Chosen Objective Function Research Articles

Structural topology optimization under limit analysis

The objective of this paper is to look for structural designs arising from topological optimization procedures that aim at maximizing the loading capacity regarding incipient plastic collapse. The mechanical problem is described by limit analysis (LA) formulation that allows a direct determination of the load that produces the plastic collapse phenomenon without information about the load history. In case of proportional loading processes, LA consists of computing a critical load factor such that the structure undergoes plastic collapse when the reference load is amplified by this factor. In this case, LA can be cast mathematically as a convex constrained optimization problem. The design optimization is formally stated as the maximization of the collapse load factor subject to a fixed quantity of available material. The design is controlled by solid isotropic microstructure with penalization (SIMP) technique. In the particular case of the chosen objective function, the solution of the adjoint problem in sensitivity analysis coincides with the Newton–Raphson update vector obtained at the convergence of the procedure developed to solve the LA optimization problem, fact that reduces the numerical cost of gradient calculations. In order to keep the implementation straightforward, the optimality conditions are solved by a classical heuristic element-by-element density updating algorithm, well known in the literature. The set of tested examples brings encouraging results with structures being stressed to ultimate bearing states. Implementation was kept as simple as possible, leaving the field open to further investigations. Numerical tests show that, despite having similar geometries, plastic collapse factor obtained with compliance optimal designs are lower than those obtained with present formulation.

Applying Operations Research to Scheduling Work Cells in a Manufacturing Environment

Constant competition in the manufacturing sector forces companies to continually decrease their costs while satisfying customer needs. These companies could be more efficient and achieve better results if they automated many of the tasks that they now schedule manually. In this paper, we describe how one department of Johnson Electric, a leading manufacturer of electromechanical components, automated and improved its scheduling process through the application of operations research. We created an easy-to-use Excel Solver-based tool for scheduling self-directed work cells. This tool does not require a user to have any knowledge of mathematical programming, because it automatically adds the objective function and constraints in the background. Our results show that the time required to create schedules decreases drastically and that the quality of the schedules improves significantly depending on the chosen objective function. We illustrate how fundamental knowledge of single-machine scheduling can add significant practical value in manufacturing. Moreover, our work shows that advances in computer interface development tools (e.g., Visual Basic for Applications) are making it possible to efficiently implement operations research concepts.

Discretisation and duality of optimal Skorokhod embedding problems

We prove a strong duality result for a linear programming problem which has the interpretation of being a discretised optimal Skorokhod embedding problem, and we recover this continuous time problem as a limit of the discrete problems. With the discrete setup we show that for a suitably chosen objective function, the optimiser takes the form of a hitting time for a random walk. In the limiting problem we then reprove the existence of the Root, Rost, and cave embedding solutions of the Skorokhod embedding problem.The main strength of this approach is that we can derive properties of the discrete problem more easily than in continuous time, and then prove that these properties hold in the limit. For example, a consequence of the strong duality result is that dual optimisers exist, and our limiting arguments can be used to derive properties of the continuous time dual functions. These arguments are applied in Cox and Kinsley (2017), where the existence of dual solutions is required to prove characterisation results for optimal barriers in a financial application.

Metropolis\u2013Hastings Monte Carlo Method for Neutron Emissivity Tomographic Inversion in Tokamak Plasma

The article presents a new approach to plasma neutron emissivity reconstruction based on the Metropolis–Hastings Monte Carlo algorithm. The algorithm is based on a biased random walk. A dedicated computer code generates pseudo-random samples within the domain that contains the solution. The properly chosen objective function ensures convergence to the desired solution. The method allows to overcome the problem of trapping in local minima by accepting, with some finite probability, changes in the direction opposite to that indicated by the objective function. The developed method was tested using a synthetic data set. The results show that the method provides reliable reconstructions and thus can be used as an alternative or complementary method to the commonly applied ones. The method capabilities were also tested against noise present in the line-integrated projections.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers.

Numerical modeling of airflow over column of vehicles using Ansys® package

Growing needs in transportation determinate systems development which improve efficiency of travel and reduce harmful influence to environment. Computational Fluid Dynamic (CFD) uses numerical analysis to find optimal solutions in terms of chosen objective function. Time save and reduce costs for experiments on prototypes are one of the advantages of this method. The aim of this research is to analyze airflow around different motor vehicles which are moving together in the same direction. To reduce fuel consumption and, at the same time, decrease negative influence to environment, the primary target was reducing total drag force during a ride. The vehicles were set in a column - one after another. In this work considered three types of vehicles: Car, Van and a Truck. Presented vehicles were organized into appropriate groups, creating different configuration. Additional parameter in simulation was distance between vehicles. Simulations of singular vehicles were also done. It allows to evaluate influence of moving vehicles in a column for generated drag force. Described traffic situation were modeled and numerically calculated using ANSYS® package. The purpose of this work was to assess the impact of the distance between vehicles, in a given configuration, for generated drag force.

