• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.1-7
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• 1993

Vector optimization problems consist of two or more objective functions and constraints. Optimization entails obtaining efficient solutions. Geoffrion [3] introduced the definition of the properly efficient solution in order to eliminate efficient solutions causing unbounded trade-offs between objective functions. In 1974, Isermann [7] obtained a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with linear constraints and showed that every efficient solution is a properly efficient solution. Since then, many authors [1, 2, 4, 5, 6] have extended the Isermann's results. In particular, Gulati and Islam [4] derived a necessary and sufficient condition for an efficient solution of a linear vector optimization problem with nonlinear constraints, under certain assumptions. In this paper, we consider the following nonlinear vector optimization problem (NVOP): (Fig.) where for each i, f$_{i}$ is a differentiable function from R$^{n}$ into R and g is a differentiable function from R$^{n}$ into R$^{m}$ .

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.1
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• pp.119-125
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• 2005

The current automotive is seeking the improvement of performance, the prevention of environmental pollution and the saving of energy resources according to miniaturization and lightweight of the components. And the variance analysis on the basis of structure analysis and DOE is applied to the lower control am. We have proposed a statistical design model to evaluate the effect of structural modification by performing the practical multi-objective optimization considering weight, stress and fatigue lift. The lower control arm is performed the fatigue analysis using the load history of real road test. The design model is determined using the optimization of acquired load history with the fatigue characteristic. The characteristic function is made use of the optimization according to fatigue characteristics to consider constrained function in the optimization of DOE. The structure optimization of a lower control arm according to fatigue characteristics is performed. And the optimized design variable is D=47 m, T=36mm, W=12 mm. In the real engineering problem of considering many objective functions, the multi-objective optimization process using the mathematical programming and the characteristic function is derived an useful design solution.

• Journal of Mechanical Science and Technology
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• v.19 no.5
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• pp.1080-1086
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• 2005

The preliminary design optimization of multi-stage spur gear reduction units has been a subject of considerable interest, since many high-performance power transmission applications (e.g., automotive and aerospace) require high-performance gear reduction units. There are multiple objectives in the optimal design of multi-stage spur gear reduction unit, such as minimizing the volume and maximizing the surface fatigue life. It is reasonable to formulate the design of spur gear reduction unit as a multi-objective optimization problem, and find an appropriate approach to solve it. In this paper an interactive physical programming approach is developed to place physical programming into an interactive framework in a natural way. Class functions, which are used to represent the designer's preferences on design objectives, are fixed during the interactive physical programming procedure. After a Pareto solution is generated, a preference offset is added into the class function of each objective based on whether the designer would like to improve this objective or sacrifice the objective so as to improve other objectives. The preference offsets are adjusted during the interactive physical programming procedure, and an optimal solution that satisfies the designer's preferences is supposed to be obtained by the end of the procedure. An optimization problem of three-stage spur gear reduction unit is given to illustrate the effectiveness of the proposed approach.

• Steel and Composite Structures
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• v.32 no.4
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• pp.455-466
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• 2019

Despite the rapid advancement in computing resources, many real-life design and optimization problems in structural engineering involve huge computation costs. To counter such challenges, approximate models are often used as surrogates for the highly accurate but time intensive finite element models. In this paper, surrogates for first-order shear deformation based finite element models are built using a polynomial regression approach. Using statistical techniques like Box-Cox transformation and ANOVA, the effectiveness of the surrogates is enhanced. The accuracy of the surrogate models is evaluated using statistical metrics like $R^2$, $R^2{_{adj}}$, $R^2{_{pred}}$ and $Q^2{_{F3}}$. By combining these surrogates with nature-inspired multi-criteria decision-making algorithms, namely multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), the optimal combination of various design variables to simultaneously maximize fundamental frequency and frequency separation is predicted. It is seen that the proposed approach is simple, effective and good at inexpensively producing a host of optimal solutions.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.110.4-110
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• 2002

In practical control area, there are many examples with multiple objectives which may conflict or compete with each other like overhead crane control, automatic train operation, and refuse incinerator plant control, etc. These kinds of control problems are called multiobjective control problems, where it is difficult to provide the desired performance with control strategies based on single-objective optimization. Because the conventional control theories usually treat the control problem as the single objective optimization problem , the methods are not adequate to treat the multiobjective control problems. Particularly, in case of large scale systems or ill-defined systems, the multiple obj..

