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

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Generation of Pareto Sets based on Resource Reduction for Multi-Objective Problems Involving Project Scheduling and Resource Leveling (프로젝트 일정과 자원 평준화를 포함한 다목적 최적화 문제에서 순차적 자원 감소에 기반한 파레토 집합의 생성)

  • Jeong, Woo-Jin;Park, Sung-Chul;Yim, Dong-Soon
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.43 no.2
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    • pp.79-86
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    • 2020
  • To make a satisfactory decision regarding project scheduling, a trade-off between the resource-related cost and project duration must be considered. A beneficial method for decision makers is to provide a number of alternative schedules of diverse project duration with minimum resource cost. In view of optimization, the alternative schedules are Pareto sets under multi-objective of project duration and resource cost. Assuming that resource cost is closely related to resource leveling, a heuristic algorithm for resource capacity reduction (HRCR) is developed in this study in order to generate the Pareto sets efficiently. The heuristic is based on the fact that resource leveling can be improved by systematically reducing the resource capacity. Once the reduced resource capacity is given, a schedule with minimum project duration can be obtained by solving a resource-constrained project scheduling problem. In HRCR, VNS (Variable Neighborhood Search) is implemented to solve the resource-constrained project scheduling problem. Extensive experiments to evaluate the HRCR performance are accomplished with standard benchmarking data sets, PSPLIB. Considering 5 resource leveling objective functions, it is shown that HRCR outperforms well-known multi-objective optimization algorithm, SPEA2 (Strength Pareto Evolutionary Algorithm-2), in generating dominant Pareto sets. The number of approximate Pareto optimal also can be extended by modifying weight parameter to reduce resource capacity in HRCR.

Multi-Objective Optimization of Electromagnetic Device Based on Design Sensitivity Analysis and Reliability Analysis (설계 민감도와 신뢰도 분석에 근거한 전자기기의 다목적 최적화)

  • Ren, Ziyan;Zhang, Dianhai;Park, Chanhyuk;Koh, Chang Seop
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.1
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    • pp.49-56
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    • 2013
  • In this paper, for constrained optimization problem, one multi-objective optimization algorithm that ensures both performance robustness and constraint feasibility is proposed when uncertainties are involved in design variables. In the proposed algorithm, the gradient index of objective function assisted by design sensitivity with the help of finite element method is applied to evaluate robustness; the reliability calculated by the sensitivity-assisted Monte Carlo simulation method is used to assess the feasibility of constraint function. As a demonstration, the performance and numerical efficiency of the proposed method is investigated through application to the optimal design of TEAM problem 22--a superconducting magnetic energy storage system.

Shape Optimization of the Lower Control Arm using the Characteristic Function and the Fatigue Analysis (특성함수와 피로해석을 이용한 로워컨트롤암의 형상최적설계)

  • Park Youngchul;Lee Donghwa
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.1
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    • pp.119-125
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    • 2005
  • The current automotive is seeking the improvement of performance, the prevention of environmental pollution and the saving of energy resources according to miniaturization and lightweight of the components. And the variance analysis on the basis of structure analysis and DOE is applied to the lower control am. We have proposed a statistical design model to evaluate the effect of structural modification by performing the practical multi-objective optimization considering weight, stress and fatigue lift. The lower control arm is performed the fatigue analysis using the load history of real road test. The design model is determined using the optimization of acquired load history with the fatigue characteristic. The characteristic function is made use of the optimization according to fatigue characteristics to consider constrained function in the optimization of DOE. The structure optimization of a lower control arm according to fatigue characteristics is performed. And the optimized design variable is D=47 m, T=36mm, W=12 mm. In the real engineering problem of considering many objective functions, the multi-objective optimization process using the mathematical programming and the characteristic function is derived an useful design solution.

Energy absorption characteristics of diamond core columns under axial crushing loads

  • Azad, Nader Vahdat;Ebrahimi, Saeed
    • Steel and Composite Structures
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    • v.21 no.3
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    • pp.605-628
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    • 2016
  • The energy absorption characteristics of diamond core sandwich cylindrical columns under axial crushing process depend greatly on the amount of material which participates in the plastic deformation. Both the single-objective and multi-objective optimizations are performed for columns under axial crushing load with core thickness and helix pitch of the honeycomb core as design variables. Models are optimized by multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). Results show that optimization improves the energy absorption characteristics with constrained and unconstrained peak crashing load. Also, it is concluded that the aluminum tube has a better energy absorption capability rather than steel tube at a certain peak crushing force. The results justify that the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. A ranking technique for order preference (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a multi-criteria decision which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. Furthermore, local and global sensitivity analyses are performed to assess the effect of design variable values on the SEA and PCF functions in design domain. Based on the sensitivity analysis results, it is concluded that for both models, the helix pitch of the honeycomb core has greater effect on the sensitivity of SEA, while, the core thickness has greater effect on the sensitivity of PCF.

