Maximum Objective Function Research Articles

Optimal Design and Analysis of a Novel Reluctance Axial Flux Magnetic Gear

This paper proposes modelling and optimization of a new reluctance axial flux magnetic gear (RAMG) with stationary outer rotor and advantages of lower permanent magnet usage. Due to the less use of the PMs, this structure has a higher economic interest, more reliability, and very simple and robust structure than its conventional ones. Gear ratio and operating principles are extracted and verificated using 3-D finite element method (FEM) simulations. Finally, a parametric optimization is done based on effective dimensions in design procedure with maximum torque density objective function. The magnetic flux distributions of optimized RAMG are calculated by 3-D FEM, as well as static and dynamic magnetic torques are derived correspondingly.

Оптимизация в конечномерном евклидовом пространстве

In this paper, optimization models in Euclidean space are divided into four complexity classes. Ef-fective algorithms have been developed to solve the problems of the first two classes of complexity. These are the primal-dual interior-point methods. Discrete and combinatorial optimization problems of the third complexity class are recommended to be converted to the fourth complexity class with continuous change of variables. Effective algorithms have not been developed for problems of the third and fourth complexity classes, with the exception of a narrow class of problems that are unimodal. The general optimization problem is formulated as a minimum (maximum) objective function in the presence of constraints. The complexity of the problem depends on the structure of the objective function and its feasible region. If the functions that determine the optimization model are quadratic or polynomial, then semidefinite programming can be used to obtain estimates of so-lutions in such problems. Effective methods have been developed for semidefinite optimization problems. Sometimes it’s enough to develop an algorithm without building a mathematical model. We see such an example when sorting an array of numbers. Effective algorithms have been devel-oped to solve this problem. In the work for sorting problems, an optimization model is constructed, and it coincides with the model of the assignment problem. It follows from this that the sorting problem is unimodal. Effective algorithms have not been developed to solve multimodal problems. The paper proposes a simple and effective algorithm for the optimal allocation of resources in mul-tiprocessor systems. This problem is multimodal. In the general case, for solving multimodal prob-lems, a method of exact quadratic regularization is proposed. This method has proven its compara-tive effectiveness in solving many test problems of various dimensions. Keywords: Euclidean space, optimization, unimodal problems, multimodal problems, complexity classes, numerical methods.

Maximizing technical and economical benefits of distribution systems by optimal allocation and hourly scheduling of capacitors and distributed energy resources

ABSTRACTTechnical and economic benefits of installing distributed energy resources (DERs) and capacitor banks (C-Bs) can be maximized by optimal allocation of them. The aim of this paper is to enrich technical benefits such as voltage profile, system losses and reliability and also to increase economic benefits by maximizing the savings of energy losses and decreasing the cost of energy not supplied. The work in this paper is divided into three stages; (i) optimal placement of DERs, (ii) optimal placement of C-Bs and (iii) optimal placement of C-Bs with the existence of installed optimal DERs. The daily load variations have been considered to optimally schedule fixed and switched C-Bs. Aim of this work is formulated as a maximum objective function and is solved by a modern optimization algorithm called sine cosine algorithm (SCA). The proposed SCA method is tested on standard IEEE 33 and 69-bus radial distribution systems. Results show that the developed SCA is able to maximize the annual savings and hybrid integration of DGs and C-Bs to distribution networks is preferable than integrating one of them alone. Also, superiority of the proposed algorithm is verified by comparing its results with other optimization methods and by using a non-parametric Wilcoxon statistical test.

