• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.11 s.254
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• pp.1358-1368
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• 2006

This paper proposes a Pareto artificial life algorithm for solving multi-objective optimization problems. The artificial life algorithm for optimization problem with a single objective function is improved to handle Pareto optimization problem through incorporating the new method to estimate the fitness value for a solution and the Pareto list to memorize and to improve the Pareto optimal set. The proposed algorithm was applied to the optimum design of a journal bearing which has two objective functions. The Pareto front and the optimal solution set for the application were presented to give the possible solutions to a decision maker or a designer. Furthermore, the relation between linearly combined single-objective optimization problem and Pareto optimization problem has been studied.

• Journal of Power Electronics
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• v.15 no.1
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• pp.160-176
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• 2015

This paper presents a method of designing optimal integer- and fractional-order proportional-integral-derivative (FOPID) controllers for a boost converter to gain a set of favorable characteristics at various operating points. A Pareto-based multi-objective optimization approach called strength Pareto evolutionary algorithm (SPEA) is used to obtain fast and low overshoot start-up and dynamic responses and switching stability. The optimization approach generates a set of optimal gains called Pareto set, which corresponds to a Pareto front. The Pareto front is a set of optimal results for objective functions. These results provide designers with a trade-off look-up table, in which they can easily choose any of the optimal gains based on design requirements. The SPEA also overcomes the difficulties of tuning the FOPID controller, which is an extension to the classic integer-order PID controllers and potentially promises better results. The proposed optimized FOPID controller provides an excellent start-up response and the desired dynamic response. This paper presents a detailed comparison of the optimum integer- and the fractional-order PID controllers. Extensive simulation and experimental results prove the superiority of the proposed design methodology to achieve a wide set of desired technical goals.

• Journal of Distribution Science
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• v.15 no.2
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• pp.15-20
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• 2017

Purpose - This paper aims to suggest a delivery constrained internet shopping optimization problem (DISOP) which must be solved for online recommendation system to provide a customized service considering cost and delivery conditions at the same time. Research design, data, and methodology - To solve a (DISOP), we propose a multi-objective formulation and a solution approach. By using a commercial optimization software (LINDO), a (DISOP) can be solved iteratively and a pareto optimal set can be calculated for real-sized problem. Results - We propose a new research problem which is different with internet shopping optimization problem since our problem considers not only the purchasing cost but also delivery conditions at the same time. Furthermore, we suggest a multi-objective mathematical formulation for our research problem and provide a solution approach to get a pareto optimal set by using numerical example. Conclusions - This paper proposes a multi-objective optimization problem to solve internet shopping optimization problem with delivery constraint and a solution approach to get a pareto optimal set. The results of research will contribute to develop a customized comparison and recommendation system to help more easy and smart online shopping service.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.869-874
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• 2005

This paper proposes the Pareto artificial life algorithm for a multi-objective function optimization problem. The artificial life algorithm for a single objective function optimization problem is improved through incorporating the new method to estimate the fitness value fur a solution and the Pareto list to memorize and to improve the Pareto optimal set. The proposed algorithm is applied to the optimum design of a Journal bearing which has two objective functions. The Pareto front and the optimal solution set for the application are reported to present the possible solutions to a decision maker or a designer.

• Journal of Power Electronics
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• v.12 no.1
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• pp.104-112
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• 2012

In this paper a new method for the design of a simple PI controller is presented and it has been applied in the control of a Boost based PFC rectifier. The Strength Pareto evolutionary algorithm, which is based on the Pareto Optimality concept, used in Game theory literature is implemented as a multi-objective optimization approach to gain a good transient response and a high quality input current. In the proposed method, the input current harmonics and the dynamic response have been assumed as objective functions, while the PI controller's gains of the PFC rectifier (Kpi, Tpi) are design variables. The proposed algorithm generates a set of optimal gains called a Pareto Set corresponding to a Pareto Front, which is a set of optimal results for the objective functions. All of the Pareto Front points are optimum, but according to the design priority objective function, each one can be selected. Simulation and experimental results are presented to prove the superiority of the proposed design methodology over other methods.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.3080-3085
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• 2007