Resource-constrained Scheduling at Different Project Sizes

  • Lazari, Vasiliki;Chassiakos, Athanasios;Karatzas, Stylianos
    • International conference on construction engineering and project management
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    • 2022.06a
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    • pp.196-203
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    • 2022
  • The resource constrained scheduling problem (RCSP) constitutes one of the most challenging problems in Project Management, as it combines multiple parameters, contradicting objectives (project completion within certain deadlines, resource allocation within resource availability margins and with reduced fluctuations), strict constraints (precedence constraints between activities), while its complexity grows with the increase in the number of activities being executed. Due to the large solution space size, this work investigates the application of Genetic Algorithms to approximate the optimal resource alolocation and obtain optimal trade-offs between different project goals. This analysis uses the cost of exceeding the daily resource availability, the cost from the day-by-day resource movement in and out of the site and the cost for using resources day-by-day, to form the objective cost function. The model is applied in different case studies: 1 project consisting of 10 activities, 4 repetitive projects consisting of 40 activities in total and 16 repetitive projects consisting of 160 activities in total, in order to evaluate the effectiveness of the algorithm in different-size solution spaces and under alternative optimization criteria by examining the quality of the solution and the required computational time. The case studies 2 & 3 have been developed by building upon the recurrence of the unit/sub-project (10 activities), meaning that the initial problem is multiplied four and sixteen times respectively. The evaluation results indicate that the proposed model can efficiently provide reliable solutions with respect to the individual goals assigned in every case study regardless of the project scale.

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Chance-constrained Scheduling of Variable Generation and Energy Storage in a Multi-Timescale Framework

  • Tan, Wen-Shan;Abdullah, Md Pauzi;Shaaban, Mohamed
    • Journal of Electrical Engineering and Technology
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    • v.12 no.5
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    • pp.1709-1718
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    • 2017
  • This paper presents a hybrid stochastic deterministic multi-timescale scheduling (SDMS) approach for generation scheduling of a power grid. SDMS considers flexible resource options including conventional generation flexibility in a chance-constrained day-ahead scheduling optimization (DASO). The prime objective of the DASO is the minimization of the daily production cost in power systems with high penetration scenarios of variable generation. Furthermore, energy storage is scheduled in an hourly-ahead deterministic real-time scheduling optimization (RTSO). DASO simulation results are used as the base starting-point values in the hour-ahead online rolling RTSO with a 15-minute time interval. RTSO considers energy storage as another source of grid flexibility, to balance out the deviation between predicted and actual net load demand values. Numerical simulations, on the IEEE RTS test system with high wind penetration levels, indicate the effectiveness of the proposed SDMS framework for managing the grid flexibility to meet the net load demand, in both day-ahead and real-time timescales. Results also highlight the adequacy of the framework to adjust the scheduling, in real-time, to cope with large prediction errors of wind forecasting.

An Optimal Design for Truss Core Unit of Railway Carbody of Aluminum Extrusion Plate (알루미늄 압출재를 사용한 철도차량차체의 단위 압출재 최적설계)

  • 장창두;하윤석;조영천;신광복
    • Journal of the Korean Society for Railway
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    • v.6 no.3
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    • pp.194-202
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    • 2003
  • To make railway carbody light in weight has advantages at some aspects of both manufacturing and maintenance. Recently, railway carbodys of steel structure have been lightened their weight by using aluminum extrusion plate. for the additional lightening of railway carbody, an optimal design which maintains proper strength and minimizes weight must be achieved. Optimization which is used with finite element analysis for aluminum extrusion plate has the disadvantage of consuming much time. In this paper, the method of equivalent material property which is available to FEA code is established using the method of equivalent stiffness. This method for plate is expanded into the method for railway carbody structure with plates and shells. An objective function is established for maximum stiffness of unit aluminum extrusion plate using established method of equivalent material property. We performed an multi-objective optimization using the penalty function method. As a result, recommendable shapes and sizes of unit extrusion plate for under-frame of high speed train is presented.

A Dynamic Analysis of Constrained Multibody Systems (구속된 다물체 시스템을 위한 동역학 해석론)

  • 이상호;한창수;서문석
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.9
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    • pp.2339-2348
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    • 1994
  • The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

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).

Approximate Multi-Objective Optimization of Robot Casting Considering Deflection and Weight (처짐과 무게를 고려한 주물 프레임의 다중목적 근사최적설계)

  • Choi, Ha-Young;Lee, Jongsoo;Park, Juno
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.21 no.6
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    • pp.954-960
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    • 2012
  • Nowadays, rapidly changing and unstable global economic environments request a lot of roles to engineers. In this situation, product should be designed to make more profit by cost down and to satisfy distinguished performance comparing to other competitive ones. In this research, the optimization design of the industrial robot casting will be done. The weight and deflection have to be reduced as objective functions and stress has to be constrained under some constant value. To reduce time cost, CCD (Central Composite Design) will be used to make experimental design. And RSM (Response Surface Methodology) will be taken to make regression model for objective functions and constraint function. Finally, optimization will be done with Genetic Algorithm. In this problem, the objective functions are multiple, so NSGA-II which is brilliant and efficient for such a problem will be used. For the solution quality check, the diversity between Pareto solutions will be also checked.