• Title/Summary/Keyword: Pareto optimal

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A study on the optimal design of rope way (索道線路의 最適設計에 대한 硏究)

  • 최선호;박용수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.1
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    • pp.26-35
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    • 1987
  • As an attempt to make the multi-objection for the line design of the rope way, the resulted formulas from the catenary curve as exact ones were summarized, and it was found out that the Kuhn-Tucker's optimality conditions and regions of the objective functions can analytically be expressed with dimensionless parameters. The Pareto's optimum solution set was analytically obtained through the objective function-the minimum relation of $W^{*}$, and $W^{*}$ is a trade-off relation. From this, The dimension of a rope and the value of an initial tension that are the standard in design of the rope way were determined. It was concluded that $V^{*}$ should become minimum, and that the ratio of the dimension of rope to the value of and initial tension become larger than superposition factor corresponding to curve AB.to curve AB.

Combined Economic and Emission Dispatch with Valve-point loading of Thermal Generators using Modified NSGA-II

  • Rajkumar, M.;Mahadevan, K.;Kannan, S.;Baskar, S.
    • Journal of Electrical Engineering and Technology
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    • v.8 no.3
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    • pp.490-498
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    • 2013
  • This paper discusses the application of evolutionary multi-objective optimization algorithms namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Modified NSGA-II (MNSGA-II) for solving the Combined Economic Emission Dispatch (CEED) problem with valve-point loading. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a non-smooth optimization problem. IEEE 57-bus and IEEE 118-bus systems are taken to validate its effectiveness of NSGA-II and MNSGA-II. To compare the Pareto-front obtained using NSGA-II and MNSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Furthermore, three different performance metrics such as convergence, diversity and Inverted Generational Distance (IGD) are calculated for evaluating the closeness of obtained Pareto-fronts. Numerical results reveal that MNSGA-II algorithm performs better than NSGA-II algorithm to solve the CEED problem effectively.

NSGA-II Technique for Multi-objective Generation Dispatch of Thermal Generators with Nonsmooth Fuel Cost Functions

  • Rajkumar, M.;Mahadevan, K.;Kannan, S.;Baskar, S.
    • Journal of Electrical Engineering and Technology
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    • v.9 no.2
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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).

An Efficient PSO Algorithm for Finding Pareto-Frontier in Multi-Objective Job Shop Scheduling Problems

  • Wisittipanich, Warisa;Kachitvichyanukul, Voratas
    • Industrial Engineering and Management Systems
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    • v.12 no.2
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    • pp.151-160
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    • 2013
  • In the past decades, several algorithms based on evolutionary approaches have been proposed for solving job shop scheduling problems (JSP), which is well-known as one of the most difficult combinatorial optimization problems. Most of them have concentrated on finding optimal solutions of a single objective, i.e., makespan, or total weighted tardiness. However, real-world scheduling problems generally involve multiple objectives which must be considered simultaneously. This paper proposes an efficient particle swarm optimization based approach to find a Pareto front for multi-objective JSP. The objective is to simultaneously minimize makespan and total tardiness of jobs. The proposed algorithm employs an Elite group to store the updated non-dominated solutions found by the whole swarm and utilizes those solutions as the guidance for particle movement. A single swarm with a mixture of four groups of particles with different movement strategies is adopted to search for Pareto solutions. The performance of the proposed method is evaluated on a set of benchmark problems and compared with the results from the existing algorithms. The experimental results demonstrate that the proposed algorithm is capable of providing a set of diverse and high-quality non-dominated solutions.

The Strategical Scenario Analysis for the Efficient Management of Resource in Open Access (공유자원의 효율적 경영을 위한 전략적 시나리오분석)