Multiverse Optimization Algorithm Based on Lévy Flight Improvement for Multithreshold Color Image Segmentation

Multithreshold segmentation is an indispensable part of modern image processing. Color images contain more information than gray images, therefore RGB multi-thresholding segmentation techniques have been drawn much attention during recent years. Multiverse optimization (MVO) algorithm has a strong advantage in finding the optimal solution of three channels for RGB. In this paper, an MVO algorithm based on Levy flight (LMVO) is proposed. Levy flight is an efficient strategy which can not only increase the population diversity to prevent premature convergence but also improve the ability to jump out of the local optimum. Therefore, LMVO conduces to achieve a better balance between exploration and exploitation of MVO, so that it is faster and more robust than MVO and avoids premature convergence. Further LMVO algorithm is compared with the other eight famous meta-heuristics algorithms, by maximizing the objective function of Kapur's entropy method or of Otsu method to determine the optimal threshold. The maximum objective function, peak signal-to-noise ratio (PSNR), feature similarity index (FSIM), structural similarity index (SSIM), CPU calculation time, optimal threshold value, and Wilcoxon's rank-sum test are used to evaluate the quality of the segmented image. The experimental results show that this method has obvious advantages in terms of objective function value, image quality measurement, convergence performance, and robustness.

Optimizing service life of conveyor belts while transporting bulk load

The paper considers problems concerning optimization of service life of a conveyor belt in terms of its bulk material loading. Statement of the problem of belt life optimization is in the determining minimum of difference between squared velocity of a conveyor belt and projection of horizontal component of the load velocity when it contacts a belt onto the belt motion plane. The problem was solved numerically taking into consideration the objective function, varied parameters, and their limitation. Cases of direct-flow loading and loading with the help of special devices with straight and curved trough profiles have been analyzed. Regularities of changes in the belt service life due to significant factors in terms of direct-flow loading and loading with special device have been obtained to perform comparative analysis of different variants in terms of similar value of the objective function. The variants with maximum belt life and minimum objective function have been selected. For short conveyors, in terms of direct-flow loading, belt life decreases by 1.5–2.0 times comparing to the use of a loading device, and in terms of long conveyors, it decreases by 5–6 times, if value of the objective function is 0.5–1.0 m2/s2.

Multi-Period Configuration of Forward and Reverse Integrated Supply Chain Networks with the Choice of Transport Mode

Today’s competitive business environment has resulted in increasing attention to social responsibilities and customer’s attitudes. Buying and returning have become a common practice for different reasons, including incompleteness or immature failure of the product or its failure to meet the customer’s satisfaction. Before the buying and returning cycle can be handled appropriately, companies need a proper logistics network designed following a proper design strategic. In the present research, a forward and reverse logistics network is proposed for product distribution and collection. The contribution of this paper to the literature is the proposal of a multi-period, multi-echelon, integrated forward and reverse supply chain network design problem with transportation mode selection considered. Different kinds of decisions including the determination of optimum number and locations of facilities, facilities opening time and transportation mode selection among different facilities have been considered in this paper. Due to multi-period nature of the problem, the problem is flexible for future periods. A new mixed integer nonlinear programming model was proposed for the introduced problem considering different levels of facility capacities with the maximum profit objective function. As another contribution, a genetic algorithm was developed to cope with problem’s complexity when the problem size goes large.

A Modified Variant of Grey Wolf Optimizer

The original version of Grey Wolf Optimization (GWO) algorithm has small number of disadvantages of low solving accuracy, bad local searching ability and slow convergence rate. In order to overcome these disadvantages of Grey Wolf Optimizer, a new version of Grey Wolf Optimizer algorithm has been proposed by modifying the encircling behavior and position update equations of Grey Wolf Optimization Algorithm. The accuracy and convergence performance of modified variant is tested on several well known classical further more like sine dataset and cantilever beam design functions. For verification, the results are compared with some of the most powerful well known algorithms i.e. Particle Swarm Optimization, Grey Wolf Optimizer and Mean Grey Wolf Optimization. The experimental solutions demonstrate that the modified variant is able to provide very competitive solutions in terms of improved minimum objective function value, maximum objective function value, mean, standard deviation and convergence rate.

