• Title/Summary/Keyword: Multi-objective Optimization Problem

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Internet Shopping Optimization Problem With Delivery Constraints

  • Chung, Ji-Bok
    • 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.

Multi-objective Optimization of Fuzzy System Using Membership Functions Defined by Normed Method (노음방법에 의해 정의된 소속함수를 사용한 퍼지계의 다목적 최적설계)

  • 이준배;이병채
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.8
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    • pp.1898-1909
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    • 1993
  • In this paper, a convenient scheme for solving multi-objective optimization problems including fuzzy information in both objective functions and constraints is presented. At first, a multi-objective problem is converted into single objective problem based on the norm method, and a merbership function is constructed by selecting its type and providing the parameters defined by the norm method. Finally, this fuzzy programming problem is converted into an ordinary optimization problem which can be solved by usual nonlinear programming techniques. With this scheme, a designer can conveniently obtain pareto optimal solutions of a fuzzy system only by providing some parameters corresponding to the importance of the objectiv functions. Proposed scheme is simple and efficient in treating multi-objective fuzzy systems compared with and method by with membership function value is provided interactively. To show the validity of the scheme, a simple 3-bar truss example and optimal cutting problem are solved, and the results show that the scheme is very useful and easy to treat multi-objective fuzzy systems.

Multi-objective Optimization of Vehicle Routing with Resource Repositioning (자원 재배치를 위한 차량 경로계획의 다목적 최적화)

  • Kang, Jae-Goo;Yim, Dong-Soon
    • 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.

Fuzzy multi-objective optimization of the laminated composite beam (복합재 적층 보의 퍼지 다목적 최적설계)

  • 이강희;구만회;이종호;홍영기;우호길
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2000.04a
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    • pp.143-148
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    • 2000
  • In this article, we presents multi-objective design optimization of laminated composite beam using Fuzzy programming method. At first, the two design objectives are minimizing the structural weight and maximizing the buckling load respectively. Fuzzy multi-optimization problem can be formulated based on results of single optimizations. Due to different relative importance of design objectives, membership functions are constructed by adding exponential parameters for different objective's weights. Finite element analysis of composite beam for buckling behavior are carried by Natural mode method proposed by J.Argyris and computational time of analysis can be reduced. With this scheme, a designer can conveniently obtain a compromise optimal solution of a multi-objective optimization problem only by providing some exponential parameters corresponding to the importance of the objective functions.

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Study on multi-objective optimization method for radiation shield design of nuclear reactors

  • Yao Wu;Bin Liu;Xiaowei Su;Songqian Tang;Mingfei Yan;Liangming Pan
    • Nuclear Engineering and Technology
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    • v.56 no.2
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    • pp.520-525
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    • 2024
  • The optimization design problem of nuclear reactor radiation shield is a typical multi-objective optimization problem with almost 10 sub-objectives and the sub-objectives are always demanded to be under tolerable limits. In this paper, a design method combining multi-objective optimization algorithms with paralleling discrete ordinate transportation code is developed and applied to shield design of the Savannah nuclear reactor. Three approaches are studied for light-weighted and compact design of radiation shield. Comparing with directly optimization with 10 objectives and the single-objective optimization, the approach by setting sub-objectives representing weight and volume as optimization objectives while treating other sub-objectives as constraints has the best performance, which is more suitable to reactor shield design.

Multi-factor Evolution for Large-scale Multi-objective Cloud Task Scheduling

  • Tianhao Zhao;Linjie Wu;Di Wu;Jianwei Li;Zhihua Cui
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.17 no.4
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    • pp.1100-1122
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    • 2023
  • Scheduling user-submitted cloud tasks to the appropriate virtual machine (VM) in cloud computing is critical for cloud providers. However, as the demand for cloud resources from user tasks continues to grow, current evolutionary algorithms (EAs) cannot satisfy the optimal solution of large-scale cloud task scheduling problems. In this paper, we first construct a large- scale multi-objective cloud task problem considering the time and cost functions. Second, a multi-objective optimization algorithm based on multi-factor optimization (MFO) is proposed to solve the established problem. This algorithm solves by decomposing the large-scale optimization problem into multiple optimization subproblems. This reduces the computational burden of the algorithm. Later, the introduction of the MFO strategy provides the algorithm with a parallel evolutionary paradigm for multiple subpopulations of implicit knowledge transfer. Finally, simulation experiments and comparisons are performed on a large-scale task scheduling test set on the CloudSim platform. Experimental results show that our algorithm can obtain the best scheduling solution while maintaining good results of the objective function compared with other optimization algorithms.

