Search results for: pareto optimal solution

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: A. Graa, I. Ziane, F. Benhamida, S. Souag

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This paper presents a comparative analysis study of an efficient and reliable quadratic programming (QP) to solve economic load dispatch (ELD) problem with considering transmission losses in a power system. The proposed QP method takes care of different unit and system constraints to find optimal solution. To validate the effectiveness of the proposed QP solution, simulations have been performed using Algerian test system. Results obtained with the QP method have been compared with other existing relevant approaches available in literatures. Experimental results show a proficiency of the QP method over other existing techniques in terms of robustness and its optimal search.

Keywords: economic dispatch, quadratic programming, Algerian network, dynamic load

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Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

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In recent years, new techniques for solving complex problems in engineering are proposed. One of these techniques is JPSO algorithm. With innovative changes in the nature of the jump algorithm JPSO, it is possible to construct a graph-based solution with a new algorithm called G-JPSO. In this paper, a new algorithm to solve the optimal control problem Fletcher-Powell and optimal control of pumps in water distribution network was evaluated. Optimal control of pumps comprise of optimum timetable operation (status on and off) for each of the pumps at the desired time interval. Maximum number of status on and off for each pumps imposed to the objective function as another constraint. To determine the optimal operation of pumps, a model-based optimization-simulation algorithm was developed based on G-JPSO and JPSO algorithms. The proposed algorithm results were compared well with the ant colony algorithm, genetic and JPSO results. This shows the robustness of proposed algorithm in finding near optimum solutions with reasonable computational cost.

Keywords: G-JPSO, operation, optimization, pumping station, water distribution networks

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Authors: Ali Allahverdi, Harun Aydilek, Asiye Aydilek

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Minimizing the number of tardy jobs is an important factor to consider while making scheduling decisions. This is because on-time shipments are vital for lowering cost and increasing customers’ satisfaction. This paper addresses the single machine scheduling problem with the objective of minimizing the number of tardy jobs. The only known information is the lower and upper bounds for processing times, and deterministic job due dates. A dominance relation is established, and an algorithm is proposed. Several heuristics are generated from the proposed algorithm. Computational analysis indicates that the performance of one of the heuristics is very close to the optimal solution, i.e., on average, less than 1.5 % from the optimal solution.

Keywords: single machine scheduling, number of tardy jobs, heuristi, lower and upper bounds

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Authors: Xinhuang Wu, Yousef Sardahi

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A hybrid and optimal multi-loop control structure combining linear and nonlinear control algorithms are introduced in this paper to regulate the position of a quadcopter unmanned aerial vehicle (UAV) driven by four brushless DC motors. To this end, a nonlinear mathematical model of the UAV is derived and then linearized around one of its operating points. Using the nonlinear version of the model, a sliding mode control is used to derive the control laws of the motor thrust forces required to drive the UAV to a certain position. The linear model is used to design two controllers, XG-controller and YG-controller, responsible for calculating the required roll and pitch to maneuver the vehicle to the desired X and Y position. Three attitude controllers are designed to calculate the desired angular rates of rotors, assuming that the Euler angles are minimal. After that, a many-objective optimization problem involving 20 design parameters and ten objective functions is formulated and solved by HypE (Hypervolume estimation algorithm), one of the widely used many-objective optimization algorithms approaches. Both stability and performance constraints are imposed on the optimization problem. The optimization results in terms of Pareto sets and fronts are obtained and show that some of the design objectives are competing. That is, when one objective goes down, the other goes up. Also, Numerical simulations conducted on the nonlinear UAV model show that the proposed optimization method is quite effective.

Keywords: optimal control, many-objective optimization, sliding mode control, linear control, cascade controllers, UAV, drones

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Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

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To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II

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Authors: Hannah F. Opayinka, Adedayo A. Adepoju

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This study is an extension of a prior study on the modification of the existing m-out-of-n (moon) bootstrap method for heavy-tailed distributions in which modified m-out-of-n (mmoon) was proposed as an alternative method to the existing moon technique. In this study, both moon and mmoon techniques were applied to two real income datasets which followed Lognormal and Pareto distributions respectively with finite variances. The performances of these two techniques were compared using Standard Error (SE) and Root Mean Square Error (RMSE). The findings showed that mmoon outperformed moon bootstrap in terms of smaller SEs and RMSEs for all the sample sizes considered in the two datasets.