Thermo-economic analysis based on objective functions of an organic Rankine cycle for waste heat recovery from marine diesel engine

This paper presents the parametric optimization and performance analysis of the organic Rankine cycle (ORC) system for waste heat recovery from marine engine exhaust. The engine exhaust heat under operating conditions has been field-measured and evaluated. The thermo-economic optimization based on multi-objective evaluations is conducted numerically. This study aims to determine the optimal design evaporation temperature and condensation temperature, and to select suitable working fluids. The cooling water loop is taken into accounted for the whole ORC system. The parametric optimization with objective functions is compared. The economic objective function is defined as the ratio of net power output to total heat exchanger area, and the comprehensive objective function is determined as the weight-sum of exergy efficiency and economic objective function. The results show that there is the optimal evaporation temperature under the fixed expansion ratio in the ORC system for achieving the maximum thermal efficiency. The optimal condensation temperature for achieving the maximum economic objective function or comprehensive objective function is determined respectively. The parametric optimization with comprehensive objective function is better. With multi-objective evaluations, R141b performs the most satisfactorily with the maximum net power output of 97 kW, followed by R113 and cyclohexane, and R600a performs the least favorably. The optimized ORC system with R141b under various operating conditions is technically feasible and economically attractive.

Best subset binary prediction

We consider a variable selection problem for the prediction of binary outcomes. We study the best subset selection procedure by which the covariates are chosen by maximizing Manski (1975, 1985)’s maximum score objective function subject to a constraint on the maximal number of selected variables. We show that this procedure can be equivalently reformulated as solving a mixed integer optimization problem, which enables computation of the exact or an approximate solution with a definite approximation error bound. In terms of theoretical results, we obtain non-asymptotic upper and lower risk bounds when the dimension of potential covariates is possibly much larger than the sample size. Our upper and lower risk bounds are minimax rate-optimal when the maximal number of selected variables is fixed and does not increase with the sample size. We illustrate usefulness of the best subset binary prediction approach via Monte Carlo simulations and an empirical application of the work-trip transportation mode choice.

FFBF: cluster-based Fuzzy Firefly Bayes Filter for noise identification and removal from grayscale images

Image denoising gains more attention in the field of image processing, which is essential to sustain the originality of the digital images in order to preserve all the essential information buried in the image. Even though lots of denoising techniques are available, the existing methods failed to denoise the image efficiently, and they are applicable only with lower noise probability. Thus, this paper proposes a Fuzzy Firefly Bayes Filter (FFBF) to perform the noise identification and removal. FFBF employs the Ck-based firefly Bayes algorithm and probabilistic clustering for identifying the presence of noisy pixel in the input image. The Ck-based Firefly Bayes algorithm is newly proposed by integrating the cuckoo search optimization, firefly optimization, and Bayes Classifier and it is based on the maximum posterior probability objective function. The proposed algorithm provides the best solution for the formulation of the binary matrix using the Bayes Classifier, which is subjected to fuzzy-based image denoising. The paper uses two standard images for experimentation, and the comparative analysis is performed in order to determine the superiority of the proposed method. The PSNR, SSIM, and SDME obtained for the proposed method are greater when compared with the existing methods, and the proposed method attained a maximum PSNR, SSIM, and SDME of 45.1696 dB, 0.8260, and 59.9684 dB.

Virtual machine placement for elastic infrastructures in overbooked cloud computing datacenters under uncertainty

Infrastructure as a Service (IaaS) providers must support requests for virtual resources in highly dynamic cloud computing environments. Due to the randomness of customer requests, Virtual Machine Placement (VMP) problems should be formulated under uncertainty. This work presents a novel two-phase optimization scheme for the resolution of VMP problems for cloud computing under uncertainty of several relevant parameters, combining advantages of online and offline formulations in dynamic environments considering service elasticity and overbooking of physical resources. In this context, a formulation of a VMP problem is presented, considering the optimization of the following four objective functions: (i) power consumption, (ii) economical revenue, (iii) resource utilization and (iv) reconfiguration time. The proposed two-phase optimization scheme includes novel methods to decide when to trigger a placement reconfiguration through migration of virtual machines (VMs) between physical machines (PMs) and what to do with VMs requested during the placement recalculation time. An experimental evaluation against state-of-the-art alternative approaches for VMP problems was performed considering 400 scenarios. Experimental results indicate that the proposed methods outperform other evaluated alternatives, improving the quality of solutions in a scenario-based uncertainty model considering the following evaluation criteria: (i) average, (ii) maximum and (iii) minimum objective function costs.

