scholarly journals A Generic Optimization Algorithm for the Allocation of DP Actuators

2011 ◽  
Author(s):  
E. F. G. van Daalen ◽  
J. L. Cozijn ◽  
C. Loussouarn ◽  
P. W. Hemker
Keyword(s):  
Optimization Algorithm ◽  
Lagrange Multipliers ◽  
Linear Equations ◽  
Exact Expression ◽  
Computational Effort ◽  
Total Power ◽  
Linear Solution ◽  
Multipliers Method ◽  
Non Linear ◽  
The Cost

In this paper we present a generic optimization algorithm for the allocation of dynamic positioning actuators, such as azimuthing thrusters and fixed thrusters. The algorithm is based on the well-known Lagrange multipliers method. In the present approach the Lagrangian functional represents not only the cost function (the total power delivered by all actuators), but also all constraints related to thruster saturation and forbidden zones for azimuthing thrusters. In the presented approach the application of the Lagrange multipliers method leads to a nonlinear set of equations, because an exact expression for the total power is applied and the actuator limitations are accounted for in an implicit manner, by means of nonlinear constraints. It is solved iteratively with the Newton-Raphson method and a step by step implementation of the constraints related to the actuator limitations. In addition, the results from the non-linear solution method were compared with the results from a simplified set of linear equations, based on an approximate (quadratic) expression for the thruster power. The non-linear solution was more accurate, while requiring only a slightly higher computational effort. An example is shown for a thruster configuration with 8 azimuthing thrusters, typical for a DP semi-submersible. The results show that the optimization algorithm is very stable and efficient. Finally, some options for improvements and future enhancements — such as including thruster-thruster and thruster-hull interactions and the effects of current — are discussed.

scholarly journals PENERAPAN COCKROACH SWARM OPTIMIZATION ALGORITHM (CSOA) PADA PENYELESAIAN PERSAMAAN POLINOMIAL YANG MEMILIKI AKAR KOMPLEKS

2018 ◽  
Vol 18 (2) ◽  
pp. 81
Author(s):  
Ema Fahma Farikha ◽  
Rusli Hidayat ◽  
Muhammad Ziaul Arif
Keyword(s):  
Optimization Algorithm ◽  
Linear Equations ◽  
Food Sources ◽  
Polynomial Equations ◽  
Metaheuristic Algorithm ◽  
Swarm Optimization ◽  
Non Linear Equation ◽  
Complex Roots ◽  
Non Linear ◽  
Newton Raphson

In this paper, we use a metaheuristic algorithm for solving non-linear equations (polynomial equations) which have a set of complex roots (complex numbers). The metaheuristic algorithm is the Cockroach Swarm Optimization Algorithm (CSOA) which imitate various types of natural cockroach behaviors such as chase-swarming, dispersing and ruthlessness when hunting for food sources. In this study, several examples of non-linear polynomial equations were used for evaluating the accuracy of CSOA. In this simulation, the accuracy comparison has been accomplished. It is shown that CSOA results are more accurate compared to the Newton-Raphson results. Keywords: Cockroach Swarm Optimization Algorithm, Complex roots of polynomial, Newton-Raphson, Non-Linear equation.

Topology Optimization of Non-Linear Elastic Structures by Using SLP

2009 ◽  
Author(s):  
Niclas Stro¨mberg
Keyword(s):  
Topology Optimization ◽  
Linear Equations ◽  
Internal Force ◽  
Elastic Structures ◽  
Fully Integrated ◽  
Non Linear ◽  
Lagrange Strain ◽  
The Cost ◽  
Nonlinear Elastic ◽  
Nested Approach

In this paper a method for topology optimization of nonlinear elastic structures is suggested. The method is developed by starting from a total Lagrangian formulation of the system. The internal force is defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St. Venant law. The state of equilibrium is obtained by first deriving the consistency stiffness matrix and then using Newton’s method to solve the non-linear equations. The design parametrization of the internal force is obtained by adopting the SIMP approach. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by SLP. This is done by using a nested approach where the equilibrium equation is linearized and the sensitivity of the cost function is calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

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