Multicarrier energy systems: Optimization model based on real data and application to a case study

Multicarrier energy systems are increasingly used for a number of applications, among which the supply of electricity, heating, and cooling in buildings. The possibility of switching between different energy sources is a crucial advantage for the optimal fulfillment of the energy demand. The flexibility of these systems can benefit from the integration with smart grids, which have strong variations in time during their operation. The energy price is the parameter that is usually considered, but also the primary energy factor and the greenhouse gases emissions need to be accounted. This paper presents an application of an operational optimization method for a multicarrier energy system, based on real data-driven model and applied to different countries. The generation plant of a hospital is considered as case study, coping with multiple energy needs by relying on different conversion technologies. The optimal operation of the system shows a wide range of variability, depending on the chosen objective function, the hour of the day, the season, and the country. The results are affected mostly by the energy mix of the electricity supplied from the power grid, which has a direct influence on the primary energy consumption and the greenhouse gases emissions and an indirect influence on the electricity prices.

Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data

Recent work in CT image reconstruction has seen increasing interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed heuristic which provides an automatic procedure to ‘superiorize’ an iterative image reconstruction algorithm with respect to a chosen objective function, such as TV. Under certain conditions, the superiorized algorithm is guaranteed to find a solution that is as satisfactory as any found by the original algorithm with respect to satisfying the constraints of the problem; this solution is also expected to be superior with respect to the chosen objective.Most work on superiorization has used reconstruction algorithms which assume a linear measurement model, which in the case of CT corresponds to data generated from a monoenergetic x-ray beam. Many CT systems generate x-rays from a polyenergetic spectrum, however, in which the measured data represent an integral of object attenuation over all energies in the spectrum. This inconsistency with the linear model produces the well-known beam hardening artifacts, which impair analysis of CT images.In this work we superiorize an iterative algorithm for reconstruction from polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply the superiorized algorithm in numerical phantom experiments modeling both sparse-view and limited-angle scenarios. In our experiments, the superiorized algorithm successfully finds solutions which are as constraints-compatible as those found by the original algorithm, with significantly reduced TV and ATV values. The superiorized algorithm thus produces images with greatly reduced sparse-view and limited angle artifacts, which are also largely free of the beam hardening artifacts that would be present if a superiorized version of a monoenergetic algorithm were used.

Design of Zirconia-Aluminum Functionally Graded Material for Buckling and Vibration Characteristics Enhancement of Beam/Column Structure

This paper presents a design method to optimize the material distribution of zirconia/aluminum-functionally graded material with respect to some buckling and vibration properties. The distribution of volume fractions of the FGM constituents is defined through the beam or column length by a trigonometric law. The finite element method is used for the buckling and vibration analysis, and a genetic algorithm is utilized for optimization of the chosen objective function. The efficiency of the method is demonstrated by two design problems. In the first design problem, FGM is used to maximize the buckling crical load to weight ratio. In the second design problem, the kinetic energy of a vibrating FGM beam is minimized at a specific excitation frequency. These design problems show that material tailoring of beam/column structures using FGM can result in substantial improvements of their buckling and vibration characteristics.

Non-Iterative Enhanced SDP Relaxations for Optimal Scheduling of Distributed Energy Storage in Distribution Systems

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second-order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter semidefinite programming (SDP) relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder.

Design of in-plane functionally graded material plates for improved vibration characteristics

A method for improving the vibration characteristics of plate structures is proposed. This method uses functionally graded material (FGM) instead of isotropic material to construct the plates. The volume fraction of each material constituent is defined in the plane of the plate by a 2D trigonometric law, while the material properties through the thickness are assumed constant. The finite element method is used for modal and harmonic analysis, and a genetic algorithm is utilized for optimization of the chosen objective function. The efficacy of the method is demonstrated by two design problems. In the first design problem, FGM is used to maximize the fundamental frequencies of plates with different boundary conditions. In the second design problem, the kinetic energy of a vibrating FGM plate is minimized at a specific excitation frequency. These example design problems show that material tailoring of plate structures using FGM can result in substantial improvements of their vibration characteristics. The results can be used to guide the practical design of FGM plates to enhance their dynamic properties.