  • Choi, Jong-Du
    • The Journal of Fisheries Business Administration
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    • v.42 no.3
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    • pp.31-39
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    • 2011
  • This paper attempts to extend such analysis to the rather more difficult problem of optimal management of transnational fish stocks jointly owned by two countries. Transboundary fish such as Mackerel creates an incentive to harvest fish before a competitor does and leads to over-exploitation. This tendency is especially poignant for transnational stocks since, in the absence of an enforceable, international agreement, there is little or no reason for either government or the fishing industry to promote resource conservation and economic efficiency. In the current paper I examine a game theoretic setting in which cooperative management can provide more benefits than noncooperative management. A dynamic model of Mackerel fishery is combined with Nash's theory of two countries cooperative games. A characteristic function game approach is applied to describe the sharing of the surplus benefits from cooperation and noncooperation. A bioeconomic model was used to compare the economic yield of the optimal strategies for two countries, under joint maximization of net benefits in joint ocean. The results suggest as follows. First, the threat points represent the net benefits for two countries in absence of cooperation. The net benefits to Korea and China in threat points are 2,000 billion won(${\pi}^0_{KO}$) and 1,130 billion won(${\pi}^0_{CH}$). Total benefits are 3,130 billion won. Second, if two countries cooperate one with another, they reach the solution payoffs such as Pareto efficient. The net benefits to Korea and China in Pareto efficient are 2,785 billion won(${\pi}^0_{KO}$) and 1,605 billion won(${\pi}^0_{CH}$) or total benefits of 4,390 billion won : a gain of 1,260 billion won. Third, the different price effects under the two scenarios show that total benefit rise as price increases.

A Genetic Algorithm using A Modified Order Exchange Crossover for Rural Postman Problem with Time Windows (MOX 교차 연산자를 이용한 Rural Postman Problem with Time Windows 해법)

  • Kang koung-Ju
    • Journal of the Korea Society of Computer and Information
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    • v.10 no.5 s.37
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    • pp.179-186
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    • 2005
  • This paper describes a genetic algorithm and compares three crossover operators for Rural Postman Problem with Time Windows (RPPTW). The RPPTW which is a multiobjective optimization problem, is an extension of Rural Postman Problem(RPP) in which some service places (located at edge) require service time windows that consist of earliest time and latest time. Hence, RPM is a m띤tieect optimization Problem that has minimal routing cost being serviced within the given time at each service Place. To solve the RPPTW which is a multiobjective optimization problem, we obtain a Pareto-optimal set that the superiority of each objective can not be compared. This Paper performs experiments using three crossovers for 12 randomly generated test problems and compares the results. The crossovers using in this Paper are Partially Matched Exchange(PMX) Order Exchange(OX), and Modified Order Exchange(MOX) which is proposed in this paper. For each test problem, the results show the efficacy of MOX method for RPPTW.

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Optimal LAN Design Using a Pareto Stratum-Niche Cubicle Genetic Algorithm (PS-NC GA를 이용한 최적 LAN 설계)

  • Choi, Kang-Hee;Jung, Kyoung-Hee
    • Journal of the Korea Computer Industry Society
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    • v.6 no.3
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    • pp.539-550
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    • 2005
  • The spanning tree, which is being used the most widely in indoor wiring network, is chosen for the network topology of the optimal LAN design. To apply a spanning tree to GA, the concept of $Pr\ddot{u}fer$ numbers is used. $Pr\ddot{u}fer$ numbers can express he spanning tree in an efficient and brief way, and also can properly represent the characteristics of spanning trees. This paper uses Pareto Stratum-Niche Cubicle(PS-NC) GA by complementing the defect of the same priority allowance in non-dominated solutions of pareto genetic algorithm(PGA). By applying the PS-NC GA to the LAN design areas, the optimal LAN topology design in terms of minimizing both message delay time and connection-cost could be accomplished in a relatively short time. Numerical analysis has been done for a hypothetical data set. The results show that the proposed algorithm could provide better or good solutions for the multi-objective LAN design problem in a fairly short time.

