scholarly journals The method of conditional minimization based on the selection of the optimal value of the objective function

2019 ◽  
Vol 1158 ◽  
pp. 042040
Author(s):  
I Ya Zabotin ◽  
K E Kazaeva ◽  
O N Shulgina
Keyword(s):  
Objective Function ◽  
Optimal Value ◽  
Conditional Minimization ◽  
Selection Of

scholarly journals Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 80
Author(s):  
John Fernando Martínez-Gil ◽  
Nicolas Alejandro Moyano-García ◽  
Oscar Danilo Montoya ◽  
Jorge Alexander Alarcon-Villamil
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Phase Distribution ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Discrete Version ◽  
Optimal Selection ◽  
Flow Method ◽  
Three Phase ◽  
Selection Of

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

scholarly journals An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs

2021 ◽  
Author(s):  
E. Alper Yıldırım
Keyword(s):  
Objective Function ◽  
Convex Relaxation ◽  
Large Family ◽  
Quadratic Program ◽  
Feasible Region ◽  
Recession Cone ◽  
Convex Relaxations ◽  
Quadratic Programs ◽  
Alternative Perspective ◽  
Optimal Value

AbstractWe study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that the convex relaxation is feasible if and only if the nonconvex quadratic program is feasible. We observe that each convex relaxation in this family implicitly induces a convex underestimator of the objective function on the feasible region of the quadratic program. This alternative perspective on convex relaxations enables us to establish several useful properties of the corresponding convex underestimators. In particular, if the recession cone of the feasible region of the quadratic program does not contain any directions of negative curvature, we show that the convex underestimator arising from the copositive relaxation is precisely the convex envelope of the objective function of the quadratic program, strengthening Burer’s well-known result on the exactness of the copositive relaxation in the case of nonconvex quadratic programs. We also present an algorithmic recipe for constructing instances of quadratic programs with a finite optimal value but an unbounded relaxation for a rather large family of convex relaxations including the doubly nonnegative relaxation.

A new representation for a robot grasping quality measure

Robotica ◽  
1995 ◽  
Vol 13 (3) ◽  
pp. 287-295 ◽  
Author(s):  
Venugopal K. Varma ◽  
Uri Tasch
Keyword(s):  
Objective Function ◽  
Material Properties ◽  
Graphical Representation ◽  
Contact Forces ◽  
Geometric Constraints ◽  
Objective Functions ◽  
Finger Force ◽  
Finger Forces ◽  
Robot Grasping ◽  
Selection Of

SummaryWhen an object is held by a multi-fingered hand, the values of the contact forces can be multivalued. An objective function, when used in conjunction with the frictional and geometric constraints of the grasp, can however, give a unique set of finger force values. The selection of the objective function in determining the finger forces is dependent on the type of grasp required, the material properties of the object, and the limitations of the röbot fingers. In this paper several optimization functions are studied and their merits highlighted. The paper introduces a graphical representation of the finger force values and the objective functions that enable one to select and compare various grasping configurations. The impending motion of the object at different torque and finger force values are determined by observing the normalized coefficient of friction plots.

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

scholarly journals Performance of Static Iot Networks using RPL Objective Functions

2019 ◽  
Vol 8 (4) ◽  
pp. 8972-8977 ◽  
Keyword(s):  
Objective Function ◽  
Routing Protocol ◽  
Routing Algorithms ◽  
Transmission Protocol ◽  
Objective Functions ◽  
Lossy Networks ◽  
Hop Count ◽  
Efficient Data ◽  
Selection Of ◽  
Better Than

Internet of Things, abbreviated as IoT is a network used mainly for the communication where different devices are connected for the retrieval, examination and execution of the necessary task. One of IoT’s biggest challenge is that, they are resource-constrained. Hence, it is essential to use an efficient data transmission protocol for routing. An effective routing protocol for static IoT network is the Routing protocol for Low Power and Lossy Networks (RPL). It is essential to assess the effectiveness of the RPL with the selection of best objective function for different static model. In this paper, the performance of different routing algorithms is compared in connection with different static topologies. Hence, the objective function’s performance is compared for different topologies i.e., Butterfly, Ring and Umbrella topologies. We consider two objective functions: namely Minimum Rank with Hysteresis Objective Function (MRHOF) and Objective Function Zero (OF0). MRHOF considers Expected Transmission Count (ETX) as its metric and the metric considered under OF0 is hop count. It is observed that the objective function OF0 performs better than MRHOF for the metric of energy and successful receiving of data.

scholarly journals Optimal synthesis of a four-bar linkage by method of controlled deviation

2004 ◽  
Vol 31 (3-4) ◽  
pp. 265-280 ◽  
Author(s):  
Radovan Bulatovic ◽  
Stevan Djordjevic
Keyword(s):  
Objective Function ◽  
Optimal Synthesis ◽  
Straight Line ◽  
Individual Comparison ◽  
Four Bar Linkage ◽  
The Given ◽  
Initial Selection ◽  
Selection Of ◽  
Process Calculation ◽  
Made In

