International Science Index
Reliability and Cost Focused Optimization Approach for a Communication Satellite Payload Redundancy Allocation Problem
A typical reliability engineering problem regarding communication satellites has been considered to determine redundancy allocation scheme of power amplifiers within payload transponder module, whose dominant function is to amplify power levels of the received signals from the Earth, through maximizing reliability against mass, power, and other technical limitations. Adding each redundant power amplifier component increases not only reliability but also hardware, testing, and launch cost of a satellite. This study investigates a multi-objective approach used in order to solve Redundancy Allocation Problem (RAP) for a communication satellite payload transponder, focusing on design cost due to redundancy and reliability factors. The main purpose is to find the optimum power amplifier redundancy configuration satisfying reliability and capacity thresholds simultaneously instead of analyzing respectively or independently. A mathematical model and calculation approach are instituted including objective function definitions, and then, the problem is solved analytically with different input parameters in MATLAB environment. Example results showed that payload capacity and failure rate of power amplifiers have remarkable effects on the solution and also processing time.
Personnel Selection Based on Step-Wise Weight Assessment Ratio Analysis and Multi-Objective Optimization on the Basis of Ratio Analysis Methods
Personnel selection process is considered as one of the most important and most difficult issues in human resources management. At the stage of personnel selection, the applicants are handled according to certain criteria, the candidates are dealt with, and efforts are made to select the most appropriate candidate. However, this process can be more complicated in terms of the managers who will carry out the staff selection process. Candidates should be evaluated according to different criteria such as work experience, education, foreign language level etc. It is crucial that a rational selection process is carried out by considering all the criteria in an integrated structure. In this study, the problem of choosing the front office manager of a 5 star accommodation enterprise operating in Antalya is addressed by using multi-criteria decision-making methods. In this context, SWARA (Step-wise weight assessment ratio analysis) and MOORA (Multi-Objective Optimization on the basis of ratio analysis) methods, which have relatively few applications when compared with other methods, have been used together. Firstly SWARA method was used to calculate the weights of the criteria and subcriteria that were determined by the business. After the weights of the criteria were obtained, the MOORA method was used to rank the candidates using the ratio system and the reference point approach. Recruitment processes differ from sector to sector, from operation to operation. There are a number of criteria that must be taken into consideration by businesses in accordance with the structure of each sector. It is of utmost importance that all candidates are evaluated objectively in the framework of these criteria, after these criteria have been carefully selected in the selection of suitable candidates for employment. In the study, staff selection process was handled by using SWARA and MOORA methods together.
A Biomimetic Approach for the Multi-Objective Optimization of Kinetic Façade Design
A kinetic façade responds to user requirements and environmental conditions. In designing a kinetic façade, kinetic patterns play a key role in determining its performance. This paper proposes a biomimetic method for the multi-objective optimization for kinetic façade design. The autonomous decentralized control system is combined with flocking algorithm. The flocking agents are autonomously reacting to sensor values and bring about kinetic patterns changing over time. A series of experiments were conducted to verify the potential and limitations of the flocking based decentralized control. As a result, it could show the highest performance balancing multiple objectives such as solar radiation and openness among the comparison group.
A Study on Performance Prediction in Early Design Stage of Apartment Housing Using Machine Learning
As the development of information and communication technology, the convergence of machine learning of the ICT area and design is attempted. In this way, it is possible to grasp the correlation between various design elements, which was difficult to grasp, and to reflect this in the design result. In architecture, there is an attempt to predict the performance, which is difficult to grasp in the past, by finding the correlation among multiple factors mainly through machine learning. In architectural design area, some attempts to predict the performance affected by various factors have been tried. With machine learning, it is possible to quickly predict performance. The aim of this study is to propose a model that predicts performance according to the block arrangement of apartment housing through machine learning and the design alternative which satisfies the performance such as the daylight hours in the most similar form to the alternative proposed by the designer. Through this study, a designer can proceed with the design considering various design alternatives and accurate performances quickly from the early design stage.
