A new multi-objective discrete robust optimization algorithm for engineering design

Sun, Guangyong; Zhang, Huile; Fang, Jianguang; Li, Guangyao; Li, Qing

doi:10.1016/j.apm.2017.08.016

Cited by 99 publications

(39 citation statements)

References 41 publications

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“…In ɛ-constraint technique, the most prominent objective among others is chosen as the primary objective function. Other objective functions are considered as constraints of the optimization model [46][47][48][49][50]. The first objective function is the most important one in this model.…”

Section: ɛ-Constraint Methodsmentioning

confidence: 99%

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Amin¹,

Mulligan-Gow²,

Zhang³

2020

Application of Decision Science in Business and Management

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It is a problem that concerns us all: what should we eat on a day-to-day basis to meet our health goals? Scientists have been utilizing mathematical programming to answer this question. Through the use of operations research techniques, it is possible to find a list of foods that, in a certain quantity, can provide all nutrient recommendations in a day. In this research, a multi-objective programming model is provided to determine the selected food items for a diet problem. Two solution approaches are developed to solve this problem including weighted-sums and ε-constraint methods. Two sources of uncertainty have been considered in the model. To handle these sources, a scenario-based approach is utilized. The application of this model is shown using a case study in Canada. Using the proposed model and the solution approaches, the best food items can be selected and purchased to minimize the total cost and maximize health.

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Section: ɛ-Constraint Methodsmentioning

confidence: 99%

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Amin¹,

Mulligan-Gow²,

Zhang³

2020

Application of Decision Science in Business and Management

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“…Commonly, a full factorial design can create the experimental matrix, but it requires a large number of experiments. Therefore, the TM is alternated with a sufficient number of experiments [22][23][24][25]. Although the TM reduces the number of experiments, it only optimizes a single quality response, while this study needs to solve the multiobjective responses, simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Efficient Hybrid Method of FEA‐Based RSM and PSO Algorithm for Multi‐Objective Optimization Design for a Compliant Rotary Joint for Upper Limb Assistive Device

Chau

Dao

et al. 2019

Mathematical Problems in Engineering

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This paper proposes an efficient hybrid methodology for multi-objective optimization design of a compliant rotary joint (CRJ). A combination of the Taguchi method (TM), finite element analysis (FEA), the response surface method (RSM), and particle swarm optimization (PSO) algorithm is developed to solving the optimization problem. Firstly, the TM is applied to determine the number of numerical experiments. And then, 3D models of the CRJ is built for FEA simulation, and mathematical models are formed using the RSM. Subsequently, the suitability of the regression equation is assessed. At the same time, the calculation of weight factors is identified based on the series of statistical equations. Based on the well-established equations, a minimum mass and a maximum rotational angle are simultaneously optimized through the PSO algorithm. Analysis of variance is used to analyze the contribution of design variables. The behavior of the proposed method is compared to the adaptive elitist differential evolution and cuckoo search algorithm through the Wilcoxon signed rank test and Friedman test. The results determined the weight factors of the mass and rotational angle are about 0.4983 and 0.5017, respectively. The results found that the optimum the mass and rotational angle are 0.0368 grams and 59.1928 degrees, respectively. It revealed that the maximum stress of 335 MPa can guarantee a long working time. The results showed that the proposed hybrid method outperforms compared to other evolutionary algorithms. The predicted results are close to the validation results. The proposed method is useful for related engineering fields.

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“…Common methods for experimental design are orthogonal design and central composite design (CCD). In addition, Taguchi robust design has been applied in experimental design for its better performance [25]. To describe how to construct sample points and determine the optimal number of samples by orthogonal design and CCD, the procedural details of the two design methods can be separately summarized as follows.…”

Section: Design Of Experimentsmentioning

confidence: 99%

“…. , in (25) can be calculated in terms of the principle of least squares. Similarly, a quadratic polynomial model is usually constructed as in expression (26) and the cubic polynomial surface can be obtained in the same manner.…”

Section: Establishment Of Surrogate Modelmentioning

confidence: 99%

“…For instance, for obtaining robust optimal solutions, a multiobjective optimization algorithm that combines particle swarm optimization and the gradient search technique was introduced [24], and Sun et al [25] proposed a novel effective algorithm that 2 Mathematical Problems in Engineering aims to solve engineering design problems that involve uncertainties. To obtain a faster convergence rate and improve the stability of convergence and efficiency for solving engineering design problems, numerical algorithms gradually attracted increased attention from researchers [26,27].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Fan

Yoshino

et al. 2018

Mathematical Problems in Engineering

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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.

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A new multi-objective discrete robust optimization algorithm for engineering design

Cited by 99 publications

References 41 publications

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Efficient Hybrid Method of FEA‐Based RSM and PSO Algorithm for Multi‐Objective Optimization Design for a Compliant Rotary Joint for Upper Limb Assistive Device

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

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