Multiobjective Hybrid Optimization–Antioptimization for Force Design of Tensegrity Structures

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Makoto Ohsaki ◽  
Jingyao Zhang ◽  
Isaac Elishakoff
Keyword(s):  
Optimization Problem ◽  
Hybrid Approach ◽  
Programming Approach ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Tensegrity Structures ◽  
Tangent Stiffness Matrix ◽  
Lowest Eigenvalue

Properties of Pareto optimal solutions considering bounded uncertainty are first investigated using an illustrative example of a simple truss. It is shown that the nominal values of the Pareto optimal solutions considering uncertainty are slightly different from those without considering uncertainty. Next a hybrid approach of multiobjective optimization and antioptimization is presented for force design of tensegrity structures. We maximize the lowest eigenvalue of the tangent stiffness matrix and minimize the deviation of forces from the specified target distribution. These objective functions are defined as the worst values due to the possible errors in the fabrication and construction processes. The Pareto optimal solutions are found by solving the two-level optimization–antioptimization problems using a nonlinear programming approach for the upper optimization problem and enumeration of the vertices of the uncertain region for the lower antioptimization problem.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

Analysis and Optimization of Staggered Partial Diffuser Vanes in a Centrifugal Pump

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Hyeon-Seok Shim ◽  
Sang-Hoon Kim ◽  
Kwang-Yong Kim
Keyword(s):  
Centrifugal Pump ◽  
Stokes Equations ◽  
Maximum Pressure ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Baseline Design ◽  
Operating Range ◽  
Full Height

Abstract A performance analysis and three-objective design optimization were performed for the staggered partial diffuser vanes in a centrifugal pump using three-dimensional Reynolds-averaged Navier–Stokes equations. First, the performance of the diffuser vanes was evaluated for four different arrangements: full-height diffuser vanes, vaneless diffuser, half vanes attached to the hub, half vanes attached to the shroud, and staggered vanes attached alternately to the hub and the shroud. The staggered partial diffuser vanes were optimized using the following design variables: the installation angle of the vanes, the heights of the vanes attached to the hub and shroud, and the angle of rotation of the straight part on the pressure surface of the vanes. The objective functions were the hydraulic efficiency, the flowrate of the maximum pressure recovery, and the operating range of the diffuser. The Kriging model was used to construct surrogate models of the objective functions based on the results at the design points obtained by Latin hypercube sampling. The Pareto-optimal solutions were obtained by a multi-objective genetic algorithm (MOGA). The representative Pareto-optimal solutions for the staggered diffuser vanes obtained by the K-means clustering showed the improved performances in terms of both the hydraulic performance and operating range compared with the full-height diffuser vanes and the baseline design.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

2015 ◽  
Vol 32 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Chun-An Liu ◽  
Yuping Wang ◽  
Aihong Ren
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Multi Objective ◽  
Time Period ◽  
Pareto Fronts

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

scholarly journals Sensitivity analysis for parametric vector optimization problems using differential equations approach

2001 ◽  
Vol 25 (9) ◽  
pp. 621-628
Author(s):  
Fatma M. Ali
Keyword(s):  
Differential Equations ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Parametric Vector Optimization ◽  
Local Solutions

A new method for obtaining sensitivity information for parametric vector optimization problems(VOP)vis presented, where the parameters in the objective functions and anywhere in the constraints. This method depends on using differential equations technique for solving multiobjective nonlinear programing problems which is very effective in finding many local Pareto optimal solutions. The behavior of the local solutions for slight perturbation of the parameters in the neighborhood of their chosen initial values is presented by using the technique of trajectory continuation. Finally some examples are given to show the efficiency of the proposed method.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

Pareto-Optimal Solutions Using Kinematic and Dynamic Functions for a Scho¨nflies Parallel Manipulator

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Charles Pinto ◽  
Bogdan Sandru ◽  
Enrique Amezua
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Frobenius Norm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Motion Generation ◽  
Dimensional Parameters

The search of Pareto-optimal solutions for the optimal design of Low-Mobility Parallel Manipulators with Scho¨nflies motion is the subject of this paper. As a working example, a four-degree-of-freedom symmetric parallel manipulator for Scho¨nflies-motion generation is taken. In previous work, analytically found objective functions for the optimal design were used. As a consequence, some limitations were detected and new functions are required. First, a manipulator description is made, and kinematic and dynamic problems are solved. Next, an operational and dexterous workspace along with its volume is found making use of a discretization. Further, the variation of this volume with dimensional parameters is shown for purpose of optimal design. Similarly, the manipulator’s dexterity based on the Frobenius norm is found and weighted with the measure of dispersion. Then, upon a type of testing trajectory over this workspace, kinematic and dynamic results in the actuators are proposed as objective functions in multiobjective optimization.

scholarly journals Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

2020 ◽  
pp. 15-21
Author(s):  
Т.Т. Lebedeva ◽  
◽  
N.V. Semenova ◽  
T.I. Sergienko ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Vector Criterion

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

scholarly journals Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Paolo Bevilacqua ◽  
Gianni Bosi ◽  
Magalì Zuanon
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Design Space ◽  
Pareto Optimal ◽  
Multiobjective Optimization Problem ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Maximal Elements ◽  
Compact Design

We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.

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