Optimal Design of Multimachine Power System Stabilizers Using Improved Multi-Objective Particle Swarm Optimization Algorithm
In this paper, the concept of a non-dominated sorting multi-objective particle swarm optimization with local search (NSPSO-LS) is presented for the optimal design of multimachine power system stabilizers (PSSs). The controller design is formulated as an optimization problem in order to shift the system electromechanical modes in a pre-specified region in the s-plan. A composite set of objective functions comprising the damping factor and the damping ratio of the undamped and lightly damped electromechanical modes is considered. The performance of the proposed optimization algorithm is verified for the 3-machine 9-bus system. Simulation results based on eigenvalue analysis and nonlinear time-domain simulation show the potential and superiority of the NSPSO-LS algorithm in tuning PSSs over a wide range of loading conditions and large disturbance compared to the classic PSO technique and genetic algorithms.
Multi-Objective Optimization of a Solar-Powered Triple-Effect Absorption Chiller for Air-Conditioning Applications
In this paper, a detailed simulation model of a solar-powered triple-effect LiBr–H2O absorption chiller is developed to supply both cooling and heating demand of a large-scale building, aiming to reduce the fossil fuel consumption and greenhouse gas emissions in building sector. TRNSYS 17 is used to simulate the performance of the system over a typical year. A combined energetic-economic-environmental analysis is conducted to determine the system annual primary energy consumption and the total cost, which are considered as two conflicting objectives. A multi-objective optimization of the system is performed using a genetic algorithm to minimize these objectives simultaneously. The optimization results show that the final optimal design of the proposed plant has a solar fraction of 72% and leads to an annual primary energy saving of 0.69 GWh and annual CO2 emissions reduction of ~166 tonnes, as compared to a conventional HVAC system. The economics of this design, however, is not appealing without public funding, which is often the case for many renewable energy systems. The results show that a good funding policy is required in order for these technologies to achieve satisfactory payback periods within the lifetime of the plant.
Performance Evaluation of Karanja Oil Based Biodiesel Engine Using Modified Genetic Algorithm
This paper presents the evaluation of performance (BSFC and BTE), combustion (Pmax) and emission (CO, NOx, HC and smoke opacity) parameters of karanja biodiesel in a single cylinder, four stroke, direct injection diesel engine by considering significant engine input parameters (blending ratio, compression ratio and load torque). Multi-objective optimization of performance, combustion and emission parameters is also carried out in a karanja biodiesel engine using hybrid RSM-NSGA-II technique. The pareto optimum solutions are predicted by running the hybrid RSM-NSGA-II technique. Each pareto optimal solution is having its own importance. Confirmation tests are also conducted at randomly selected few pareto solutions to check the authenticity of the results.
Multi-Objective Optimization of Electric Discharge Machining for Inconel 718
Electric discharge machining (EDM) is one of the most widely used non-conventional manufacturing process to shape difficult-to-cut materials. The process yield, in terms of material removal rate, surface roughness and tool wear rate, of EDM may considerably be improved by selecting the optimal combination(s) of process parameters. This paper employs Multi-response signal-to-noise (MRSN) ratio technique to find the optimal combination(s) of the process parameters during EDM of Inconel 718. Three cases v.i.z. high cutting efficiency, high surface finish, and normal machining have been taken and the optimal combinations of input parameters have been obtained for each case. Analysis of variance (ANOVA) has been employed to find the dominant parameter(s) in all three cases. The experimental verification of the obtained results has also been made. MRSN ratio technique found to be a simple and effective multi-objective optimization technique.
Multi-Objective Random Drift Particle Swarm Optimization Algorithm Based on RDPSO and Crowding Distance Sorting
In this paper, we presented a Multi-Objective Random
Drift Particle Swarm Optimization algorithm (MORDPSO-CD) based
on RDPSO and crowding distance sorting to improve the convergence
and distribution with less computation cost. MORDPSO-CD makes
the most of RDPSO to approach the true Pareto optimal solutions
fast. We adopt the crowding distance sorting technique to update and
maintain the archived optimal solutions. Introducing the crowding
distance technique into MORDPSO can make the leader particles
find the true Pareto solution ultimately. The simulation results reveal
that the proposed algorithm has better convergence and distribution.