Multi-Phase Optimization of Quill Type Machine Structures(1) (Static Compliance Analysis & Multi-Objective Function Optimization) (퀼형 공작기계구조물의 다단계 최적화(1) (정강성 해석 및 다목적함수 최적화))

  • Lee, Yeong-U;Seong, Hwal-Gyeong
    • Journal of the Korean Society for Precision Engineering
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    • v.18 no.11
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    • pp.155-160
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    • 2001
  • To achieve high precision cutting as well as production capability in the machine tool, it is needed to develop excellent rigidity statically, dynamically and thermally as well. In order to predict the qualitative behavior of a machine tool, simultaneous analysis of mechanics and heat transfer is required. Generally, machine tool designers have solved designing problems based on partial estimation of the specified rigidity. This study clears the inter-relationship between therm, and propose multi-phase optimization of machine tool structure using a genetic algorithm. The multi-phase solution method is consists of a series of mechanical design problem. At this first phase of static design problem, multi-objective optimization for the purpose of minimization of the total weight and static compliance minimization is solved using the Pareto Genetic Algorithm.

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Multi-objective Fuzzy-optimization of Crowbar Resistances for the Low-Voltage Ride-through of Doubly Fed Induction Wind Turbine Generation Systems

  • Zhang, Wenjuan;Ma, Haomiao;Zhang, Junli;Chen, Lingling;Qu, Yang
    • Journal of Power Electronics
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    • v.15 no.4
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    • pp.1119-1130
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    • 2015
  • This study investigates the multi-objective fuzzy optimization of crowbar resistance for the doubly fed induction generator (DFIG) low-voltage ride-through (LVRT). By integrating the crowbar resistance of the crowbar circuit as a decision variable, a multi-objective model for crowbar resistance value optimization has been established to minimize rotor overcurrent and to simultaneously reduce the DFIG reactive power absorbed from the grid during the process of LVRT. A multi-objective genetic algorithm (MOGA) is applied to solve this optimization problem. In the proposed GA, the value of the crowbar resistance is represented by floating-point numbers in the GA population. The MOGA emphasizes the non-dominated solutions and simultaneously maintains diversity in the non-dominated solutions. A fuzzy-set-theory-based is employed to obtain the best solution. The proposed approach has been evaluated on a 3 MW DFIG LVRT. Simulation results show the effectiveness of the proposed approach for solving the crowbar resistance multi-objective optimization problem in the DFIG LVRT.

Ammunition Allocation Model using an Interactive Multi-objective Optimization(MOO) Method (상호작용 다목적 최적화 방법론을 이용한 전시 탄약 할당 모형)

  • Jeong, Min-Seop;Park, Myeong-Seop
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.11a
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    • pp.513-524
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    • 2006
  • The ammunition allocation problem is a Multi-objective optimization(MOO) problem, maximizing fill-rate of multiple user troops and minimizing transportation time. Recent studies attempted to solve this problem by the prior preference articulation approach such as goal programming. They require that all the preference information of decision makers(DM) should be extracted prior to solving the problem. However, the prior preference information is difficult to implement properly in a rapidly changing state of war. Moreover they have some limitations such as heavy cognitive effort required to DM. This paper proposes a new ammunition allocation model based on more reasonable assumptions and uses an interactive MOO method to the ammunition allocation problem to overcome the limitations mentioned above. In particular, this article uses the GDF procedure, one of the well-known interactive optimization methods in the MOO liter-ature, in solving the ammunition allocation problem.

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Multi-Objective Optimization of Multistory Shear Building Under Seismic Loads (지진하중을 받는 다층 뼈대구조물의 다목적 최적설계)

  • 조효남;민대홍;정봉교
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.255-262
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    • 2002
  • In this paper, an improved multi-objective optimmum design method is proposed. And it is applied to steel frames under seismic loads. The multi-objective optimization problem is formulated with three optimality criteria, namely, minimum structural weight and maximum strain energy and stability. The Pareto curve can be obtained by performing the multi-objective optimization for multistory shear buildings. In order to efficiently solve the multi-objective optimization problem the decomposition method that separates both system-level and element-level is used. In addition, various techniques such as effective reanalysis technique with respect to intermediate variables and sensitivity analysis using an automatic differentiation (AD) we incorporated. Moreover, the relationship function among section properties induced from the profile is used in order to link system-level and element level. From the results of numerical investigation, it may be stated that the proposed method will lead to the more rational design compared with the conventional one.

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