Search results for: Pareto optimization

Authors: S. Farahat, E. Khorasani Nejad, S. M. Hoseini Sarvari

Abstract:

In this paper multi-objective genetic algorithms are employed for Pareto approach optimization of ideal Turboshaft engines. In the multi-objective optimization a number of conflicting objective functions are to be optimized simultaneously. The important objective functions that have been considered for optimization are specific thrust (F/m& 0), specific fuel consumption ( P S ), output shaft power 0 (& /&) shaft W m and overall efficiency( ) O η . These objectives are usually conflicting with each other. The design variables consist of thermodynamic parameters (compressor pressure ratio, turbine temperature ratio and Mach number). At the first stage single objective optimization has been investigated and the method of NSGA-II has been used for multiobjective optimization. Optimization procedures are performed for two and four objective functions and the results are compared for ideal Turboshaft engine. In order to investigate the optimal thermodynamic behavior of two objectives, different set, each including two objectives of output parameters, are considered individually. For each set Pareto front are depicted. The sets of selected decision variables based on this Pareto front, will cause the best possible combination of corresponding objective functions. There is no superiority for the points on the Pareto front figure, but they are superior to any other point. In the case of four objective optimization the results are given in tables.

Keywords: Multi-objective, Genetic algorithm, Turboshaft Engine.

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Authors: Kyoungwoo Park, Byeong Sam Kim, Juhee Lee, Kwang Soo Kim

Abstract:

The Prediction of aerodynamic characteristics and shape optimization of airfoil under the ground effect have been carried out by integration of computational fluid dynamics and the multiobjective Pareto-based genetic algorithm. The main flow characteristics around an airfoil of WIG craft are lift force, lift-to-drag ratio and static height stability (H.S). However, they show a strong trade-off phenomenon so that it is not easy to satisfy the design requirements simultaneously. This difficulty can be resolved by the optimal design. The above mentioned three characteristics are chosen as the objective functions and NACA0015 airfoil is considered as a baseline model in the present study. The profile of airfoil is constructed by Bezier curves with fourteen control points and these control points are adopted as the design variables. For multi-objective optimization problems, the optimal solutions are not unique but a set of non-dominated optima and they are called Pareto frontiers or Pareto sets. As the results of optimization, forty numbers of non- dominated Pareto optima can be obtained at thirty evolutions.

Keywords: Aerodynamics, Shape optimization, Airfoil on WIGcraft, Genetic algorithm, Computational fluid dynamics (CFD).

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Authors: Maria Kalinina, Aron Larsson, Leif Olsson

Abstract:

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper, is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the reference point may be adjusted to represent the preferences of a decision making agent. Preference information about objective weights from a decision maker may be expressed imprecisely. The developed elicitation procedure provides an opportunity to obtain surrogate numerical weights for the objectives, and thus, to manage impreciseness of preference. The proposed method is a scalable to many objectives and can be used independently or as complementary to the various visualization techniques in the multidimensional case.

Keywords: Imprecise weights, Multiple objectives, Pareto optimality, Visualization.

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Authors: Yiqiong Yuan, Jun Sun, Dongmei Zhou, Jianan Sun

Abstract:

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.

Keywords: Multi-objective optimization, random drift particle swarm optimization, crowding distance, Pareto optimal solution.

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Authors: Mohsen Nikaein

Abstract:

Because of importance of energy, optimization of power generation systems is necessary. Gas turbine cycles are suitable manner for fast power generation, but their efficiency is partly low. In order to achieving higher efficiencies, some propositions are preferred such as recovery of heat from exhaust gases in a regenerator, utilization of intercooler in a multistage compressor, steam injection to combustion chamber and etc. However thermodynamic optimization of gas turbine cycle, even with above components, is necessary. In this article multi-objective genetic algorithms are employed for Pareto approach optimization of Regenerative-Intercooling-Gas Turbine (RIGT) cycle. In the multiobjective optimization a number of conflicting objective functions are to be optimized simultaneously. The important objective functions that have been considered for optimization are entropy generation of RIGT cycle (Ns) derives using Exergy Analysis and Gouy-Stodola theorem, thermal efficiency and the net output power of RIGT Cycle. These objectives are usually conflicting with each other. The design variables consist of thermodynamic parameters such as compressor pressure ratio (Rp), excess air in combustion (EA), turbine inlet temperature (TIT) and inlet air temperature (T0). At the first stage single objective optimization has been investigated and the method of Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used for multi-objective optimization. Optimization procedures are performed for two and three objective functions and the results are compared for RIGT Cycle. In order to investigate the optimal thermodynamic behavior of two objectives, different set, each including two objectives of output parameters, are considered individually. For each set Pareto front are depicted. The sets of selected decision variables based on this Pareto front, will cause the best possible combination of corresponding objective functions. There is no superiority for the points on the Pareto front figure, but they are superior to any other point. In the case of three objective optimization the results are given in tables.