Multi-Objective Optimization Contingent on Subcarrier-Wise Beamforming for Multiuser MIMO-OFDM Interference Channels
We address the problem of interference over all the channels in multiuser MIMO-OFDM systems. This paper contributes three beamforming strategies designed for multiuser multiple-input and multiple-output by way of orthogonal frequency division multiplexing, in which the transmit and receive beamformers are acquired repetitious by secure-form stages. In the principal case, the transmit (TX) beamformers remain fixed then the receive (RX) beamformers are computed. This eradicates one interference span for every user by means of extruding the transmit beamformers into a null space of relevant channels. Formerly, by gratifying the orthogonality condition to exclude the residual interferences in RX beamformer for every user is done by maximizing the signal-to-noise ratio (SNR). The second case comprises mutually optimizing the TX and RX beamformers from controlled SNR maximization. The outcomes of first case is used here. The third case also includes combined optimization of TX-RX beamformers; however, uses the both controlled SNR and signal-to-interference-plus-noise ratio maximization (SINR). By the standardized channel model for IEEE 802.11n, the proposed simulation experiments offer rapid beamforming and enhanced error performance.
Multi-Objective Optimization of an Aerodynamic Feeding System Using Genetic Algorithm
Considering the challenges of short product life cycles
and growing variant diversity, cost minimization and manufacturing
flexibility increasingly gain importance to maintain a competitive
edge in today’s global and dynamic markets. In this context, an
aerodynamic part feeding system for high-speed industrial assembly
applications has been developed at the Institute of Production
Systems and Logistics (IFA), Leibniz Universitaet Hannover. The
aerodynamic part feeding system outperforms conventional systems
with respect to its process safety, reliability, and operating speed. In
this paper, a multi-objective optimisation of the aerodynamic feeding
system regarding the orientation rate, the feeding velocity, and the
required nozzle pressure is presented.
Multi-Objective Optimization in End Milling of Al-6061 Using Taguchi Based G-PCA
In this study, a multi objective optimization for end
milling of Al 6061 alloy has been presented to provide better
surface quality and higher Material Removal Rate (MRR). The input
parameters considered for the analysis are spindle speed, depth of cut
and feed. The experiments were planned as per Taguchis design of
experiment, with L27 orthogonal array. The Grey Relational Analysis
(GRA) has been used for transforming multiple quality responses
into a single response and the weights of the each performance
characteristics are determined by employing the Principal Component
Analysis (PCA), so that their relative importance can be properly and
objectively described. The results reveal that Taguchi based G-PCA
can effectively acquire the optimal combination of cutting parameters.
A Multi-Objective Evolutionary Algorithm of Neural Network for Medical Diseases Problems
This paper presents an evolutionary algorithm for
solving multi-objective optimization problems-based artificial neural
network (ANN). The multi-objective evolutionary algorithm used in
this study is genetic algorithm while ANN used is radial basis
function network (RBFN). The proposed algorithm named memetic
elitist Pareto non-dominated sorting genetic algorithm-based RBFN
(MEPGAN). The proposed algorithm is implemented on medical
diseases problems. The experimental results indicate that the
proposed algorithm is viable, and provides an effective means to
design multi-objective RBFNs with good generalization capability
and compact network structure. This study shows that MEPGAN
generates RBFNs coming with an appropriate balance between
accuracy and simplicity, comparing to the other algorithms found in
Fuzzy Optimization in Metabolic Systems
The optimization of biological systems, which is a branch of metabolic engineering, has generated a lot of industrial and academic interest for a long time. In the last decade, metabolic engineering approaches based on mathematical optimizations have been used extensively for the analysis and manipulation of metabolic networks. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, e.g., the possibility of enzyme effects. A deterministic approach does not give an adequate representation for metabolic reaction networks with uncertain characters. Fuzzy optimization formulations can be applied to cope with this problem. A fuzzy multi-objective optimization problem can be introduced for finding the optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell viability constraints. The accuracy of optimization results depends heavily on the development of essential kinetic models of metabolic networks. Kinetic models can quantitatively capture the experimentally observed regulation data of metabolic systems and are often used to find the optimal manipulation of external inputs. To address the issues of optimizing the regulatory structure of metabolic networks, it is necessary to consider qualitative effects, e.g., the resilience phenomena and cell viability constraints. Combining the qualitative and quantitative descriptions for metabolic networks makes it possible to design a viable strain and accurately predict the maximum possible flux rates of desired products. Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. Two case studies will present in the conference to illustrate the phenomena.