A Nonlinear Programming Approach to Determine a Generalized Equilibrium for N-Person Normal Form Games

A generalized equilibrium (GE) for finite [Formula: see text]-person normal form games is defined as a collection of mixed strategies with the following property: no player in some subset [Formula: see text] of the players can achieve a better expected payoff if players in an associated set [Formula: see text] change strategies unilaterally. A GE is proved to exist for a game if and only if the maximum objective function value of a certain nonlinear programming problem is zero, in which case the solution to the nonlinear program yields a GE.

A comparative thermo-ecological performance analysis of generalized irreversible solar-driven heat engines

In this study, an analysis based upon thermo-ecology criteria has been performed for an irreversible solar-driven heat engine. In the conceived heat engine, heat is transferred by using simultaneous radiation and convection mode from the source at high temperature to the heat engine side and by using convection mode from the heat engine to the source at low temperature. The influences of the optimization variables on the thermo-ecologic performance have been observed by using the ecologic objective function and the ecological coefficient of performance (ECOP). Also various performance factors of the heat engine, such as thermal efficiency, power output, loss rate of availability and temperatures of the working fluid have been discussed in detail by considering the maximum ecological coefficient of performance, maximum ecological function and maximum power output conditions. The entropy generation rate at maximum ECOP is less than at maximum ecologic objective function conditions, while the power output at maximum ECOP is less than at maximum ecologic objective function conditions.

Economic design of variable-parameter X-Shewhart control chart used to monitor continuous production

Control charts are a quantitative management tool used in statistical process control to monitor product quality in production processes. This study proposes a new economic design of the variable-parameter (Vp) -Shewhart control chart for monitoring a continuous production process. In this design, the mean monitoring quality may exhibit an upward or downward shift due to two types of assignable causes. In certain continuous production settings, product quality directly affects production profit; the mean shift in monitoring quality influences lost cost, unit income and product yield. Thus, for modelling continuous production, using a maximum profit objective function for the optimization algorithm of this economic model is more appropriate than using minimum cost. Therefore, the Vp -Shewhart control chart uses an economic criterion for optimum parameter design to maximize the anticipated quality-related profit. The assignable cause occurrence is assumed to be an exponentially distributed random variable; Markov chain theory with a 9 × 9 transition probability matrix is used to subdivide the process operation into three actual states and three necessary actions. A numerical investigation is used to demonstrate the superiority of the proposed profit model compared to existing models. The proposed Vp -Shewhart control chart is applied to an example case to show its feasibility and practical application.

Analysis and optimization with ecological objective function of irreversible single resonance energy selective electron heat engines

Ecological performance of a single resonance ESE heat engine with heat leakage is conducted by applying finite time thermodynamics. By introducing Nielsen function and numerical calculations, expressions about power output, efficiency, entropy generation rate and ecological objective function are derived; relationships between ecological objective function and power output, between ecological objective function and efficiency as well as between power output and efficiency are demonstrated; influences of system parameters of heat leakage, boundary energy and resonance width on the optimal performances are investigated in detail; a specific range of boundary energy is given as a compromise to make ESE heat engine system work at optimal operation regions. Comparing performance characteristics with different optimization objective functions, the significance of selecting ecological objective function as the design objective is clarified specifically: when changing the design objective from maximum power output into maximum ecological objective function, the improvement of efficiency is 4.56%, while the power output drop is only 2.68%; when changing the design objective from maximum efficiency to maximum ecological objective function, the improvement of power output is 229.13%, and the efficiency drop is only 13.53%.