Keywords: Exergy, Entropy Generation, Brayton Cycle, DesignParameters, Optimization, Genetic Algorithm, Multi-Objective.

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Authors: Seyed Habib A. Rahmati

Abstract:

During last decades, developing multi-objective evolutionary algorithms for optimization problems has found considerable attention. Flexible job shop scheduling problem, as an important scheduling optimization problem, has found this attention too. However, most of the multi-objective algorithms that are developed for this problem use nonprofessional approaches. In another words, most of them combine their objectives and then solve multi-objective problem through single objective approaches. Of course, except some scarce researches that uses Pareto-based algorithms. Therefore, in this paper, a new Pareto-based algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our considered objectives are makespan, critical machine work load, and total work load of machines. The proposed algorithm is also compared with one the best Pareto-based algorithms of the literature on some multi-objective criteria, statistically.

Keywords: Scheduling, Flexible job shop scheduling problem, controlled elitism non-dominated sorting genetic algorithm

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Authors: M. Farshbaf, M. R. Feizi-Derakhshi

Abstract:

Graph partitioning is a NP-hard problem with multiple conflicting objectives. The graph partitioning should minimize the inter-partition relationship while maximizing the intra-partition relationship. Furthermore, the partition load should be evenly distributed over the respective partitions. Therefore this is a multiobjective optimization problem (MOO). One of the approaches to MOO is Pareto optimization which has been used in this paper. The proposed methods of this paper used to improve the performance are injecting best solutions of previous runs into the first generation of next runs and also storing the non-dominated set of previous generations to combine with later generation's non-dominated set. These improvements prevent the GA from getting stuck in the local optima and increase the probability of finding more optimal solutions. Finally, a simulation research is carried out to investigate the effectiveness of the proposed algorithm. The simulation results confirm the effectiveness of the proposed method.

Keywords: Graph partitioning, Genetic algorithm, Multiobjective optimization, Pareto front.

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Authors: S. Panda, S. C. Swain, A. K. Baliarsingh, A. K. Mohanty, C. Ardil

Abstract:

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.

Keywords: Multi-objective optimisation, thyristor controlled series compensator, power system stability, genetic algorithm, pareto solution set, fuzzy ranking.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: Flur R. Ismagilov, Irek Kh. Khayrullin, Vyacheslav E. Vavilov, Ruslan D. Karimov, Anton S. Gorbunov, Danis R. Farrakhov

Abstract:

The paper presents another structural scheme of high-temperature starter-generator with external rotor to be installed on High Pressure Shaft (HPS) of aircraft engines (AE) to implement More Electrical Engine concept. The basic materials to make this starter-generator (SG) were selected and justified. Multi-criteria optimization of the developed structural scheme was performed using a genetic algorithm and Pareto method. The optimum (in Pareto terms) active length and thickness of permanent magnets of SG were selected as a result of the optimization. Using the dimensions obtained, allowed to reduce the weight of the designed SG by 10 kg relative to a base option at constant thermal loads. Multidisciplinary computer simulation was performed on the basis of the optimum geometric dimensions, which proved performance efficiency of the design. We further plan to make a full-scale sample of SG of HPS and publish the results of its experimental research.

Keywords: High-temperature starter-generator, More electrical engine, multi-criteria optimization, permanent magnet.

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Authors: Mahmood Reza Shakarami, Reza Sedaghati

Abstract:

Recently, distributed generation technologies have received much attention for the potential energy savings and reliability assurances that might be achieved as a result of their widespread adoption. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering wind turbines. The main objective of the DFR is to minimize the deviation of the bus voltage. Since the DFR is a nonlinear optimization problem, we apply the Adaptive Modified Firefly Optimization (AMFO) approach to solve it. As a result of the conflicting behavior of the single- objective function, a fuzzy based clustering technique is employed to reach the set of optimal solutions called Pareto solutions. The approach is tested on the IEEE 32-bus standard test system.

Keywords: Adaptive Modified Firefly Optimization (AMFO), Pareto solutions, feeder reconfiguration, wind turbines, bus voltage.