Forecasting Optimal Production Program Using Profitability Optimization by Genetic Algorithm and Neural Network
In our business field today, one of the most important issues for any enterprises is cost minimization and profit maximization. Second issue is how to develop a strong and capable model that is able to give us desired forecasting of these two issues. Many researches deal with these issues using different methods. In this study, we developed a model for multi-criteria production program optimization, integrated with Artificial Neural Network.
The prediction of the production cost and profit per unit of a product, dealing with two obverse functions at same time can be extremely difficult, especially if there is a great amount of conflict information about production parameters.
Feed-Forward Neural Networks are suitable for generalization, which means that the network will generate a proper output as a result to input it has never seen. Therefore, with small set of examples the network will adjust its weight coefficients so the input will generate a proper output.
This essential characteristic is of the most important abilities enabling this network to be used in variety of problems spreading from engineering to finance etc.
From our results as we will see later, Feed-Forward Neural Networks has a strong ability and capability to map inputs into desired outputs.
Proposal of a Model Supporting Decision-Making Based On Multi-Objective Optimization Analysis on Information Security Risk Treatment
Management is required to understand all information security risks within an organization, and to make decisions on which information security risks should be treated in what level by allocating how much amount of cost. However, such decision-making is not usually easy, because various measures for risk treatment must be selected with the suitable application levels. In addition, some measures may have objectives conflicting with each other. It also makes the selection difficult. Moreover, risks generally have trends and it also should be considered in risk treatment. Therefore, this paper provides the extension of the model proposed in the previous study. The original model supports the selection of measures by applying a combination of weighted average method and goal programming method for multi-objective analysis to find an optimal solution. The extended model includes the notion of weights to the risks, and the larger weight means the priority of the risk.
Proposal of a Model Supporting Decision-Making on Information Security Risk Treatment
Management is required to understand all information security risks within an organization, and to make decisions on which information security risks should be treated in what level by allocating how much amount of cost. However, such decision-making is not usually easy, because various measures for risk treatment must be selected with the suitable application levels. In addition, some measures may have objectives conflicting with each other. It also makes the selection difficult. Therefore, this paper provides a model which supports the selection of measures by applying multi-objective analysis to find an optimal solution. Additionally, a list of measures is also provided to make the selection easier and more effective without any leakage of measures.
Multi-Objective Optimization of a Steam Turbine Stage
The design of a steam turbine is a very complex
engineering operation that can be simplified and improved thanks to
computer-aided multi-objective optimization. This process makes use
of existing optimization algorithms and losses correlations to identify
those geometries that deliver the best balance of performance (i.e.
This paper deals with a one-dimensional multi-objective and
multi-point optimization of a single-stage steam turbine. Using a
genetic optimization algorithm and an algebraic one-dimensional
ideal gas-path model based on loss and deviation correlations, a code
capable of performing the optimization of a predefined steam turbine
stage was developed. More specifically, during this study the
parameters modified (i.e. decision variables) to identify the best
performing geometries were solidity and angles both for stator and
rotor cascades, while the objective functions to maximize were totalto-
static efficiency and specific work done.
Finally, an accurate analysis of the obtained results was carried
Optimization of Car Seat Considering Whiplash Injury
Development of motor car safety devices has reduced
fatality rates in car accidents. Yet despite this increase in car safety,
neck injuries resulting from rear impact collisions, particularly at low
speed, remain a primary concern. In this study, FEA(Finite Element
Analysis) of seat was performed to evaluate neck injuries in rear
impact. And the FEA result was verified by comparison with the actual
test results. The dummy used in FE model and actual test is BioRID II
which is regarded suitable for rear impact collision analysis. A
threshold of the BioRID II neck injury indicators was also proposed to
upgrade seat performance in order to reduce whiplash injury. To
optimize the seat for a low-speed rear impact collision, a method was
proposed, which is multi-objective optimization idea using DOE
(Design of Experiments) results.
Design Optimization of Aerocapture with Aerodynamic-Environment-Adaptive Variable Geometry Flexible Aeroshell
This paper proposes the concept of aerocapture with
aerodynamic-environment-adaptive variable geometry flexible
aeroshell that vehicle deploys. The flexible membrane is composed
of thin-layer film or textile as its aeroshell in order to solve some
problems obstructing realization of aerocapture technique.