Shape optimization of the 3-dimensional WIG airfoil with 3.0-aspect ratio has been performed by using the multi-objective genetic algorithm. The WIG ship effectively floating above the surface by the ram effect and the virtual additional aspect ratio by a ground is one of next-generation and cost-effective transportations. Unlike the airplane flying out of the ground effect, a WIG ship has possibility to capsize because of unsatisfying the static stability. The WIG ship should satisfy aerodynamic properties as well as a static stability. They tend to strong contradict and it is difficult to satisfy aerodynamic properties and static stability simultaneously. It is inevitable that lift force has to scarify to obtain a static stability. Multi-objective optimization technique that the individual objectives are considered separately instead of weighting can overcome the conflict. Due to handling individual objectives, the optimum cannot be unique but a set of nondominated potential solutions: pareto optimum. There are three objectives; lift coefficient, lift-to-drag ratio and static stability. After a few evolutions, the non-dominated pareto individuals can be obtained. Pareto sets are all the set of possible and excellent solution across the design space. At any selections of the pareto set, these are no better solutions in all design space

• Smart Structures and Systems
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• v.22 no.4
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• pp.469-479
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• 2018

The present research study utilizes a multi-objective optimization method for Pareto optimization of an eight-degree of freedom full vehicle vibration model, adopting a non-dominated sorting genetic algorithm II (NSGA-II). In this research, a full set of ride comfort as well as ride safety parameters are considered as objective functions. These objective functions are divided in to two groups (ride comfort group and ride safety group) where the ones in one group are in conflict with those in the other. Also, in this research, a special optimizing technique and combinational method consisting of weighted sum method and Pareto optimization are applied to transform Pareto double-objective optimization to Pareto full-objective optimization which can simultaneously minimize all objectives. Using this technique, the full set of ride parameters of three dimensional vehicle model are minimizing simultaneously. In derived Pareto front, unique trade-off design points can selected which are non-dominated solutions of optimizing the weighted sum comfort parameters versus weighted sum safety parameters. The comparison of the obtained results with those reported in the literature, demonstrates the distinction and comprehensiveness of the results arrived in the present study.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.11 s.254
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• pp.1084-1092
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• 2006

Shape optimization of airfoil in WIG craft has been performed by considering the ground effect. The WIG craft should satisfy various aerodynamic characteristics such as lift, lift to drag ratio, and static height stability. However, they show a strong trade-off phenomenon so that it is difficult to satisfy aerodynamic properties simultaneously. Optimization is carried out through the multi-objective genetic algorithm. A multi-objective optimization means that each objective is considered separately instead of weighting. Due to the trade-off, pareto sets and non-dominated solutions can be obtained instead of the unique solution. NACA0015 airfoil is considered as a baseline model, shapes of airfoil are parameterized and rebuilt with four-Bezier curves. There are eighteen design variables and three objective functions. The range of design variables and their resolutions are two primary keys for the successful optimization. By two preliminary optimizations, the variation can be reduced effectively. After thirty evolutions, the non-dominated pareto individuals of twenty seven are obtained. Pareto sets are all the set of possible and excellent solution across the design space. At any selections of the pareto set, these are no better solutions in all design space.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.2
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• pp.36-42
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• 2021

This paper deals with a vehicle routing problem with resource repositioning (VRPRR) which is a variation of well-known vehicle routing problem with pickup and delivery (VRPPD). VRPRR in which static repositioning of public bikes is a representative case, can be defined as a multi-objective optimization problem aiming at minimizing both transportation cost and the amount of unmet demand. To obtain Pareto sets for the problem, famous multi-objective optimization algorithms such as Strength Pareto Evolutionary Algorithm 2 (SPEA2) can be applied. In addition, a linear combination of two objective functions with weights can be exploited to generate Pareto sets. By varying weight values in the combined single objective function, a set of solutions is created. Experiments accomplished with a standard benchmark problem sets show that Variable Neighborhood Search (VNS) applied to solve a number of single objective function outperforms SPEA2. All generated solutions from SPEA2 are completely dominated by a set of VNS solutions. It seems that local optimization technique inherent in VNS makes it possible to generate near optimal solutions for the single objective function. Also, it shows that trade-off between the number of solutions in Pareto set and the computation time should be considered to obtain good solutions effectively in case of linearly combined single objective function.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.869-874
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• 2007

In searching for solutions to multiobjective optimization problem, we find that there is no single optimal solution but rather a set of solutions known as 'Pareto optimal set'. To find approximation of ideal pareto optimal set, search capability of diverse individuals at population space can determine the performance of evolutionary algorithms. This paper propose the method to maintain population diversify and to find non-dominated alternatives in Game model based Co-Evolutionary Algorithm.