Heterogeneous facility location without money

The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-life scenarios. Specifically, we propose and analyze heterogeneous facility location without money, a novel model wherein: (i) we have multiple heterogeneous (i.e., serving different purposes) facilities, (ii) agents' locations are disclosed to the mechanism and (iii) agents bid for the set of facilities they are interested in (as opposed to bidding for their position on the network).We study the heterogeneous facility location problem under two different objective functions, namely: social cost (i.e., sum of all agents' costs) and maximum cost. For either objective function, we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line. For the social cost objective function, we devise an (n−1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm. As regards the maximum cost objective function, we propose a 3-approximate deterministic strategyproof algorithm, and prove a 3/2 approximation lower bound for deterministic strategyproof mechanisms. Furthermore, we propose a 3/2-approximate randomized strategyproof algorithm and prove a 4/3 approximation lower bound for randomized strategyproof algorithms.

Ecological analysis of a thermally regenerative electrochemical cycle

The performance of a TREC (thermally regenerative electrochemical cycle) has been investigated based on the finite time analysis. The impacts of the cell material, heat exchangers, and heat sources on the maximum ecological objective function and its corresponding power output and efficiency have been analyzed. For prescribed heat sources, the efficiency corresponding to the maximum ecological criterion is always less than that corresponding to the maximum power. Results also reveal that materials with larger isothermal coefficient and specific charge/discharge capacity and lower internal resistance and specific heat lead to a larger maximum ecological objective function and the corresponding power output and efficiency. Heat exchangers with much higher performance are of no practical use to enhance the performance of the TREC system, and the characteristics of the heat sources also present significant impacts on the performance of the TREC under the maximum ecological criterion. As the ecological criterion considers both the energy benefit and loss, the results in this paper may contribute in designing high performance TREC devices.

An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of λ in SSM. The risk preference degree of λ could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers’ net benefit reaches to [8.949, 12.442] × 108 RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.

Modelling and optimization of organic Rankine cycle based on a small-scale radial inflow turbine

In most of the organic Rankine cycle (ORC) studies, constant expander efficiency is considered for a wide range of cycle operating conditions and for various working fluids. This study presents an optimized modelling approach for the ORC based on radial inflow turbine, where the constant expander efficiency is replaced by dynamic efficiency that is unique for each set of cycle operating conditions and working fluid properties. Considering the size and performance of the ORC, the model was used to identify the key input variables that have significant effects on the turbine overall size and the cycle net electric power output. These parameters were then included in the optimization process using the DIRECT algorithm to maximize the ratio of cycle net electric power output to the turbine overall size (objective function) for six organic fluids. Results showed that, dynamic efficiency approach predicted considerable differences in the turbine efficiencies of various working fluids. The maximum difference of 6.13% between the turbine efficiencies of R245fa and isobutane was predicted. Also the optimization results showed that, the maximum objective function of 0.5748kW/mm was achieved by isobutane with the cycle net electric power output and the turbine overall size of 90.3kW and 157.2mm respectively. Such results are better than the other studies and highlight the potential of the optimization technique to further improve the performance and reduce the size of the ORC based on small-scale radial turbines.

Multi-disciplinary design optimization and performance evaluation of a single stage transonic axial compressor

The multidisciplinary design optimization method, which integrates aerodynamic performance and structural stability, was utilized in the development of a single-stage transonic axial compressor. An approximation model was created using artificial neural network for global optimization within given ranges of variables and several design constraints. The genetic algorithm was used for the exploration of the Pareto front to find the maximum objective function value. The final design was chosen after a second stage gradient-based optimization process to improve the accuracy of the optimization. To validate the design procedure, numerical simulations and compressor tests were carried out to evaluate the aerodynamic performance and safety factor of the optimized compressor. Comparison between numerical optimal results and experimental data are well matched. The optimum shape of the compressor blade is obtained and compared to the baseline design. The proposed optimization framework improves the aerodynamic efficiency and the safety factor.