Keywords: Bootstrap, income data, lognormal distribution, Pareto distribution

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Authors: Silas A. Ihedioha

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In this work; it is considered that an investor’s portfolio is comprised of two assets; a risky stock which price process is driven by the geometric Brownian motion and a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aimed at the optimization of the investor’s expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation HJB) was obtained from which an ordinary differential equation (ODE) obtained via elimination of variables. The solution to the ODE gave the closed form solution of the investor’s problem. It was found the optimal investment in the risky asset is horizon dependent and a ratio of the total amount available for investment and the relative risk aversion coefficient.

Keywords: optimal, investment, Ornstein-Uhlenbeck, utility maximization, stochastic interest rate, maximum principle

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Onur Kaya, Halit Bayer

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Global grocery and supermarket sales are among the largest markets in the world and perishable products such as fresh produce, dairy and meat constitute the biggest section of these markets. Due to their deterioration over time, the demand for these products depends highly on their freshness. They become totally obsolete after a certain amount of time causing a high amount of wastage and decreases in grocery profits. In addition, customers are asking for higher product variety in perishable product categories, leading to less predictable demand per product and to more out-dating. Effective management of these perishable products is an important issue since it is observed that billions of dollars’ worth of food is expired and wasted every month. We consider coordinated inventory and pricing decisions for perishable products with a time and price dependent random demand function. We use stochastic dynamic programming to model this system for both periodically-reviewed and continuously-reviewed inventory systems and prove certain structural characteristics of the optimal solution. We prove that the optimal ordering decision scenario has a monotone structure and the optimal price value decreases by time. However, the optimal price changes in a non-monotonic structure with respect to inventory size. We also analyze the effect of 1 different parameters on the optimal solution through numerical experiments. In addition, we analyze simple-to-implement heuristics, investigate their effectiveness and extract managerial insights. This study gives valuable insights about the management of perishable products in order to decrease wastage and increase profits.

Keywords: age-dependent demand, dynamic programming, perishable inventory, pricing

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

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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: Rim Chang Hyon, Song Hak Jin, Song Kwang Hyok, Jong Ki Hun

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The calibration of the articulated arm coordinate measuring machine (AACMM) is key to improving calibration accuracy and saving calibration time. To reduce the time consumed for calibration, we should choose the proper calibration gauges and develop a reasonable calibration method. In addition, we should get the exact optimal solution by accurately removing the rough errors within the experimental data. In this paper, we present a calibration method of the portable coordinate measuring arm (PCMA) using the 1.2m long bar guage with cone-holes. First, we determine the locations of the bar gauge and establish an optimal objective function for identifying the structural parameter errors. Next, we make a mathematical model of the calibration algorithm and present a new mathematical method to remove the rough errors within calibration data. Finally, we find the optimal solution to identify the kinematic parameter errors by using Levenberg-Marquardt algorithm. The experimental results show that our calibration method is very effective in saving the calibration time and improving the calibration accuracy.

Keywords: AACMM, kinematic model, parameter identify, measurement accuracy, calibration

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Authors: Tamas Hartvanyi, Zoltan Andras Nagy, Miklos Szabo

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The dynamic and static capacity are two opposing aspect of warehouse design. Static capacity optimization aims to maximize the space-usage for goods storing, while dynamic capacity needs more free place to handling them. They are opposing by the building structure and the area utilization. According to Pareto principle: the 80% of the goods are the 20% of the variety. From the origin of this statement, it worth to store the big amount of same products by fulfill the space with minimal corridors, meanwhile the rest 20% of goods have the 80% variety of the whole range, so there is more important to be fast-reachable instead of the space utilizing, what makes the space fulfillment numbers worse. The warehouse design decisions made in present practice by intuitive and empiric impressions, the planning method is formed to one selected technology, making this way the structure of the warehouse homogeny. Of course the result can’t be optimal for the inhomogeneous demands. A new innovative model based on our research will be introduced in this paper to describe the technic capacities, what makes possible to define optimal cluster of technology. It is able to optimize the space fulfillment and the dynamic operation together with this cluster application.