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.987-992
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• 2002

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. This algorithm is based on Continuous Evolutionary Algorithms to solve single objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method fur fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto-optimal tradeoff surface. Finally, the validity of this method has been demonstrated through a numerical example.

• Korean Journal of Computational Design and Engineering
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• v.17 no.5
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• pp.375-386
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• 2012

Most engineering design problems require analyses or simulations to evaluate objective functions. However, a single simulation can take many hours or even days to finish for many real world problems. As a result, design optimization becomes impossible since they require hundreds or thousands of simulation evaluations. The surrogate-based optimization (SBO) strategy became a remedy for such computationally expensive analyses and simulations. A surrogate-based optimization strategy has been developed in this study in order to improve global optimization performance. The strategy is a heuristic algorithm and it exploits not only multiple surrogates, but also multiple optimizers. Multiple optimizations of multiple surrogate models yield multiple candidate design points of optima. During the sequential sampling process, the algorithm ranks candidate design points, selects the points as many as specified, and builds the improved surrogate model. Various mathematical functions with different numbers of design variables are chosen to compare the proposed method with the other most recent algorithm, MSEGO. The proposed method shows superior performance to the other method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.697-708
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• 1995

For many practical optimization problems where the system components are stochastic, the objective functions can not be represented analytically. Furthermore, many of these problems are characterized by the presence of multiple and conflicting objectives. In this research, we introduce a new algorithm through an interactive cutting plane method for solving this multi-criteria simulation optimization problem. Then a turning process is evaluated through the proposed algorithm.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1017-1024
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• 2010

Under the Kyoto Protocol many countries have been requested to participate in emissions trading with the assigned $CO_2$ emissions. In this environment, it is inevitable to change the system and market operation in deregulated power systems, and then ensuring safety margin is becoming more important for balancing system security, economy and $CO_2$ emissions. Nowadays, available transfer capability (ATC) is a key index of the remaining capability of a transmission system for future transactions. This paper presents a novel approach to the ATC evaluation with $CO_2$ emissions using multi-objective particle swarm optimization (MOPSO) technique. This technique evolves a multi-objective version of PSO by proposing redefinition of global best and local best individuals in multi-objective optimization domain. The optimal power flow (OPF) method using MOPSO is suggested to solve multi-objective functions including fuel cost and $CO_2$ emissions simultaneously. To show its efficiency and effectiveness, the results of the proposed method is comprehensively realized by a comparison with the ATC which is not including $CO_2$ emissions for the IEEE 30-bus system, and is found to be quite promising.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.4
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• pp.750-769
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• 2015

The geometry of engineering systems affects their performances. For this reason, the shape of engineering systems needs to be optimized in the initial design stage. However, engineering system design problems consist of multi-objective optimization and the performance analysis using commercial code or numerical analysis is generally time-consuming. To solve these problems, many engineers perform the optimization using the approximation model (response surface). The Response Surface Method (RSM) is generally used to predict the system performance in engineering research field, but RSM presents some prediction errors for highly nonlinear systems. The major objective of this research is to establish an optimal design method for multi-objective problems and confirm its applicability. The proposed process is composed of three parts: definition of geometry, generation of response surface, and optimization process. To reduce the time for performance analysis and minimize the prediction errors, the approximation model is generated using the Backpropagation Artificial Neural Network (BPANN) which is considered as Neuro-Response Surface Method (NRSM). The optimization is done for the generated response surface by non-dominated sorting genetic algorithm-II (NSGA-II). Through case studies of marine system and ship structure (substructure of floating offshore wind turbine considering hydrodynamics performances and bulk carrier bottom stiffened panels considering structure performance), we have confirmed the applicability of the proposed method for multi-objective side constraint optimization problems.