• Title/Summary/Keyword: weighted multi-objective optimization

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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).

RSM-based Practical Optimum Design of TMD for Control of Structural Response Considering Weighted Multiple Objectives (가중 다목적성을 고려한 구조물 응답 제어용 TMD의 RSM 기반 실용적 최적 설계)

  • Do, Jeongyun;Guk, Seongoh;Kim, Dookie
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.21 no.6
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    • pp.113-125
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    • 2017
  • In spite of bulk literature about the tuning of TMD, the effectiveness of TMD in reducing the seismic response of engineering structures is still in a row. This paper deals with the optimum tuning parameters of a passive TMD and simulated on MATLAB with a ten-story numerical shear building. A weighted multi-objective optimization method based on computer experiment consisting of coupled with central composite design(CCD) central composite design and response surface methodology(RSM) was applied to find out the optimum tuning parameters of TMD. After the optimization, the so-conceived TMD turns out to be optimal with respect to the specific seismic event, hence allowing for an optimum reduction in seismic response. The method was employed on above structure by assuming first the El Centro seismic input as a sort of benchmark excitation, and then additional recent strong-motion earthquakes. It is found that the RSM based weighted multi-objective optimized damper improves frequency responses and root mean square displacements of the structure without TMD by 31.6% and 82.3% under El Centro earthquake, respectively, and has an equal or higher performance than the conventionally designed dampers with respect to frequency responses and root mean square displacements and when applied to earthquakes.

A Univariate Loss Function Approach to Multiple Response Surface Optimization: An Interactive Procedure-Based Weight Determination (다중반응표면 최적화를 위한 단변량 손실함수법: 대화식 절차 기반의 가중치 결정)

  • Jeong, In-Jun
    • Knowledge Management Research
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    • v.21 no.1
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    • pp.27-40
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    • 2020
  • Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

Shape Optimization of a Rotating Two-Pass Duct with a Guide Vane in the Turning Region (회전하는 냉각유로의 곡관부에 부착된 가이드 베인의 형상 최적설계)

  • Moon, Mi-Ae;Kim, Kwang-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.14 no.1
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    • pp.66-76
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    • 2011
  • The heat transfer and pressure loss characteristics of a rotating two-pass channel with a guide vane in the turning region have been studied using three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis, and the shape of the guide vane has been optimized using surrogate modeling optimization technique. For the optimization, thickness, location and angle of the guide vanes have been selected as design variables. The objective function has been defined as a linear combination of the heat transfer and the friction loss related terms with a weighting factor. Latin hypercube sampling has been applied to determine the design points as design of experiments. A weighted-average surrogate model, PBA has been used as the surrogate model. The guide vane in the turning region does not influence the heat transfer in the first passage upstream of the turning region, but enhances largely the heat transfer in the turning region and the second passage. In an example of the optimization, the objective function has been increased by 13.6%.

Fundamental framework toward optimal design of product platform for industrial three-axis linear-type robots

  • Sawai, Kana;Nomaguchi, Yutaka;Fujita, Kikuo
    • Journal of Computational Design and Engineering
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    • v.2 no.3
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    • pp.157-164
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    • 2015
  • This paper discusses an optimization-based approach for the design of a product platform for industrial three-axis linear-type robots, which are widely used for handling objects in manufacturing lines. Since the operational specifications of these robots, such as operation speed, working distance and orientation, weight and shape of loads, etc., will vary for different applications, robotic system vendors must provide various types of robots efficiently and effectively to meet a range of market needs. A promising step toward this goal is the concept of a product platform, in which several key elements are commonly used across a series of products, which can then be customized for individual requirements. However the design of a product platform is more complicated than that of each product, due to the need to optimize the design across many products. This paper proposes an optimization-based fundamental framework toward the design of a product platform for industrial three-axis linear-type robots; this framework allows the solution of a complicated design problem and builds an optimal design method of fundamental features of robot frames that are commonly used for a wide range of robots. In this formulation, some key performance metrics of the robot are estimated by a reducedorder model which is configured with beam theory. A multi-objective optimization problem is formulated to represent the trade-offs among key design parameters using a weighted-sum form for a single product. This formulation is integrated into a mini-max type optimization problem across a series of robots as an optimal design formulation for the product platform. Some case studies of optimal platform design for industrial three-axis linear-type robots are presented to demonstrate the applications of a genetic algorithm to such mathematical models.