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

Abstract:

Composite patching is a common way for reinforcing the cracked pipes and cylinders. The effects of composite patch reinforcement on fracture parameters of a cracked pipe depend on a variety of parameters such as number of layers, angle, thickness, and material of each layer. Therefore, stacking sequence optimization of composite patch becomes crucial for the applications of cracked pipes. In this study, in order to obtain the optimal stacking sequence for a composite patch that has minimum weight and maximum resistance in propagation of cracks, a coupled Multi-Objective Genetic Algorithm (MOGA) and Finite Element Method (FEM) process is proposed. This optimization process has done for longitudinal and transverse semi-elliptical cracks and optimal stacking sequences and Pareto’s front for each kind of cracks are presented. The proposed algorithm is validated against collected results from the existing literature.

Keywords: Multi objective optimization, Pareto front, composite patch, cracked pipe.

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Authors: Francisco Aparisi, Marco A. de Luna

Abstract:

In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.

Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.

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Authors: G. Bhushan, S. Dhingra, K. K. Dubey

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This paper presents the evaluation of performance (BSFC and BTE), combustion (P_max) and emission (CO, NO_x, 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.

Keywords: Karanja biodiesel, single cylinder direct injection diesel engine, response surface methodology, central composite rotatable design, genetic algorithm.

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Authors: C. Chitra, P. Subbaraj

Abstract:

The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated SortingGenetic Algorithm, Routing, Weighted sum.

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Authors: Alvise Pellegrini, Ernesto Benini

Abstract:

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. Pareto-optimal points). 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 out.

Keywords: Steam turbine, optimization, genetic algorithms.

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Authors: Saif Ullah, Guan Zailin, Xu Xianhao, He Zongdong, Wang Baoxi

Abstract:

Assembly line balancing problem is aimed to divide the tasks among the stations in assembly lines and optimize some objectives. In assembly lines the workload on stations is different from each other due to different tasks times and the difference in workloads between stations can cause blockage or starvation in some stations in assembly lines. Buffers are used to store the semi-finished parts between the stations and can help to smooth the assembly production. The assembly line balancing and buffer sizing problem can affect the throughput of the assembly lines. Assembly line balancing and buffer sizing problems have been studied separately in literature and due to their collective contribution in throughput rate of assembly lines, balancing and buffer sizing problem are desired to study simultaneously and therefore they are considered concurrently in current research. Current research is aimed to maximize throughput, minimize total size of buffers in assembly line and minimize workload variations in assembly line simultaneously. A multi objective optimization objective is designed which can give better Pareto solutions from the Pareto front and a simple example problem is solved for assembly line balancing and buffer sizing simultaneously. Current research is significant for assembly line balancing research and it can be significant to introduce optimization approaches which can optimize current multi objective problem in future.

Keywords: Assembly line balancing, Buffer sizing, Pareto solutions.

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Authors: Yuekun Chen, Yousef Sardahi, Salam Hajjar, Christopher Greer

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This paper presents a multi-objective optimal design of a cascade control system for an underactuated mechanical system. Cascade control structures usually include two control algorithms (inner and outer). To design such a control system properly, the following conflicting objectives should be considered at the same time: 1) the inner closed-loop control must be faster than the outer one, 2) the inner loop should fast reject any disturbance and prevent it from propagating to the outer loop, 3) the controlled system should be insensitive to measurement noise, and 4) the controlled system should be driven by optimal energy. Such a control problem can be formulated as a multi-objective optimization problem such that the optimal trade-offs among these design goals are found. To authors best knowledge, such a problem has not been studied in multi-objective settings so far. In this work, an underactuated mechanical system consisting of a rotary servo motor and a ball and beam is used for the computer simulations, the setup parameters of the inner and outer control systems are tuned by NSGA-II (Non-dominated Sorting Genetic Algorithm), and the dominancy concept is used to find the optimal design points. The solution of this problem is not a single optimal cascade control, but rather a set of optimal cascade controllers (called Pareto set) which represent the optimal trade-offs among the selected design criteria. The function evaluation of the Pareto set is called the Pareto front. The solution set is introduced to the decision-maker who can choose any point to implement. The simulation results in terms of Pareto front and time responses to external signals show the competing nature among the design objectives. The presented study may become the basis for multi-objective optimal design of multi-loop control systems.

Keywords: Cascade control, multi-loop control systems, multi-objective optimization, optimal control.

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Authors: W. K. Wong, Z. X. Guo, P.Y. Mok

Abstract:

This paper presents a multi-objective order allocation planning problem with the consideration of various real-world production features. A novel hybrid intelligent optimization model, integrating a multi-objective memetic optimization process, a Monte Carlo simulation technique and a heuristic pruning technique, is proposed to handle this problem. Experiments based on industrial data are conducted to validate the proposed model. Results show that (1) the proposed model can effectively solve the investigated problem by providing effective production decision-making solutions, which outperformsan NSGA-II-based optimization process and an industrial method.