Multi-objective optimization study is conducted to investigate
solutions and derive design guidelines. As a result, solutions which
can avoid aerodynamic heating and enlarge the corridor width up
to 10% are obtained successfully, so that the effectiveness of this
concept can be demonstrated. The deformation-use optimum
solution changes its drag coefficient from 1.6 to 1.1, along with the
change in dynamic pressure. Moreover, optimization results show
that deformation-use solution requires the membrane for which
upper temperature limit and strain limit are more than 700 K and
120%, respectively, and elasticity (Young-s modulus) is of order of
Multi-criteria Optimization of Square Beam using Linear Weighted Average Model
Increasing energy absorption is a significant parameter
in vehicle design. Absorbing more energy results in decreasing
occupant damage. Limitation of the deflection in a side impact results
in decreased energy absorption (SEA) and increased peak load (PL).
Hence a high crash force jeopardizes passenger safety and vehicle
integrity. The aims of this paper are to determine suitable dimensions
and material of a square beam subjected to side impact, in order to
maximize SEA and minimize PL. To achieve this novel goal, the
geometric parameters of a square beam are optimized using the
response surface method (RSM).multi-objective optimization is
performed, and the optimum design for different response features is
The Multi-objective Optimization for the SLS Process Parameters Based on Analytic Hierarchy Process
The forming process parameters of Selective Laser
Sintering(SLS) directly affect the forming efficiency and forming
quality. Therefore, to determine reasonable process parameters is
particularly important. In this paper, the weight of each target of the
forming quality and efficiency is firstly calculated with the Analytic
Hierarchy Process. And then the size of each target is measured by
orthogonal experiment. Finally, the sum of the product of each target
with the weight is compared to the process parameters in each group
and obtained the optimal molding process parameters.
Evolutionary Multi-objective Optimization for Positioning of Residential Houses
The current study describes a multi-objective optimization technique for positioning of houses in a residential neighborhood. The main task is the placement of residential houses in a favorable configuration satisfying a number of objectives. Solving the house layout problem is a challenging task. It requires an iterative approach to satisfy design requirements (e.g. energy efficiency, skyview, daylight, roads network, visual privacy, and clear access to favorite views). These design requirements vary from one project to another based on location and client preferences. In the Gulf region, the most important socio-cultural factor is the visual privacy in indoor space. Hence, most of the residential houses in this region are surrounded by high fences to provide privacy, which has a direct impact on other requirements (e.g. daylight and direction to favorite views). This investigation introduces a novel technique to optimally locate and orient residential buildings to satisfy a set of design requirements. The developed technique explores the search space for possible solutions. This study considers two dimensional house planning problems. However, it can be extended to solve three dimensional cases.
Evolutionary Algorithms for Learning Primitive Fuzzy Behaviors and Behavior Coordination in Multi-Objective Optimization Problems
Evolutionary robotics is concerned with the design of
intelligent systems with life-like properties by means of simulated
evolution. Approaches in evolutionary robotics can be categorized
according to the control structures that represent the behavior and the
parameters of the controller that undergo adaptation. The basic idea
is to automatically synthesize behaviors that enable the robot to
perform useful tasks in complex environments. The evolutionary
algorithm searches through the space of parameterized controllers
that map sensory perceptions to control actions, thus realizing a
specific robotic behavior. Further, the evolutionary algorithm
maintains and improves a population of candidate behaviors by
means of selection, recombination and mutation. A fitness function
evaluates the performance of the resulting behavior according to the
robot-s task or mission. In this paper, the focus is in the use of
genetic algorithms to solve a multi-objective optimization problem
representing robot behaviors; in particular, the A-Compander Law is
employed in selecting the weight of each objective during the
optimization process. Results using an adaptive fitness function show
that this approach can efficiently react to complex tasks under
On the Joint Optimization of Performance and Power Consumption in Data Centers
We model the process of a data center as a multi- objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consump¬tion and response time (makespan) subject to the constraints of deadlines and architectural requirements. A simple technique based on multi-objective goal programming is proposed that guarantees Pareto optimal solution with excellence in convergence process. The proposed technique also is compared with other traditional approach. The simulation results show that the proposed technique achieves superior performance compared to the min-min heuristics, and com¬petitive performance relative to the optimal solution implemented in UNDO for small-scale problems.
