• 품질경영학회지
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• 제40권4호
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• pp.481-496
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• 2012

Purpose: This paper aims at improving inefficiency of an existing posterior preference articulation method proposed for dual response surface optimization. The method generates a set of non-dominated solutions and then allows a decision maker (DM) to select the best solution among them through an interval selection strategy. Methods: This paper proposes an iterative posterior preference articulation method, which repeatedly generates the predetermined number of non-dominated solutions in an interval which becomes gradually narrower over rounds. Results: The existing method generates a good number of non-dominated solutions not used in the DM's selection process, while the proposed method generates the minimal number of non-dominated solutions necessitated in the selection process. Conclusion: The proposed method enables a satisfactory compromise solution to be achieved with minimal cognitive burden of the DM as well as with light computation load in generating non-dominated solutions.

• 대한산업공학회지
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• 제43권3호
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• pp.164-175
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• 2017

Dual response surface optimization (DRSO) attempts to optimize mean and variability of a process response variable using a response surface methodology. In general, mean and variability of the response variable are often in conflict. In such a case, the process engineer need to understand the tradeoffs between the mean and variability in order to obtain a satisfactory solution. Recently, a Posterior preference articulation approach to DRSO (P-DRSO) has been proposed. P-DRSO generates a number of non-dominated solutions and allows the process engineer to select the most preferred solution. By observing the non-dominated solutions, the DM can explore and better understand the trade-offs between the mean and variability. However, the non-dominated solutions generated by the existing P-DRSO is often incomprehensive and unevenly distributed which limits the practicability of the method. In this regard, we propose a modified P-DRSO using multiple objective genetic algorithms. The proposed method has an advantage in that it generates comprehensive and evenly distributed non-dominated solutions.

• Journal of Electrical Engineering and Technology
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• 제9권2호
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• pp.423-432
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• 2014

Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied for solving Combined Economic Emission Dispatch (CEED) problem with valve-point loading of thermal generators. This CEED problem with valve-point loading is a nonlinear, constrained multi-objective optimization problem, with power balance and generator capacity constraints. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a nonsmooth optimization problem. To validate its effectiveness of NSGA-II, two benchmark test systems, IEEE 30-bus and IEEE 118-bus systems are considered. To compare the Pareto-front obtained using NSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Comparison with other optimization techniques showed the superiority of the NSGA-II approach and confirmed its potential for solving the CEED problem. Numerical results show that NSGA-II algorithm can provide Pareto-front in a single run with good diversity and convergence. An approach based on Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) is applied on non-dominated solutions obtained to determine Best Compromise Solution (BCS).

• Industrial Engineering and Management Systems
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• 제10권2호
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• pp.134-139
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• 2011

The problem of scheduling in permutation flowshops has been extensively investigated by many researchers. Recently, attempts are being made to consider more than one objective simultaneously and develop algorithms to obtain a set of Pareto-optimal solutions. Varadharajan et al. (2005) presented a multi-objective simulated-annealing algorithm (MOSA) for the problem of permutation-flowshop scheduling with the objectives of minimizing the makespan and the total flowtime of jobs. The MOSA uses two initial sequences obtained using heuristics, and seeks to obtain non-dominated solutions through the implementation of a probability function, which probabilistically selects the objective of minimizing either the makespan or the total flowtime of jobs. In this paper, the same problem of heuristically developing non-dominated sequences is considered. We propose an effective heuristics based on simulated annealing (SA), in which the weighted sum of the makespan and the total flowtime is used. The essences of the heuristics are in selecting the initial sequence, setting the weight and generating a solution in the search process. Using a benchmark problem provided by Taillard (1993), which was used in the MOSA, these conditions are extracted in a large-scale experiment. The non-dominated sets obtained from the existing algorithms and the proposed heuristics are compared. It was found that the proposed heuristics drastically improved the performance of finding the non-dominated frontier.

• 대한기계학회논문집B
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• 제20권11호
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• pp.3655-3665
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• 1996

An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.666-668
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• 1998

In this paper, we consider a bi-objective vehicle routing problem to minimize total distance traveled and maximize minimum integrated satisfaction level of selecting desirable routes in an fuzzy graph. The fuzzy graph reflects a real delivery situation in which there are a depot, some demand points, paths linking them, and distance and integrated satisfaction level are associated with each route. For solving the vi-objective problem we introduce a concept of routing vector and define non-dominated solution for comparing vectors. An efficient algorithm involving a selection method of non-dominated solutions based on DEA is proposed for the vehicle routing problem with rigid distance and integrated satisfaction level.

• 한국지능시스템학회논문지
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• 제17권7호
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• pp.869-874
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• 2007

다목적 함수의 최적화 문제(Multiobjective optimization problems)의 경우에는 하나의 최적해가 존재하는 것이 아니라 '파레토 최적해 집합(Pareto optimal set)'이라고 알려진 해들의 집합이 존재한다. 이러한 이상적 파레토 최적해 집합과 가까운 최적해를 찾기 위한 다양한 해탐색 능력은 진화 알고리즘의 성능을 결정한다. 본 논문에서는 게임 모델에 기반한 공진화 알고리즘(GCEA: Game model based Co-Evolutionary Algorithm)에서 해집단의 다양성을 유지하여, 다양한 비지배적 파레토 대안해(non-dominated alternatives)들을 찾기 위한 방법을 제안한다.

• 대한기계학회논문집B
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• 제30권11호
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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.

• International Journal of Naval Architecture and Ocean Engineering
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• 제10권4호
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• pp.439-449
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• 2018

In this paper, multi-objective optimization of a multi-bubble pressure cabin in the underwater glider with Blended-Wing-Body (BWB) is carried out using Kriging and the Non-dominated Sorting Genetic Algorithm (NSGA-II). Two objective functions are considered: buoyancy-weight ratio and internal volume. Multi-bubble pressure cabin has a strong compressive capacity, and makes full use of the fuselage space. Parametric modeling of the multi-bubble pressure cabin structure is automatic generated using UG secondary development. Finite Element Analysis (FEA) is employed to study the structural performance using the commercial software ANSYS. The weight of the primary structure is determined from the volume of the Finite Element Structure (FES). The stress limit is taken into account as the constraint condition. Finally, Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) method is used to find some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. The best solution is compared with the initial design results to prove the efficiency and applicability of this optimization method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권1호
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• pp.1-20
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• 2018

Service composition in the Inter-Cloud raises new challenges that are caused by the different Quality of Service (QoS) requirements of the users, which are served by different geo-distributed Cloud providers. This paper aims to explore how to select and compose such services while considering how to reach high efficiency on cost and response time, low network latency, and high reliability across multiple Cloud providers. A new hybrid multi-objective evolutionary algorithm to perform the above task called LS-NSGA-II-DE is proposed, in which the differential evolution (DE) algorithm uses the adaptive mutation operator and crossover operator to replace the those of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to get the better convergence and diversity. At the same time, a Local Search (LS) method is performed for the Non-dominated solution set F{1} in each generation to improve the distribution of the F{1}. The simulation results show that our proposed algorithm performs well in terms of the solution distribution and convergence, and in addition, the optimality ability and scalability are better compared with those of the other algorithms.