scholarly journals Fuel-Optimal Ascent Trajectory Problem for Launch Vehicle via Theory of Functional Connections

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Shiyao Li ◽  
Yushen Yan ◽  
Kun Zhang ◽  
Xinguo Li
Keyword(s):  
Optimization Problem ◽  
Search Space ◽  
Launch Vehicle ◽  
Functional Connections ◽  
Constrained Problem ◽  
Unconstrained Optimization Problem ◽  
Interpolation Technique ◽  
Matlab Implementation ◽  
Unconstrained Problem ◽  
Trajectory Problem

In this study, we develop a method based on the Theory of Functional Connections (TFC) to solve the fuel-optimal problem in the ascending phase of the launch vehicle. The problem is first transformed into a nonlinear two-point boundary value problem (TPBVP) using the indirect method. Then, using the function interpolation technique called the TFC, the problem’s constraints are analytically embedded into a functional, and the TPBVP is transformed into an unconstrained optimization problem that includes orthogonal polynomials with unknown coefficients. This process effectively reduces the search space of the solution because the original constrained problem transformed into an unconstrained problem, and thus, the unknown coefficients of the unconstrained expression can be solved using simple numerical methods. Finally, the proposed algorithm is validated by comparing to a general nonlinear optimal control software GPOPS-II and the traditional indirect numerical method. The results demonstrated that the proposed algorithm is robust to poor initial values, and solutions can be solved in less than 300 ms within the MATLAB implementation. Consequently, the proposed method has the potential to generate optimal trajectories on-board in real time.

scholarly journals A Functional Interpolation Approach to Compute Periodic Orbits in the Circular-Restricted Three-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1210
Author(s):  
Hunter Johnston ◽  
Martin W. Lo ◽  
Daniele Mortari
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Optimization Problem ◽  
Nonlinear Least Squares ◽  
Interpolation Scheme ◽  
Three Body Problem ◽  
Functional Connections ◽  
Unconstrained Optimization Problem ◽  
Comparable Accuracy ◽  
Three Body

In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Functional Connections (TFC). Using this technique, a periodic constraint is analytically embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.

scholarly journals GENO – Optimization for Classical Machine Learning Made Fast and Easy

2020 ◽  
Vol 34 (09) ◽  
pp. 13620-13621
Author(s):  
Sören Laue ◽  
Matthias Mitterreiter ◽  
Joachim Giesen
Keyword(s):  
Machine Learning ◽  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Specific Problem ◽  
Optimization Problems ◽  
Modeling Language ◽  
Large Margin ◽  
Unconstrained Optimization Problem

Most problems from classical machine learning can be cast as an optimization problem. We introduce GENO (GENeric Optimization), a framework that lets the user specify a constrained or unconstrained optimization problem in an easy-to-read modeling language. GENO then generates a solver, i.e., Python code, that can solve this class of optimization problems. The generated solver is usually as fast as hand-written, problem-specific, and well-engineered solvers. Often the solvers generated by GENO are faster by a large margin compared to recently developed solvers that are tailored to a specific problem class.An online interface to our framework can be found at http://www.geno-project.org.

Space Contraction and Partition Algorithm for Combinatorial Optimization

2011 ◽  
Vol 421 ◽  
pp. 559-563
Author(s):  
Yong Chao Gao ◽  
Li Mei Liu ◽  
Heng Qian ◽  
Ding Wang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Solution Space ◽  
Search Space ◽  
Small Scale ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Intelligent Algorithms ◽  
Combinatorial Optimization Problems

The scale and complexity of search space are important factors deciding the solving difficulty of an optimization problem. The information of solution space may lead searching to optimal solutions. Based on this, an algorithm for combinatorial optimization is proposed. This algorithm makes use of the good solutions found by intelligent algorithms, contracts the search space and partitions it into one or several optimal regions by backbones of combinatorial optimization solutions. And optimization of small-scale problems is carried out in optimal regions. Statistical analysis is not necessary before or through the solving process in this algorithm, and solution information is used to estimate the landscape of search space, which enhances the speed of solving and solution quality. The algorithm breaks a new path for solving combinatorial optimization problems, and the results of experiments also testify its efficiency.

scholarly journals Location histogram privacy by Sensitive Location Hiding and Target Histogram Avoidance/Resemblance

2019 ◽  
Vol 62 (7) ◽  
pp. 2613-2651
Author(s):  
Grigorios Loukides ◽  
George Theodorakopoulos
Keyword(s):  
Price Discrimination ◽  
Optimization Problem ◽  
Optimal Algorithm ◽  
Search Space ◽  
Greedy Heuristic ◽  
Optimal Solutions ◽  
Area Of Interest ◽  
Minority Member ◽  
Specific Search