Optimal diameter of nozzles of synthetic jet actuators based on electrodynamic transducers

The formulation of the optimization problem was based on the maximization of an objective function, which was alternatively selected from the four integral quantities: volumetric flux, momentum flux, kinetic energy flux, and energetic efficiency. With two potential applications intended (active flow control and heat transfer enhancement), the most appropriate objective function is suggested to be the momentum flux.In the experimental part of this study, an axisymmetric actuator was investigated in several variants. Two transducers (loudspeakers) and nine nozzle diameters were tested for ten supplied power levels. The working fluid was air, and the driving frequency was adjusted near the first resonance of the actuator. The velocity profiles at the actuator nozzle exit were measured by a hot-wire anemometer.In the theoretical part of this study, a lumped element model was used with an assumption of an incompressible working fluid. The optimal diameter of the nozzle was found and its dependence on the chosen objective function was revealed. Moreover, the theoretical results were generalized into explicit relationships between the dimensionless optimal nozzle diameter and the loudspeaker parameters. A maximum overall energetic efficiency of 15% was achieved. Outstanding agreement between the theoretical and experimental results was concluded.

Development of Pareto topology optimization considering thermal loads

In this research, we developed a level-set based topology optimization with a topological derivative formulation considering thermal load. Thermo-elasticity equations were utilized to obtain the sensitivity of the objective function after inserting a small hole in the domain. Total strain energy and the maximum stress in the design domain were taken as the objective functions. After taking the thermal loading effect into account, the total strain energy density function became a nonhomogeneous function of the strain. In addition, temperature variation changed Hooke’s law from a linear homogeneous to a linear nonhomogeneous expression including a zero order term. We derived the sensitivity value of the selected objective functions with respect to a perturbation in the structural domain under mechanical and thermal loads while considering these changes in the governing equations. We performed several numerical optimization problems to demonstrate the validity of the present level-set based Pareto topology optimization. Two types of examples (compliance and stress minimization) were solved based on the chosen objective functions. Furthermore, in the stress minimization examples, the derived formula was extended to consider thermal effects in the failure theories for pressure independent and dependent materials.

Integration of Hydrogen Systems in Petroleum Refinery

Considering the importance of hydrogen in crude oil refining, it is necessary to ensure its most efficient use to satisfy refinery hydrogen requirements. Effective hydrogen management provides maximum utilization of hydrogen. The mass balance of streams containing hydrogen plays a key role in addressing the hydrogen-network optimization problem. The purpose of this work was to analyze the refinery hydrogen network, composed of hydrogen sources and sinks. Mass integration principles and techniques have been applied in the optimization of the refinery hydrogen network. The methodology of hydrogen network integration is presented in a case study of a local petroleum refinery. The main objectives are to provide different solutions for reducing the amount of hydrogen not properly used in the local refinery and which is mostly sent to the fuel system, as well as the operating costs. Hydrogen pinch analysis is applied for targeting the minimum hydrogen consumption of the hydrogen system. A superstructure- based mathematical model of the hydrogen network is developed to minimize the total operating costs. The non-linear programming optimization problem is solved by using optimization software GAMS. An additional hydrogen purification unit is introduced in the existing hydrogen network and the effect on the overall network is investigated. Network design with two hydrogen purification units has proved to be an optimal solution, with respect to the chosen objective function. These analyses and their results can assist the refinery to reduce and improve the efficiency of hydrogen management. The analyses covered only the existing equipment without additional investment.

Adaptive Firefly Algorithm based OPF for AC/DC Systems

Optimal Power Flow (OPF) is an important operational and planning problem in minimizing the chosen objective functions of the power systems. The recent developments in power electronics have enabled introduction of dc links in the AC power systems with a view of making the operation more flexible, secure and economical. This paper formulates a new OPF to embrace dc link equations and presents a heuristic optimization technique, inspired by the behavior of fireflies, for solving the problem. The solution process involves AC/DC power flow and uses a self adaptive technique so as to avoid landing at the suboptimal solutions. It presents simulation results of IEEE test systems with a view of demonstrating its effectiveness.