Multi-objective Optimization with Fuzzy Based Ranking for TCSC Supplementary Controller to Improve Rotor Angle and Voltage Stability
Many real-world optimization problems involve multiple conflicting objectives and the use of evolutionary algorithms to solve the problems has attracted much attention recently. This paper investigates the application of multi-objective optimization technique for the design of a Thyristor Controlled Series Compensator (TCSC)-based controller to enhance the performance of a power system. The design objective is to improve both rotor angle stability and system voltage profile. A Genetic Algorithm (GA) based solution technique is applied to generate a Pareto set of global optimal solutions to the given multi-objective optimisation problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Simulation results are presented to show the effectiveness and robustness of the proposed approach.
Optimization of CO2 Emissions and Cost for Composite Building Design with NSGA-II
Environmental pollution problems have been globally
main concern in all fields including economy, society and culture into
the 21st century. Beginning with the Kyoto Protocol, the reduction on
the emissions of greenhouse gas such as CO2 and SOX has been a
principal challenge of our day. As most buildings unlike durable goods
in other industries have a characteristic and long life cycle, they
consume energy in quantity and emit much CO2. Thus, for green
building construction, more research is needed to reduce the CO2
emissions at each stage in the life cycle. However, recent studies are
focused on the use and maintenance phase. Also, there is a lack of
research on the initial design stage, especially the structure design.
Therefore, in this study, we propose an optimal design plan
considering CO2 emissions and cost in composite buildings
simultaneously by applying to the structural design of actual building.
Seismic Response Reduction of Structures using Smart Base Isolation System
In this study, control performance of a smart base
isolation system consisting of a friction pendulum system (FPS) and a
magnetorheological (MR) damper has been investigated. A fuzzy
logic controller (FLC) is used to modulate the MR damper so as to
minimize structural acceleration while maintaining acceptable base
displacement levels. To this end, a multi-objective optimization
scheme is used to optimize parameters of membership functions and
find appropriate fuzzy rules. To demonstrate effectiveness of the
proposed multi-objective genetic algorithm for FLC, a numerical
study of a smart base isolation system is conducted using several
historical earthquakes. It is shown that the proposed method can find
optimal fuzzy rules and that the optimized FLC outperforms not only a
passive control strategy but also a human-designed FLC and a
conventional semi-active control algorithm.
Optimization of GAMM Francis Turbine Runner
Nowadays, the challenge in hydraulic turbine design is
the multi-objective design of turbine runner to reach higher
efficiency. The hydraulic performance of a turbine is strictly depends
on runner blades shape. The present paper focuses on the application
of the multi-objective optimization algorithm to the design of a small
Francis turbine runner. The optimization exercise focuses on the
efficiency improvement at the best efficiency operating point (BEP)
of the GAMM Francis turbine. A global optimization method based
on artificial neural networks (ANN) and genetic algorithms (GA)
coupled by 3D Navier-Stokes flow solver has been used to improve
the performance of an initial geometry of a Francis runner. The
results show the good ability of optimization algorithm and the final
geometry has better efficiency with initial geometry. The goal was to
optimize the geometry of the blades of GAMM turbine runner which
leads to maximum total efficiency by changing the design parameters
of camber line in at least 5 sections of a blade. The efficiency of the
optimized geometry is improved from 90.7% to 92.5%. Finally,
design parameters and the way of selection have been considered and
Multi-Objective Optimization for Performance-based Seismic Retrofit using Connection Upgrade
The unanticipated brittle fracture of connection of the
steel moment resisting frame (SMRF) occurred in 1994 the Northridge
earthquake. Since then, the researches for the vulnerability of
connection of the existing SMRF and for rehabilitation of those
buildings were conducted. This paper suggests performance-based
optimal seismic retrofit technique using connection upgrade. For
optimal design, a multi-objective genetic algorithm(NSGA-II) is used.
One of the two objective functions is to minimize initial cost and
another objective function is to minimize lifetime seismic damages
cost. The optimal algorithm proposed in this paper is performed
satisfying specified performance objective based on FEMA 356. The
nonlinear static analysis is performed for structural seismic
performance evaluation. A numerical example of SAC benchmark
SMRF is provided using the performance-based optimal seismic
retrofit technique proposed in this paper