintaining a comparable runtime
A Statistical Interpretation of the Maximum Subarray Problem
Maximum subarray is a classical problem in computer science that given an
array of numbers aims to find a contiguous subarray with the largest sum. We
focus on its use for a noisy statistical problem of localizing an interval with
a mean different from background. While a naive application of maximum subarray
fails at this task, both a penalized and a constrained version can succeed. We
show that the penalized version can be derived for common exponential family
distributions, in a manner similar to the change-point detection literature,
and we interpret the resulting optimal penalty value. The failure of the naive
formulation is then explained by an analysis of the estimated interval
boundaries. Experiments further quantify the effect of deviating from the
optimal penalty. We also relate the penalized and constrained formulations and
show that the solutions to the former lie on the convex hull of the solutions
to the latter.Comment: 2023 IEEE International Conference on Acoustics, Speech, and Signal
Processing. 5 pages, 7 figure
Sine Cosine Algorithm for Optimization
This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA
Stochastic Control/Stopping Problem with Expectation Constraints
We study a stochastic control/stopping problem with a series of
inequality-type and equality-type expectation constraints in a general
non-Markovian framework. We demonstrate that the stochastic control/stopping
problem with expectation constraints (CSEC) is independent of a specific
probability setting and is equivalent to the constrained stochastic
control/stopping problem in weak formulation (an optimization over joint laws
of Brownian motion, state dynamics, diffusion controls and stopping rules on an
enlarged canonical space). Using a martingale-problem formulation of controlled
SDEs in spirit of \cite{Stroock_Varadhan}, we characterize the probability
classes in weak formulation by countably many actions of canonical processes,
and thus obtain the upper semi-analyticity of the CSEC value function.
Then we employ a measurable selection argument to establish a dynamic
programming principle (DPP) in weak formulation for the CSEC value function, in
which the conditional expected costs act as additional states for constraint
levels at the intermediate horizon. This article extends the results of
\cite{Elk_Tan_2013b} to the expectation-constraint case. We extend our previous
work \cite{OSEC_stopping} to the more complicated setting where the diffusion
is controlled. Compared to that paper the topological properties of
diffusion-control spaces and the corresponding measurability are more
technically involved which complicate the arguments especially for the
measurable selection for the super-solution side of DPP in the weak
formulation.Comment: Keywords: Stochastic control/stopping problem with expectation
constraints, martingale-problem formulation, enlarged canonical space, Polish
space of diffusion controls, Polish space of stopping times, dynamic
programming principle, regular conditional probability distribution,
measurable selectio
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
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