Keywords: warehouse, warehouse capacity, warehouse design method, warehouse optimization

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Authors: Jiaqi Huang, Lu Jin

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Pervious concrete features with high water permeability rate. However, due to the lack of fine aggregates, the compressive strength is usually lower than other conventional concrete products. Optimization of pervious concrete mix design has long been recognized as an effective mechanism to achieve high compressive strength while maintaining desired permeability rate. In this paper, a Gibbs Sampling based algorithm is proposed to approximate the optimal mix design to achieve a high compressive strength of pervious concrete. We prove that the proposed algorithm efficiently converges to the set of global optimal solutions. The convergence rate and accuracy depend on a control parameter employed in the proposed algorithm. The simulation results show that, by using the proposed approach, the system converges to the optimal solution quickly and the derived optimal mix design achieves the maximum compressive strength while maintaining the desired permeability rate.

Keywords: convergence, Gibbs Sampling, high compressive strength, optimal mix design, pervious concrete

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Authors: Luis Javier Serrano Tamayo

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This research on technology makes a first approach to the selection of an amphibious landing ship with strategic capabilities, through the implementation of a multi-criteria model using Analytical Hierarchical Process (AHP), in which a significant group of alternatives of latest technology has been considered. The variables were grouped at different levels to match design and performance characteristics, which affect the lifecycle as well as the acquisition, maintenance and operational costs. The model yielded an overall measure of effectiveness and an overall measure of cost of each kind of ship that was compared each other inside the model and showed in a Pareto chart. The modeling was developed using the Expert Choice software, based on AHP method.

Keywords: analytic hierarchy process, multi-criteria decision-making, Pareto analysis, Colombian Marine Corps, projection operations, expert choice, amphibious landing ship

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, implementation, MATLAB

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Authors: A. Gopala Krishna, M. Lakshmi Chaitanya, V. Kalyana Manohar

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In the existent analysis, laser micro machining (LMM) of Silicon carbide (SiCp) reinforced Aluminum 7075 Metal Matrix Composite (Al7075/SiCp MMC) was studied. While machining, Because of the intense heat generated, A layer gets formed on the work piece surface which is called recast layer and this layer is detrimental to the surface quality of the component. The recast layer needs to be as small as possible for precise applications. Therefore, The height of recast layer and the depth of groove which are conflicting in nature were considered as the significant manufacturing criteria, Which determines the pursuit of a machining process obtained in LMM of Al7075/10%SiCp composite. The present work formulates the depth of groove and height of recast layer in relation to the machining parameters using the Response Surface Methodology (RSM) and correspondingly, The formulated mathematical models were put to use for optimization. Since the effect of machining parameters on the depth of groove and height of recast layer was contradictory, The problem was explicated as a multi objective optimization problem. Moreover, An evolutionary Non-dominated sorting genetic algorithm (NSGA-II) was employed to optimize the model established by RSM. Subsequently this algorithm was also adapted to achieve the Pareto optimal set of solutions that provide a detailed illustration for making the optimal solutions. Eventually experiments were conducted to affirm the results obtained from RSM and NSGA-II.

Keywords: Laser Micro Machining (LMM), depth of groove, Height of recast layer, Response Surface Methodology (RSM), non-dominated sorting genetic algorithm

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Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

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Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

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Authors: Zhuo Feng, Ying Gao

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Public-private partnership (PPP), as an innovative way to provide infrastructures by the private sector, is being widely used throughout the world. Compared with the traditional mode, PPP emerges largely for merits of relieving public budget constraint and improving infrastructure supply efficiency by involving private funds. However, PPP projects are characterized by large scale, high investment, long payback period, and long concession period. These characteristics make PPP projects full of risks. One of the most important risks faced by the private sector is demand risk because many factors affect the real demand. If the real demand is far lower than the forecasting demand, the private sector will be got into big trouble because operating revenue is the main means for the private sector to recoup the investment and obtain profit. Therefore, it is important to study how the government compensates the private sector when the demand risk occurs in order to achieve Pareto-improvement. This research focuses on price compensation mechanism, an ex-post compensation mechanism, and analyzes, by mathematical modeling, the impact of price compensation mechanism on payoff of the private sector and consumer surplus for PPP toll road projects. This research first investigates whether or not price compensation mechanisms can obtain Pareto-improvement and, if so, then explores boundary conditions for this mechanism. The research results show that price compensation mechanism can realize Pareto-improvement under certain conditions. Especially, to make the price compensation mechanism accomplish Pareto-improvement, renegotiation costs of the government and the private sector should be lower than a certain threshold which is determined by marginal operating cost and distortionary cost of the tax. In addition, the compensation percentage should match with the price cut of the private investor when demand drops. This research aims to provide theoretical support for the government when determining compensation scope under the price compensation mechanism. Moreover, some policy implications can also be drawn from the analysis for better risk-sharing and sustainability of PPP projects.

