Minimax multiobjective optimization in structural design

Tseng, C. H.; Lu, Tse Min

doi:10.1002/nme.1620300609

Cited by 44 publications

(26 citation statements)

References 9 publications

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“…If the joint probability density function of the random variables fx(x) is known, the reliability measure associated with the /th constraint (or probability of survival) can be obtained as (16) In practice the joint distribution of the random variables is rarely known, and also the integral evaluation is extremely difficult. Approximations for the preceding integral have been proposed by many researchers.…”

Section: Reliability Criteriamentioning

confidence: 99%

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Multiobjective optimization of large-scale structures

1993

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This paper presents a multiobjective optimization algorithm based on generalized compound scaling techniques. The algorithm handles any number of objective functions, similar to handling behavior constraints. This technique generates a partial Pareto set while solving the optimization problem. A reliability-based decision criterion is used for selecting the best compromise design. The example cases considered in this work include various disciplines in airframe structures, such as stress, displacement, and frequency with hundreds of design variables and constraints. This paper also discusses the concept of Pareto-optimal solutions in the context of a multiobjective structural optimization problem and the commonly used methods of generating Pareto-optimal solutions.

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Section: Reliability Criteriamentioning

confidence: 99%

“…Saravanos and Chamis's performance was based on multiple objectives. Tseng and Lu 16 proposed a minimax multiobjective optimization model for structural optimization. They used the three typical multiobjective optimization techniques-goal programming, compromise programming, and the surrogate worth tradeoff method-to solve truss problems.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective optimization of large-scale structures

1993

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“…It is assumed that the active constraint set remains unchanged for the perturbed problem and that the strict complementary slackness holds at the current optimum. Tseng and Lu [15] had to appeal to the ÿnite di erence computing to bypass this assumption indirectly. In their work, the Pareto optimum sensitivity analysis is used to study the variation of optimum design with respect to the upper bounds of criterion-deÿned constraints after the solving of multicriteria problems by the trade-o method.…”

Section: Introductionmentioning

confidence: 99%

On the Pareto optimum sensitivity analysis in multicriteria optimization

Zhang¹

2003

Numerical Meth Engineering

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SUMMARYTo analyse the trade-o relations among the set of criteria in multicriteria optimization, Pareto optimum sensitivity analysis is systematically studied in this paper. Original contributions cover two parts: theoretical demonstrations are ÿrstly made to validate the gradient projection method in Pareto optimum sensitivity analysis. It is shown that the projected gradient direction evaluated at a given Pareto optimum in the design variable space rigorously corresponds to the tangent direction of the Pareto curve=surface at that point in the objective space. This statement holds even for the change of the set of active constraints in the perturbed problem. Secondly, a new active constraint updating strategy is proposed, which permits the identiÿcation of the active constraint set change, to determine the in uence of this change upon the di erentiability of the Pareto curve and ÿnally to compute directional derivatives in non-di erentiable cases. This work will highlight some basic issues in multicriteria optimization. Some numerical problems are solved to illustrate these novelties.

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“…MOP always has not an optimal solution but rather a set of solutions which are called Pareto set, the corresponding objective value set called Pareto front. Traditional multi-objective optimization methods, including weighting method, constraints method, mixing method, goal programming, the maximum and minimum approach [3][4] [5], have the defects of subjectivity and inoperability, and have difficulties in solving complex problems. In the last two decades, a number of intelligent bionic calculation methods have been proposed and successfully applied to multi-objective optimization.…”

Section: Introductionmentioning

confidence: 99%

A differential evolution-based hybrid NSGA-II for multi-objective optimization

Pan

Jing

Chen

et al. 2015

2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation

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To improve the search accuracy and diversity of non-dominated sorting genetic algorithm (NSGA-II), an improved algorithm DMNSGA-II referencing to the strategy of differential evolution to strengthen local search is proposed in this paper. The algorithm uses mutation guiding operator and crossover operator of DE to replace crossover operator in NSGA-II to enhance the local search capability and improve search accuracy. while retaining the mutation operator of NSGA-II to improve diversity. We use four benchmark test problems to investigate the performance of the DMNSGA-II algorithm, and simulation results demonstrate that the proposed algorithm can achieve a good overall performance in multi-objective optimization.

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Minimax multiobjective optimization in structural design

Cited by 44 publications

References 9 publications

Multiobjective optimization of large-scale structures

Multiobjective optimization of large-scale structures

On the Pareto optimum sensitivity analysis in multicriteria optimization

A differential evolution-based hybrid NSGA-II for multi-objective optimization

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