scholarly journals An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Guang Yang ◽  
Tao Xu ◽  
Xiang Li ◽  
Haohua Xiu ◽  
Tianshuang Xu
Keyword(s):  
Multiobjective Optimization ◽  
Lower Bounds ◽  
Hybrid Algorithm ◽  
High Efficiency ◽  
Optimization Problems ◽  
Simultaneous Optimization ◽  
Upper And Lower Bounds ◽  
Optimization Models ◽  
Engineering Problems ◽  
Practical Engineering

Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.

scholarly journals A Novel Hybrid Algorithm for Solving Multiobjective Optimization Problems with Engineering Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Lulu Fan ◽  
Tatsuo Yoshino ◽  
Tao Xu ◽  
Ye Lin ◽  
Huan Liu
Keyword(s):  
Multiobjective Optimization ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Primary Energy ◽  
Engineering Practice ◽  
Optimization Strategy ◽  
Frontal Collision ◽  
Multiobjective Optimization Problems ◽  
Crashworthiness Design

An effective hybrid algorithm is proposed for solving multiobjective optimization engineering problems with inequality constraints. The weighted sum technique and BFGS quasi-Newton’s method are combined to determine a descent search direction for solving multiobjective optimization problems. To improve the computational efficiency and maintain rapid convergence, a cautious BFGS iterative format is utilized to approximate the Hessian matrices of the objective functions instead of evaluating them exactly. The effectiveness of the proposed algorithm is demonstrated through a comparison study, which is based on numerical examples. Meanwhile, we propose an effective multiobjective optimization strategy based on the algorithm in conjunction with the surrogate model method. This proposed strategy has been applied to the crashworthiness design of the primary energy absorption device’s crash box structure and front rail under low-speed frontal collision. The optimal results demonstrate that the proposed methodology is promising in solving multiobjective optimization problems in engineering practice.

scholarly journals Conceptual Comparison of Population Based Metaheuristics for Engineering Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Oluwole Adekanmbi ◽  
Paul Green
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Selection Process ◽  
Population Based ◽  
Practical Applications ◽  
Wide Range ◽  
Engineering Problems ◽  
Practical Engineering ◽  
Generalized Differential ◽  
Metaheuristic Techniques

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

scholarly journals Decomposition-Based Multiobjective Optimization with Invasive Weed Colonies

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yanyan Tan ◽  
Xue Lu ◽  
Yan Liu ◽  
Qiang Wang ◽  
Huaxiang Zhang
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Algorithm ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Invasive Weed Optimization ◽  
Invasive Weed ◽  
Multiobjective Optimization Problems ◽  
Distinct Features

In order to solve the multiobjective optimization problems efficiently, this paper presents a hybrid multiobjective optimization algorithm which originates from invasive weed optimization (IWO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), a popular framework for multiobjective optimization. IWO is a simple but powerful numerical stochastic optimization method inspired from colonizing weeds; it is very robust and well adapted to changes in the environment. Based on the smart and distinct features of IWO and MOEA/D, we introduce multiobjective invasive weed optimization algorithm based on decomposition, abbreviated as MOEA/D-IWO, and try to combine their excellent features in this hybrid algorithm. The efficiency of the algorithm both in convergence speed and optimality of results are compared with MOEA/D and some other popular multiobjective optimization algorithms through a big set of experiments on benchmark functions. Experimental results show the competitive performance of MOEA/D-IWO in solving these complicated multiobjective optimization problems.

scholarly journals Application of data mining in multiobjective optimization problems

2014 ◽  
Vol 5 ◽  
pp. A15 ◽  
Author(s):  
Amir Mosavi
Keyword(s):  
Data Mining ◽  
Multiobjective Optimization ◽  
Optimization Design ◽  
Optimization Problems ◽  
Objective Functions ◽  
Design Variables ◽  
Modeling Techniques ◽  
Practical Engineering ◽  
Meta Modeling ◽  
Classification Tool

In the most engineering optimization design problems, the value of objective functions is not clearly defined in terms of design variables. Instead it is obtained by some numerical analysis such as FE structural analysis, fluid mechanic analysis, and thermodynamic analysis, etc. Usually, these analyses are considerably time consuming to obtain a value of objective functions. In order to make the number of analyses as few as possible a methodology is presented as a supporting tool for the meta-modeling techniques. Researches in meta-modeling for multiobjective optimization are relatively young and there is still much to do. It is shown that visualizing the problem on the basis of the randomly sampled geometrical data of CAD and CAE simulation results, in addition to utilizing classification tool of data mining could be effective as a supporting system to the available meta-modeling techniques. To evaluate the effectiveness of the proposed method a study case in 3D wing design is given. Along with this example, it is discussed how effective the proposed methodology could be in the practical engineering problems.

scholarly journals Quantum SDP-Solvers: Better upper and lower bounds

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 230 ◽  
Author(s):  
Joran van Apeldoorn ◽  
András Gilyén ◽  
Sander Gribling ◽  
Ronald de Wolf
Keyword(s):  
Combinatorial Optimization ◽  
Lower Bounds ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Upper And Lower Bounds ◽  
Smooth Functions ◽  
Worst Case ◽  
Semidefinite Programs ◽  
New Techniques ◽  
Combinatorial Optimization Problems

Brandão and Svore \cite{brandao2016QSDPSpeedup} recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension n of the problem and the number m of constraints, but worse in terms of various other parameters. In this paper we improve their algorithms in several ways, getting better dependence on those other parameters. To this end we develop new techniques for quantum algorithms, for instance a general way to efficiently implement smooth functions of sparse Hamiltonians, and a generalized minimum-finding procedure.We also show limits on this approach to quantum SDP-solvers, for instance for combinatorial optimization problems that have a lot of symmetry. Finally, we prove some general lower bounds showing that in the worst case, the complexity of every quantum LP-solver (and hence also SDP-solver) has to scale linearly with mn when m≈n, which is the same as classical.

scholarly journals Differential gradient evolution plus algorithm for constraint optimization problems: A hybrid approach

2021 ◽  
Vol 11 (2) ◽  
pp. 158-177
Author(s):  
Muhammad Farhan Tabassum ◽  
Sana Akram ◽  
Saadia Mahmood-ul-Hassan ◽  
Rabia Karim ◽  
Parvaiz Ahmad Naik ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Heuristic Optimization ◽  
Constraint Optimization ◽  
Local Minima ◽  
Engineering Problems ◽  
Practical Engineering ◽  
Gradient Evolution ◽  
Constraint Optimization Problems

Optimization for all disciplines is very important and applicable. Optimization has played a key role in practical engineering problems. A novel hybrid meta-heuristic optimization algorithm that is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique named Differential Gradient Evolution Plus (DGE+) are presented in this paper. The proposed algorithm hybridizes the above-mentioned algorithms with the help of an improvised dynamic probability distribution, additionally provides a new shake off method to avoid premature convergence towards local minima. To evaluate the efficiency, robustness, and reliability of DGE+ it has been applied on seven benchmark constraint problems, the results of comparison revealed that the proposed algorithm can provide very compact, competitive and promising performance.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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