This paper considers optimal synthesis of a four-bar linkage by method of controlled deviations. The advantage of this approximate method is that it allows control of motion of the coupler in the four-bar linkage so that the path of the coupler is in the prescribed environment around the given path on the segment observed. The Hooke-Jeeves?s optimization algorithm has been used in the optimization process. Calculation expressions are not used as the method of direct searching, i.e. individual comparison of the calculated value of the objective function is made in each iteration and the moving is done in the direction of decreasing the value of the objective function. This algorithm does not depend on the initial selection of the projected variables. All this is illustrated on an example of synthesis of a four-bar linkage whose coupler point traces a straight line, i.e. passes through sixteen prescribed points lying on one straight line. .

scholarly journals The organizational mechanism for the formation of programs for the renovation of cultural heritage objects on the basis of the value approach

2018 ◽  
Vol 193 ◽  
pp. 05004
Author(s):  
Vera Akristiniy
Keyword(s):  
Cultural Heritage ◽  
Objective Function ◽  
Integral Index ◽  
Organizational Mechanism ◽  
Definition Of ◽  
State Programs ◽  
Cultural Heritage Objects ◽  
Efficient Selection ◽  
Optimal Feature ◽  
Selection Of

The article discusses the issues of preservation of cultural heritage objects due to their mass loss by creating a mechanism for the efficient selection of objects subject to renovation. The algorithm for the calculation of the degree of deterioration of the building and the integral index of value is proposed. The problem of definition of the objective function with respect to which is characterized by the objective function of the optimal feature set and the problem of definition of the target functions of state programs of renovation are solving preservation.

scholarly journals Linear Regression with Optimal Rotation

Stats ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 416-425 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Linear Regression ◽  
Correlation Coefficient ◽  
Rotation Angle ◽  
Outer Region ◽  
Optimal Angle ◽  
Optimal Rotation ◽  
Optimal Value ◽  
The One ◽  
Optimal Rotation Angle ◽  
Selection Of

The paper shows how the linear regression depends on the selection of the reference frame. The slope of the fitted line and the corresponding Pearson’s correlation coefficient are expressed in terms of the rotation angle. The correlation coefficient is found to be maximized for a certain optimal angle, for which the slope attains a special optimal value. The optimal angle, the value of the optimal slope, and the corresponding maximum correlation coefficient were expressed in terms of the covariance matrix, but also in terms of the values of the slope, derived from the fitting at the nonrotated and right-angle-rotated axes. The potential of the new method is to improve the derived values of the fitting parameters by detecting the optimal rotation angle, that is, the one that maximizes the correlation coefficient. The presented analysis was applied to the linear regression of density and temperature measurements characterizing the proton plasma in the inner heliosheath, the outer region of our heliosphere.

New Approach for the Continuing Dynamic Programming

2012 ◽  
Vol 459 ◽  
pp. 575-578
Author(s):  
Peng Zhang ◽  
Xiang Huan Meng
Keyword(s):  
Dynamic Programming ◽  
Objective Function ◽  
Iteration Method ◽  
Programming Model ◽  
State Equations ◽  
New Approach ◽  
Optimal Value ◽  
Convergent Method ◽  
Optimal Values ◽  
Dynamic Programming Model

The paper proposes the discrete approximate iteration method to solve single-dimensional continuing dynamic programming model. The paper also presents a comparison of the discrete approximate iteration method and bi- convergent method to solve multi-dimensional continuing dynamic programming model. The algorithm is the following: Firstly, let state value of one of state equations be unknown and the others be known. Secondly, use discrete approximate iteration method to find the optimal value of the unknown state values, continue iterating until all state equations have found optimal values. If the objective function is convex, the algorithm is proved linear convergent. If the objective function is non-concave and non-convex, the algorithm is proved convergent.

A framework for optimising aspects of rotor blades

2011 ◽  
Vol 115 (1165) ◽  
pp. 147-161 ◽  
Author(s):  
C. S. Johnson ◽  
G. N. Barakos
Keyword(s):  
Objective Function ◽  
Stokes Equations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Computational Framework ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Artificial Neural ◽  
Optimisation Methods ◽  
Selection Of

AbstractThis work presents a computational framework for the optimisation of various aspects of rotor blades. The proposed method employs CFD combined with artificial neural networks, employed as metamodels, and optimisation methods based on genetic algorithms. To demonstrate this approach, two examples have been used, one is the optimal selection of 4- and 5-digit NACA aerofoils for rotor sections and the other is the optimisation of linear blade twist for rotors in hover. For each case, an objective function was created and the meta-model was subsequently used to evaluate this objective function during the optimisation process. The obtained results agree with real world design examples and theoretical predictions. For the selected cases, the artificial neural network was found to perform adequately though the results required a substantial amount of data for training. The genetic algorithm was found to be very effective in identifying a set of near-optimal parameters. The main CPU cost was associated with the population of the database necessary for the meta-models and this task required CFD computations based on the Reynolds-averaged Navier-Stokes equations. The framework is general enough to allow for several design or optimisation tasks to be carried out and it is based on open-source code made available by the authors.

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