Convex Optimization for DES Planning and Operation in Radial Distribution Systems With High Penetration of Photovoltaic Resources

In this paper, distributed energy storage (DES) devices, like batteries and ultra-capacitors, are used to alleviate detrimental impacts of high penetration photovoltaic (PV) resources on distribution systems. The impacts are studied at mainly two time resolutions—one minute and one hour. To determine accurately the size of the required DES for the purpose of mitigating the impacts of large-scale distributed PV, sizing procedures based on OpenDSS are proposed. After determining the total size of the required DES, optimization techniques can be used to choose the optimal locations for the DES along the feeder, which is a continuous optimization problem taking into account equality constraints of the AC power flow. The continuity of the problem and the radial network structure make it possible to apply a convex optimization technique called second order cone programming (SOCP) relaxation to obtain the globally optimal solution and avoid the problem of NP-hardness. The exactness of the introduced SOCP relaxation is sensitive to the chosen objective function and additional quadratic equalities. The necessary and sufficient condition of exactness for the SOCP relaxation of the DES optimal allocation and operation in radial distribution systems is studied. The proposed methods are applied to an actual feeder in the southwestern US with high penetration of PV using actual measured data. The simulation results demonstrate the efficacy of the proposed approaches.

Design of in-plane functionally graded material plates for optimal vibration performance

A method for improving the vibration characteristics of plate structures is proposed. This method uses functionally graded material (FGM) instead of isotropic material in constructing the plates. The distribution of volume fractions of the FGM constituent is defined in the in-plane directions by a trigonometric law. The finite element method is used for the modal and harmonic analysis of plates, and a genetic algorithm is utilized for optimization of the chosen objective function. The efficacy of the method is demonstrated by two design problems. In the first design problem, FGM is used to maximize the fundamental frequencies of plates with different boundary conditions. In the second design problem, the kinetic energy of a vibrating FGM plate is minimized at a specific excitation frequency. These example design problems show that material tailoring of plate structures using FGM can result in substantial improvements of their vibration characteristics. The results can be used to guide the practical design of FGM plates to enhance their dynamic properties.

A perspective on the density matrix purification for linear scaling electronic structure calculations

Density matrix purification is a linear scaling algorithm to solve the self‐consistent field (SCF) electronic structure problem. A brief review is made of the two usages of the purification method in SCF calculations, namely in direct energy minimization and for iterative calculation of density matrix from Hamiltonian. Density matrix purification can be viewed as a minimization algorithm of the particularly defined objective function such as , and hence, this objective function plays a key role in the developments of purification polynomials. Indeed, in this perspective, we show that a carefully chosen objective function can lead to significantly improved algorithms and numerical results. © 2015 Wiley Periodicals, Inc.

Application of Parallel Flow Line Scheduling Using GA

— A metaheuristic is an iterative process that guides and updates the operations of subordinate heuristics to efficiently produce better quality solutions. It is used in cases where exact methods are not sufficient to provide a solution so that the method of manipulation of a single solution or a collection of solutions at each iteration is deployed. This paper addresses the application of generic algorithm for a parallel machine flow line scheduling problem using the algorithm proposed for minimizing the makespan. Makespan is an important requirement to achieve effective production from process planning. As the problem chosen is NP-hard, genetic algorithm is adopted as it is one of the proven methods to search for a feasible optimal solution to the chosen objective function. The methodology is based on creating a group of random solutions for the randomly generated samples and applying the operators of cross over and mutation to improve the solutions till an acceptable fitness level is reached. The computational experiments deployed indicate that the proposed methodology and procedures are helping to arriving at better solutions faster.Keywords: Scheduling-Parallel machine – Flow shop scheduling– GA.

Regression analysis of a curved vane demister with Taguchi based optimization

Regression analysis was carried out using least squares method to develop correlations for the objective functions: friction factor (f) and droplet separation efficiency (η) of curved vane demisters used in seawater desalination. A Taguchi coupled CFD analysis performed earlier by the authors, to select the optimal geometrical parameters for a curved vane demister, was the baseline for this work. Responses of the chosen objective functions from the CFD analysis were fed to the statistical tool Minitab. ANOVA estimates were carried out for identifying the significant factors that control f, η and ranked. Linear model analysis was carried out for the signal-to-noise (S/N) ratios with ‘smaller the better’ approach for f and ‘larger the better’ approach for η. The R-square value for the correlation developed for f and η was found to be 98% and 87.9% respectively. The ranking of the parameters correlates very well with the numerical estimates. The factors like ‘vane pitch’ and ‘hook height above the vane’ were identified to have most significant influence when compared to other parameters.