Keywords: Multi-objective order allocation planning, Pareto optimization, Memetic algorithm, Mento Carlo simulation

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Authors: Vahid Hajipour, Samira V. Noshafagh, Reza Tavakkoli-Moghaddam

Abstract:

This article proposes a novel Pareto-based multiobjective meta-heuristic algorithm named non-dominated ranking genetic algorithm (NRGA) to solve multi-facility location-allocation problem. In NRGA, a fitness value representing rank is assigned to each individual of the population. Moreover, two features ranked based roulette wheel selection including select the fronts and choose solutions from the fronts, are utilized. The proposed solving methodology is validated using several examples taken from the specialized literature. The performance of our approach shows that NRGA algorithm is able to generate true and well distributed Pareto optimal solutions.

Keywords: Non-dominated ranking genetic algorithm, Pareto solutions, Multi-facility location-allocation problem.

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Authors: Tulika Bhattacharjee, A. K.Chakraborty

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Due to the deregulation of the Electric Supply Industry and the resulting emergence of electricity market, the volumes of power purchases are on the rise all over the world. In a bid to meet the customer-s demand in a reliable and yet economic manner, utilities purchase power from the energy market over and above its own production. This paper aims at developing an optimal power purchase model with two objectives viz economy and environment ,taking various functional operating constraints such as branch flow limits, load bus voltage magnitudes limits, unit capacity constraints and security constraints into consideration.The price of purchased power being an uncertain variable is modeled using fuzzy logic. DEMO (Differential Evolution For Multi-objective Optimization) is used to obtain the pareto-optimal solution set of the multi-objective problem formulated. Fuzzy set theory has been employed to extract the best compromise non-dominated solution. The results obtained on IEEE 30 bus system are presented and compared with that of NSGAII.

Keywords: Deregulation, Differential Evolution, Multi objective Optimization, Pareto Optimal Set, Optimal Power Flow

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Authors: Mohammad Mahdi Paydar, Armin Cheraghalipour, Mostafa Hajiaghaei-Keshteli

Abstract:

Nowadays, in advanced countries, agriculture as one of the most significant sectors of the economy, plays an important role in its political and economic independence. Due to farmers' lack of information about products' demand and lack of proper planning for harvest time, annually the considerable amount of products is corrupted. Besides, in this paper, we attempt to improve these unfavorable conditions via designing an effective supply chain network that tries to minimize total costs of agricultural products along with minimizing shortage in demand points. To validate the proposed model, a stochastic optimization approach by using a branch and bound solver of the LINGO software is utilized. Furthermore, to accumulate the data of parameters, a case study in Mazandaran province placed in the north of Iran has been applied. Finally, using ɛ-constraint approach, a Pareto front is obtained and one of its Pareto solutions as best solution is selected. Then, related results of this solution are explained. Finally, conclusions and suggestions for the future research are presented.

Keywords: Perishable products, stochastic optimization, agricultural supply chain, ɛ-constraint.

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Authors: Jin Xu, Albert Y.S. Lam, Victor O.K. Li

Abstract:

Stock portfolio selection is a classic problem in finance, and it involves deciding how to allocate an institution-s or an individual-s wealth to a number of stocks, with certain investment objectives (return and risk). In this paper, we adopt the classical Markowitz mean-variance model and consider an additional common realistic constraint, namely, the cardinality constraint. Thus, stock portfolio optimization becomes a mixed-integer quadratic programming problem and it is difficult to be solved by exact optimization algorithms. Chemical Reaction Optimization (CRO), which mimics the molecular interactions in a chemical reaction process, is a population-based metaheuristic method. Two different types of CRO, named canonical CRO and Super Molecule-based CRO (S-CRO), are proposed to solve the stock portfolio selection problem. We test both canonical CRO and S-CRO on a benchmark and compare their performance under two criteria: Markowitz efficient frontier (Pareto frontier) and Sharpe ratio. Computational experiments suggest that S-CRO is promising in handling the stock portfolio optimization problem.

Keywords: Stock portfolio selection, Markowitz model, Chemical Reaction Optimization, Sharpe ratio

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Authors: Fatemeh Azimi, Razeeh Sadat Aboutalebi, Amir Abbas Najafi

Abstract:

In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.