Goal-Pareto based NSGA Optimization Algorithm (Goal-Pareto 기반의 NSGA 최적화 알고리즘)

  • Park, Jun-Su;Park, Soon-Kyu;Shin, Yo-An;Yoo, Myung-Sik;Lee, Won-Cheol
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.44 no.2 s.314
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    • pp.108-115
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    • 2007
  • This paper proposes a new optimization algorithm prescribed by GBNSGA(Goal-Pareto Based Non-dominated Sorting Genetic Algorithm) whose result satisfies the user's needs and goals to enhance the performance of optimization. Typically, lots of real-world engineering problems encounter simultaneous optimization subject to satisfying prescribed multiple objectives. Unfortunately, since these objectives might be mutually competitive, it is hardly to find a unique solution satisfying every objectives. Instead, many researches have been investigated in order to obtain an optimal solution with sacrificing more than one objectives. This paper introduces a novel optimization scheme named by GBNSGA obeying both goals as well as objectives as possible as it can via allocating candidated solutions on Pareto front, which enhances the performance of Pareto based optimization. The performance of the proposed GBNSGA will be compared with that of the conventional NSGA and weighted-sum approach.

Weighted sum multi-objective optimization of skew composite laminates

  • Kalita, Kanak;Ragavendran, Uvaraja;Ramachandran, Manickam;Bhoi, Akash Kumar
    • Structural Engineering and Mechanics
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    • v.69 no.1
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    • pp.21-31
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    • 2019
  • Optimizing composite structures to exploit their maximum potential is a realistic application with promising returns. In this research, simultaneous maximization of the fundamental frequency and frequency separation between the first two modes by optimizing the fiber angles is considered. A high-fidelity design optimization methodology is developed by combining the high-accuracy of finite element method with iterative improvement capability of metaheuristic algorithms. Three powerful nature-inspired optimization algorithms viz. a genetic algorithm (GA), a particle swarm optimization (PSO) variant and a cuckoo search (CS) variant are used. Advanced memetic features are incorporated in the PSO and CS to form their respective variants-RPSOLC (repulsive particle swarm optimization with local search and chaotic perturbation) and CHP (co-evolutionary host-parasite). A comprehensive set of benchmark solutions on several new problems are reported. Statistical tests and comprehensive assessment of the predicted results show CHP comprehensively outperforms RPSOLC and GA, while RPSOLC has a little superiority over GA. Extensive simulations show that the on repeated trials of the same experiment, CHP has very low variability. About 50% fewer variations are seen in RPSOLC as compared to GA on repeated trials.

GBNSGA Optimization Algorithm for Multi-mode Cognitive Radio Communication Systems (다중모드 Cognitive Radio 통신 시스템을 위한 GBNSGA 최적화 알고리즘)

  • Park, Jun-Su;Park, Soon-Kyu;Kim, Jin-Up;Kim, Hyung-Jung;Lee, Won-Cheol
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.32 no.3C
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    • pp.314-322
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    • 2007
  • This paper proposes a new optimization algorithm named by GBNSGA(Goal-Pareto Based Non-dominated Sorting Genetic Algorithm) which determines the best configuration for CR(Cognitive Radio) communication systems. Conventionally, in order to select the proper radio configuration, genetic algorithm has been introduced so as to alleviate computational burden along the execution of the cognition cycle proposed by Mitola. This paper proposes a novel optimization algorithm designated as GBNSGA for cognitive engine which can be described as a hybrid algorithm combining well-known Pareto-based NSGA(Non-dominated Sorting Genetic Algorithm) as well as GP(Goal Programming). By conducting computer simulations, it will be verified that the proposed method not only satisfies the user's service requirements in the form of goals. It reveals the fast optimization capability and more various solutions rather than conventional NSGA or weighted-sum approach.

Utilization of a Mathematical Programming Data Structure for the Implementation of a Water Resources Planning System (수자원 운영계획 시스템의 구현을 위한 수리계획 모형 자료구조의 활용)

  • Kim, Jae-Hee;Kim, Sheung-Kown;Park, Young-Joon
    • IE interfaces
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    • v.16 no.4
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    • pp.485-495
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    • 2003
  • This paper reports on the application of the integration of mathematical programming model and database in a decision support system (DSS) for the planning of the multi-reservoir operating system. The DSS is based on a multi-objective, mixed-integer goal programming (MIGP) model, which can generate efficient solutions via the weighted-sums method (WSM). The major concern of this study is seamless, efficient integration between the mathematical model and the database, because there are significant differences in structure and content between the data for a mathematical model and the data for a conventional database application. In order to load the external optimization results on the database, we developed a systematic way of naming variable/constraint so that a rapid identification of variables/constraints is possible. An efficient database structure for planning of the multi-reservoir operating system is presented by taking advantage of the naming convention of the variable/constraint.