AbstractA location histogram is comprised of the number of times a user has visited locations as they move in an area of interest, and it is often obtained from the user in the context of applications such as recommendation and advertising. However, a location histogram that leaves a user’s computer or device may threaten privacy when it contains visits to locations that the user does not want to disclose (sensitive locations), or when it can be used to profile the user in a way that leads to price discrimination and unsolicited advertising (e.g., as “wealthy” or “minority member”). Our work introduces two privacy notions to protect a location histogram from these threats: Sensitive Location Hiding, which aims at concealing all visits to sensitive locations, and Target Avoidance/Resemblance, which aims at concealing the similarity/dissimilarity of the user’s histogram to a target histogram that corresponds to an undesired/desired profile. We formulate an optimization problem around each notion: Sensitive Location Hiding ($${ SLH}$$SLH), which seeks to construct a histogram that is as similar as possible to the user’s histogram but associates all visits with nonsensitive locations, and Target Avoidance/Resemblance ($${ TA}$$TA/$${ TR}$$TR), which seeks to construct a histogram that is as dissimilar/similar as possible to a given target histogram but remains useful for getting a good response from the application that analyzes the histogram. We develop an optimal algorithm for each notion, which operates on a notion-specific search space graph and finds a shortest or longest path in the graph that corresponds to a solution histogram. In addition, we develop a greedy heuristic for the $${ TA}$$TA/$${ TR}$$TR problem, which operates directly on a user’s histogram. Our experiments demonstrate that all algorithms are effective at preserving the distribution of locations in a histogram and the quality of location recommendation. They also demonstrate that the heuristic produces near-optimal solutions while being orders of magnitude faster than the optimal algorithm for $${ TA}$$TA/$${ TR}$$TR.

scholarly journals A Novel Hybrid Approach for Optimizing the Localization of Wireless Sensor Networks

2018 ◽  
Vol 200 ◽  
pp. 00005
Author(s):  
Halima Lakhbab
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Global Positioning System ◽  
Physical Environment ◽  
Optimization Problem ◽  
Hybrid Approach ◽  
Wireless Sensor ◽  
Swarm Optimization ◽  
Unconstrained Optimization Problem ◽  
Global Positioning

Wireless sensor networks are used for monitoring the environment and controlling the physical environment. Information gathered by the sensors is only useful if the positions of the sensors are known. One of the solutions for this problem is Global Positioning System (GPS). However, this approach is prohibitively costly; both in terms of hardware and power requirements. Localization is defined as finding the physical coordinates of a group of nodes. Localization is classified as an unconstrained optimization problem. In this work, we propose a new algorithm to tackle the problem of localization; the algorithm is based on a hybridization of Particle Swarm Optimization (PSO) and Simulated Annealing (SA). Simulation results are given to illustrate the robustness and efficiency of the presented algorithm.

scholarly journals Symmetry-Breaking for Airflow Control Optimization of an Oscillating-Water-Column System

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 895 ◽  
Author(s):  
Fares M’zoughi ◽  
Izaskun Garrido ◽  
Aitor J. Garrido
Keyword(s):  
Symmetry Breaking ◽  
Water Column ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Time ◽  
Pso Algorithm ◽  
Search Space ◽  
Oscillating Water Column ◽  
Column System ◽  
Control Optimization

Global optimization problems are mostly solved using search methods. Therefore, decreasing the search space can increase the efficiency of their solving. A widely exploited technique to reduce the search space is symmetry-breaking, which helps impose constraints on breaking existing symmetries. The present article deals with the airflow control optimization problem in an oscillating-water-column using the Particle Swarm Optimization (PSO). In an effort to ameliorate the efficiency of the PSO search, a symmetry-breaking technique has been implemented. The results of optimization showed that shrinking the search space helped to reduce the search time and ameliorate the efficiency of the PSO algorithm.

Evolutionary Algorithm Embedded With Bump-Hunting for Constrained Design Optimization

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Kamrul Hasan Rahi ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Computational Cost ◽  
Search Space ◽  
Bump Hunting ◽  
Simulation Based ◽  
Engineering Problems ◽  
Turbine Design

Abstract Real-world design optimization problems commonly entail constraints that must be satisfied for the design to be viable. Mathematically, the constraints divide the search space into feasible (where all constraints are satisfied) and infeasible (where at least one constraint is violated) regions. The presence of multiple constraints, constricted and/or disconnected feasible regions, non-linearity and multi-modality of the underlying functions could significantly slow down the convergence of evolutionary algorithms (EA). Since each design evaluation incurs some time/computational cost, it is of significant interest to improve the rate of convergence to obtain competitive solutions with relatively fewer design evaluations. In this study, we propose to accomplish this using two mechanisms: (a) more intensified search by identifying promising regions through “bump-hunting,” and (b) use of infeasibility-driven ranking to exploit the fact that optimal solutions are likely to be located on constraint boundaries. Numerical experiments are conducted on a range of mathematical benchmarks and empirically formulated engineering problems, as well as a simulation-based wind turbine design optimization problem. The proposed approach shows up to 53.48% improvement in median objective values and up to 69.23% reduction in cost of identifying a feasible solution compared with a baseline EA.

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