Keywords: infrastructure, price compensation mechanism, public-private partnership, renegotiation

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Authors: Zongjie Wang, Zhizhong Guo

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While the regular optimal power flow model focuses on a single time scan, the optimization of power systems is typically intended for a time duration with respect to a desired objective function. In this paper, a temporal optimal power flow model for a time period is proposed. To reduce the computation burden needed for calculating temporal optimal power flow, a characteristic optimal power flow model is proposed, which employs different characteristic load patterns to represent the objective function and security constraints. A numerical method based on the interior point method is also proposed for solving the characteristic optimal power flow model. Both the temporal optimal power flow model and characteristic optimal power flow model can improve the systems’ desired objective function for the entire time period. Numerical studies are conducted on the IEEE 14 and 118-bus test systems to demonstrate the effectiveness of the proposed characteristic optimal power flow model.

Keywords: optimal power flow, time period, security, economy

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Authors: Violeta Damjanovic-Behrendt

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This paper presents an approach for optimal cyber security decisions to protect instances of a federated Internet of Things (IoT) platform in the cloud. The presented solution implements the repeated Stackelberg Security Game (SSG) and a model called Stochastic Human behaviour model with AttRactiveness and Probability weighting (SHARP). SHARP employs the Subjective Utility Quantal Response (SUQR) for formulating a subjective utility function, which is based on the evaluations of alternative solutions during decision-making. We augment the repeated SSG (including SHARP and SUQR) with a reinforced learning algorithm called Naïve Q-Learning. Naïve Q-Learning belongs to the category of active and model-free Machine Learning (ML) techniques in which the agent (either the defender or the attacker) attempts to find an optimal security solution. In this way, we combine GT and ML algorithms for discovering optimal cyber security policies. The proposed security optimization components will be validated in a collaborative cloud platform that is based on the Industrial Internet Reference Architecture (IIRA) and its recently published security model.

Keywords: security, internet of things, cloud computing, stackelberg game, machine learning, naive q-learning

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Authors: Taejung Lho, Jonghwan Lee

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Most of the photovoltaic (PV) module manufacturers have recently interested in reducing the manufacturing cost. One of available solution is the use of the thin photovoltaic cell because of reducing of raw material cost. Thin PV cells, however, are damaged large deformation which causes possible microcracks inside PV cell, leading to failure problem. In this paper, deformation characteristics by heat conduction in soldering process of PV cells are analyzed through ANSYS software tool. They have been tested for different PV cell thickness and soldering temperature profile. Accordingly optimal soldering process to minimize the deformation of PV cell has been suggested.

Keywords: photovoltaic (PV) cell, infrared(IR) lamp soldering, optimal soldering temperature profile, deformation, temperature distribution, 3D scanner, ANSYS

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Authors: Gyeongbeom Yi

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The purpose of this study is to introduce the analytic solution for determining the optimal capacity (lot-size) of a multiproduct, multistage production and inventory system to meet the finished product demand. Reasonable decision-making about the capacity of processes and storage units is an important subject for industry. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ/EPQ (Economic Order Quantity/Economic Production Quantity) model, incorporated with practical experience. However, the unrealistic material flow assumption of the EOQ/EPQ model is not suitable for chemical plant design with highly interlinked processes and storage units. This study overcomes the limitation of the classical lot sizing method developed on the basis of the single product and single stage assumption. The superstructure of the plant considered consists of a network of serially and/or parallelly interlinked processes and storage units. The processes involve chemical reactions with multiple feedstock materials and multiple products as well as mixing, splitting or transportation of materials. The objective function for optimization is minimizing the total cost composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A novel production and inventory analysis method, PSW (Periodic Square Wave) model, is applied. The advantage of the PSW model comes from the fact that the model provides a set of simple analytic solutions in spite of a realistic description of the material flow between processes and storage units. The resulting simple analytic solution can greatly enhance the proper and quick investment decision for plant design and operation problem confronted in diverse economic situations.