Keywords: Evolutionary multi-objective optimization makespan, multi-mode, resource constraint, net present value.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

Abstract:

The necessity of solving multi dimensional complicated scientific problems beside the necessity of several objective functions optimization are the most motive reason of born of artificial intelligence and heuristic methods. In this paper, we introduce a new method for multiobjective optimization based on learning automata. In the proposed method, search space divides into separate hyper-cubes and each cube is considered as an action. After gathering of all objective functions with separate weights, the cumulative function is considered as the fitness function. By the application of all the cubes to the cumulative function, we calculate the amount of amplification of each action and the algorithm continues its way to find the best solutions. In this Method, a lateral memory is used to gather the significant points of each iteration of the algorithm. Finally, by considering the domination factor, pareto front is estimated. Results of several experiments show the effectiveness of this method in comparison with genetic algorithm based method.

Keywords: Function optimization, Multiobjective optimization, Learning automata.

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Authors: C. Chitra, P. Subbaraj

Abstract:

The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated Sorting Genetic Algorithm, Routing, Weighted sum.

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Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

Abstract:

The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: Stratified sampling, Optimum strata boundaries, Optimum sample size, Pareto distribution, Mathematical programming problem, Dynamic programming technique.

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Authors: Gabriel Sitler, Yousef Sardahi, Asad Salem

Abstract:

This paper presents an optimal and robust sliding mode controller (SMC) to regulate the position of the knee joint angle for patients suffering from knee injuries. The controller imitates the role of active orthoses that produce the joint torques required to overcome gravity and loading forces and regain natural human movements. To this end, a mathematical model of the shank, the lower part of the leg, is derived first and then used for the control system design and computer simulations. The design of the controller is carried out in optimal and multi-objective settings. Four objectives are considered: minimization of the control effort and tracking error; and maximization of the control signal smoothness and closed-loop system’s speed of response. Optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained. The results show that there are trade-offs among the design objectives and many optimal solutions from which the decision-maker can choose to implement. Also, computer simulations conducted at different points from the Pareto set and assuming knee squat movement demonstrate competing relationships among the design goals. In addition, the proposed control algorithm shows robustness in tracking a standard gait signal when accounting for uncertainty in the shank’s parameters.

Keywords: Optimal control, multi-objective optimization, sliding mode control, wearable knee exoskeletons.

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Authors: F. Sarhaddi, S. Farahat, M .A. Alavi, F. Sobhnamayan

Abstract:

In this paper, an attempt has been made to obtain nonsensitive solutions in the multi-objective optimization of a photovoltaic/thermal (PV/T) air collector. The selected objective functions are overall energy efficiency and exergy efficiency. Improved thermal, electrical and exergy models are used to calculate the thermal and electrical parameters, overall energy efficiency, exergy components and exergy efficiency of a typical PV/T air collector. A computer simulation program is also developed. The results of numerical simulation are in good agreement with the experimental measurements noted in the previous literature. Finally, multi-objective optimization has been carried out under given climatic, operating and design parameters. The optimized ranges of inlet air velocity, duct depth and the objective functions in optimal Pareto front have been obtained. Furthermore, non-sensitive solutions from energy or exergy point of view in the results of multi-objective optimization have been shown.

Keywords: Solar photovoltaic thermal (PV/T) air collector, Overall energy efficiency, Exergy efficiency, Multi-objectiveoptimization, Sensitivity analysis.

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Authors: Kyoungwoo Park, Ji-Won Han, Hyo-Jae Lim, Byeong-Sam Kim, Juhee Lee

Abstract:

Shape optimization of the airfoil with high aspect ratio of long endurance unmanned aerial vehicle (UAV) is performed by the multi-objective optimization technology coupled with computational fluid dynamics (CFD). For predicting the aerodynamic characteristics around the airfoil the high-fidelity Navier-Stokes solver is employed and SMOGA (Simple Multi-Objective Genetic Algorithm), which is developed by authors, is used for solving the multi-objective optimization problem. To obtain the optimal solutions of the design variable (i.e., sectional airfoil profile, wing taper ratio and sweep) for high performance of UAVs, both the lift and lift-to-drag ratio are maximized whereas the pitching moment should be minimized, simultaneously. It is found that the lift force and lift-to-drag ratio are linearly dependent and a unique and dominant solution are existed. However, a trade-off phenomenon is observed between the lift-to-drag ratio and pitching moment. As the result of optimization, sixty-five (65) non-dominated Pareto individuals at the cutting edge of design spaces that is decided by airfoil shapes can be obtained.

Keywords: Unmanned aerial vehicle (UAV), Airfoil, CFD, Shape optimization, Lift-to-drag ratio.

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