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Optimization of Data Placement using Principal Component Analysis based Pareto-optimal method for Multi-Cloud Storage Environment

  • Latha, V.L. Padma;Reddy, N. Sudhakar;Babu, A. Suresh
    • International Journal of Computer Science & Network Security
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    • v.21 no.12
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    • pp.248-256
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    • 2021
  • Now that we're in the big data era, data has taken on a new significance as the storage capacity has exploded from trillion bytes to petabytes at breakneck pace. As the use of cloud computing expands and becomes more commonly accepted, several businesses and institutions are opting to store their requests and data there. Cloud storage's concept of a nearly infinite storage resource pool makes data storage and access scalable and readily available. The majority of them, on the other hand, favour a single cloud because of the simplicity and inexpensive storage costs it offers in the near run. Cloud-based data storage, on the other hand, has concerns such as vendor lock-in, privacy leakage and unavailability. With geographically dispersed cloud storage providers, multicloud storage can alleviate these dangers. One of the key challenges in this storage system is to arrange user data in a cost-effective and high-availability manner. A multicloud storage architecture is given in this study. Next, a multi-objective optimization problem is defined to minimise total costs and maximise data availability at the same time, which can be solved using a technique based on the non-dominated sorting genetic algorithm II (NSGA-II) and obtain a set of non-dominated solutions known as the Pareto-optimal set.. When consumers can't pick from the Pareto-optimal set directly, a method based on Principal Component Analysis (PCA) is presented to find the best answer. To sum it all up, thorough tests based on a variety of real-world cloud storage scenarios have proven that the proposed method performs as expected.

Determination of Flood-limited Water Levels of Agricultural Reservoirs Considering Irrigation and Flood Control (농업용 저수지의 이·치수 기능을 고려한 홍수기 제한수위 설정 기법 개발)

  • Kim, Jihye;Kwak, Jihye;Jun, Sang Min;Lee, Sunghack;Kang, Moon Seong
    • Journal of The Korean Society of Agricultural Engineers
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    • v.65 no.6
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    • pp.23-35
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    • 2023
  • In this study, we developed a method to determine the flood-limited water levels of agricultural reservoirs, considering both their irrigation and flood control functions. Irrigation safety and flood safety indices were defined to be applied to various reservoirs, allowing for a comprehensive assessment of the irrigation and flood control properties. Seasonal flood-limited water level scenarios were established to represent the temporal characteristics of rainfall and agricultural water supply and the safety indices were analyzed according to these scenarios. The optimal scenarios were derived using a schematic solution based on Pareto front analysis. The method was applied to Obong, Yedang, and Myogok reservoirs, and the results showed that the characteristics of each reservoir were well represented in the safety indices. The irrigation safety of Obong reservoir was found to be significantly influenced by the late-stage flood-limited water level, while those of Yedang and Myogok reservoir were primarily affected by the early and mid-stage flood-limited water levels. The values of irrigation safety and flood safety indices for each scenario were plotted as points on the coordinate plane, and the optimal flood-limited water levels were selected from the Pareto front. The storage ratio of the optimal flood-limited water levels for the early, mid, and late stages were 65-70%, 70%, and 75% for Obong reservoir, 75%, 70-75%, and 65-70% for Yedang reservoir, and 75-80%, 70%, and 50% for Myogok reservoir. We expect that the method developed in this study will facilitate efficient reservoir operations.

Optimization of Tank Model Parameters Using Multi-Objective Genetic Algorithm (I): Methodology and Model Formulation (다목적 유전자알고리즘을 이용한 Tank 모형 매개변수 최적화(I): 방법론과 모형구축)

  • Kim, Tae-Soon;Jung, Il-Won;Koo, Bo-Young;Bae, Deg-Hyo
    • Journal of Korea Water Resources Association
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    • v.40 no.9
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    • pp.677-685
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    • 2007
  • The objective of this study is to evaluate the applicability of multi-objective genetic algorithm(MOGA) in order to calibrate the parameters of conceptual rainfall-runoff model, Tank model. NSGA-II, one of the most imitating MOGA implementations, is combined with Tank model and four multi-objective functions such as to minimize volume error, root mean square error (RMSE), high flow RMSE, and low flow RMSE are used. When NSGA-II is employed with more than three multi-objective functions, a number of Pareto-optimal solutions usually becomes too large. Therefore, selecting several preferred Pareto-optimal solutions is essential for stakeholder, and preference-ordering approach is used in this study for the sake of getting the best preferred Pareto-optimal solutions. Sensitivity analysis is performed to examine the effect of initial genetic parameters, which are generation number and Population size, to the performance of NSGA-II for searching the proper paramters for Tank model, and the result suggests that the generation number is 900 and the population size is 1000 for this study.