Keywords: analytic solution, optimal design, process-storage network

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Authors: Sarabjeet Singh Sidhu, Ajay Batish, Sanjeev Kumar

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This paper reports the optimal process conditions for machining of three different types of metal matrix composites (MMCs): 65vol%SiC/A356.2; 10vol%SiC-5vol%quartz/Al and 30vol%SiC/A359 using PMEDM process. Metal removal rate (MRR), tool wear rate (TWR), surface roughness (SR) and surface integrity (SI) were evaluated after each trial and contributing process parameters were identified. The four responses were then collectively optimized using the technique for order preference by similarity to ideal solution (TOPSIS) and optimal process conditions were identified for each type of MMCS. The density of reinforced particles shields the matrix material from spark energy hence the high MRR and SR was observed with lowest reinforced particle. TWR was highest with Cu-Gr electrode due to disintegration of the weakly bonded particles in the composite electrode. Each workpiece was examined for surface integrity and ranked as per severity of surface defects observed and their rankings were used for arriving at the most optimal process settings for each workpiece.

Keywords: metal matrix composites (MMCS), metal removal rate (MRR), surface roughness (SR), surface integrity (SI), tool wear rate (TWR), technique for order preference by similarity to ideal solution (TOPSIS)

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Shahul Hamid Khan, S. Santhosh, Abhinav Kumar Sharma

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Environmental performance along with social performance is becoming vital factors for industries to achieve global standards. With a good environmental policy global industries are differentiating them from their competitors. This paper concentrates on multi stage, multi product and multi period manufacturing network. Bi-objective mathematical models for total cost and total emission for the entire forward supply chain are considered. Here five different problems are considered by varying the number of suppliers, manufacturers, and environmental levels, for illustrating the taken mathematical model. GA, and Random search are used for finding the optimal solution. The input parameters of the optimal solution are used to find the tradeoff between the initial investment by the industry and the long term benefit of the environment.

Keywords: closed loop supply chain, genetic algorithm, random search, green supply chain

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

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The Markov Decision Process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, dynamic programming, Monte Carlo simulation, periodic replacement, Weibull distribution

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Authors: Ehsan Motamedian

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Finding all optimal flux distributions of a metabolic model is an important challenge in systems biology. In this paper, a new algorithm is introduced to identify all alternate optimal solutions of a large scale metabolic network. The algorithm reduces the model to decrease computations for finding optimal solutions. The algorithm was implemented on the Escherichia coli metabolic model to find all optimal solutions for lactate and acetate production. There were more optimal flux distributions when acetate production was optimized. The model was reduced from 1076 to 80 variable fluxes for lactate while it was reduced to 91 variable fluxes for acetate. These 11 more variable fluxes resulted in about three times more optimal flux distributions. Variable fluxes were from 12 various metabolic pathways and most of them belonged to nucleotide salvage and extra cellular transport pathways.

Keywords: flux variability, metabolic network, mixed-integer linear programming, multiple optimal solutions

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Authors: Ahmad Termimi Ab Ghani, Kojiro Higuchi

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In this paper, we present some results of simultaneous infinite games. We mainly work with generalized reachability games and Buechi games. These games are two-player concurrent games where each player chooses simultaneously their moves at each step. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (ε-optimal) strategy exists for both players depending on the type of games. We first show the determinacy (optimal value) and optimal (ε-optimal) strategies in generalized reachability games. We provide a simple expressions of value of this game and prove the existence of memoryless randomized ε-optimal strategy for Player I in any generalized reachability games. We then observe games with more complex objectives, games with Buechi objectives. We present how to compute an ε-optimal strategies and approximate a value of game in some way. Specifically, the results of generalized reachability games are used to show the value of Buechi games can be approximated as values of some generalized reachability games.

Keywords: optimal Strategies, generalized reachability games, Buechi games

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Authors: Abdel-Aziz M. Mohamed

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This paper presents a state-of-the-art survey of the operations research models developed for internal audit planning. Two alternative approaches have been followed in the literature for audit planning: (1) identifying the optimal audit frequency; and (2) determining the optimal audit resource allocation. The first approach identifies the elapsed time between two successive audits, which can be presented as the optimal number of audits in a given planning horizon, or the optimal number of transactions after which an audit should be performed. It also includes the optimal audit schedule. The second approach determines the optimal allocation of audit frequency among all auditable units in the firm. In our review, we discuss both the deterministic and probabilistic models developed for audit planning. In addition, game theory models are reviewed to find the optimal auditing strategy based on the interactions between the auditors and the clients.

Keywords: operations research applications, audit frequency, audit-staff scheduling, audit planning

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