Minimization Of Objective Function Research Articles

Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

Owing to advancement in advanced manufacturing technology, the reinforcement design of concrete structures has become an important topic in structural engineering. Based on bi-directional evolutionary structural optimization (BESO), a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete (SRC) structures. This approach combines a minimum compliance objective function with a hybrid truss-continuum model. Furthermore, a modified bi-directional evolutionary structural optimization (M-BESO) method is proposed to control the level of tensile stress in concrete. To fully utilize the tensile strength of steel and the compressive strength of concrete, the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete. To demonstrate the effectiveness of the proposed procedures, reinforcement layout optimizations of a simply supported beam, a corbel, and a wall with a window are conducted. Clear steel trajectories of SRC structures can be obtained using both methods. The area of critical tensile stress in concrete yielded by the M-BESO is more than 40% lower than that yielded by the uniform design and BESO. Hence, the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

Load Frequency Control of One and Two Areas Power System Using Grasshopper Optimization Based Fractional Order PID Controller

In this paper, grasshopper optimization based fractional order PID controller for load frequency control of single and multi-area power system is presented. It is paramount to minimize large frequency deviation in power system control. Large frequency deviation occurs when the parameter values of the various generating units of the power system like generators, turbine and governors keeps changing due to numerous on/off witching in the load side. As such, for a more realistic study, nonlinearities and boiler dynamics has been introduced into the power system design and measures also put in place to mitigate large frequency deviation. This is because large frequency deviation can damage equipment at the generation level and the consumer devices at the distribution level. Anti-windup control will then be used to compensate the effects of the nonlinearities. The gain of the FOPID controller will be optimized using grasshopper optimization algorithm and objective function for minimization is the Integral Square Error (ISE). The Errors to be minimized are the summation of frequency deviation, tie-line power deviation and the area control errors. Simulations were carried out on the designed power system using MATLAB/Simulink and results obtained show a significant improvement in mitigating frequency deviation. However, the proposed method took a longer time to balance the generated power and load demand. This is because the proposed method considers boiler dynamics and nonlinearities in the power system designed and results were compared with other designed method for power system without nonlinearities.

Numerical and experimental study of the dynamic behaviour of a polymer-metal worm drive

Polymer-metal worm drives are common in automotives and mechatronic systems. Despite this, there is a lack of studies on this type of transmission, especially when it comes to their dynamic behaviour. With the modern orientation of Industry 4.0 towards advancing technology in predictive maintenance, it is of a great importance to consider the study of the dynamic behaviour of this mechanism. It is first proposed to introduce an appropriate dynamic model to correctly simulate, by numerical means, the behaviour of a non-defective polymer-metal worm drive. For this purpose, it is necessary to correctly model the Gear Mesh Stiffness (GMS) of the gearing system. The GMS depends on the nature of the worm and worm gear materials. It is assumed that no deformation occurs in the steel worm, in contrast to the polymer worm whose viscoelastic behaviour must be accurately modelled. Generalized Maxwell Model (GMM) is chosen to model this behaviour. Eventually, the vibration signals from the numerical model are compared with those determined by the experimental tests. To obtain more similarities between the numerical and experimental signals, it is proposed to perform an optimisation. The procedure consists in using the Nelder-Mead simplex method to obtain a minimum residual objective function. After optimisation, an accuracy of 94% between the experimental and numerical results is achieved.

Investigating the effect of the presence of a pulsating heat pipe on the geometrical parameters of the microchannel heat sink

In this study, the effect of the presence of a pulsating heat pipe on the geometrical parameters of the microchannel heat sink will be investigated. The embedding of a pulsating heat pipe (PHP) in the solid part of the microchannel heat sink (MCHS) increases the cooling performance of the MCHS and reduces the maximum temperature of the electronic piece. A numerical investigation of MCHS equipped with a PHP is investigated and compared with an optimized conventional MCHS without PHP. The inverse problem solution approach is used to optimize the geometric parameters of the MCHS. The geometrical variables in the optimization process are N (number of channels), α (aspect ratio of the channel), and β (width ratio of the channel to pitch). The pumping power is considered a constraint and is tried to reach the minimized objective function (thermal resistance (R)). Results show that the optimal values of geometrical and physical parameters change from N = 100, α = 13.9, β = 0.6, R = 0.0268, in conventional MCHS to N = 120, α = 14.3, β = 0.7, R = 0.0231 in MCHS with PHP. At this point, the system’s thermal performance improved by 16.02% compared to the previous optimal state.

Trade-offs between economic and environmental goals of production-inventory-routing problem for multiple perishable products

In this paper, we study an integrated production-inventory-routing problem for multiple perishable products (MPPIRP). We introduce two models to evaluate the trade-off between total emissions and total costs. The first model concentrates on minimizing carbon emissions from production, inventory, and routing activities. Notably, carbon emission in transportation depends on several factors, including vehicle load (empty load and carried load), velocity, and traveled distance. The other model considers the value loss of products due to deterioration during their lifetime in the total cost minimization objective function. We impose constraints that perishable products cannot be held, delivered, or used after their lifetimes have expired in both models. Then, we devise a PSO-based method to solve them. Computational experiments verify the effectiveness of the PSO-based method and the rationality of models. Furthermore, we compare costs, emissions, and key performance indicators under both objective functions. The impact of shelf-life on both objectives also has been analyzed. Computational results help us gain significant insights on generating strategy of production, inventory, and routing to minimize total costs or achieve a fully environmental-friendly goal.

Formula omitted]-divergence NMF with biorthogonal regularization for data representation

Non-Negative Matrix Factorization (NMF) has become a commonly used method for data representation. Orthogonal NMF improves the clustering performance by adding orthogonal constraints to the decomposed matrices. The existing orthogonal NMF methods typically use Euclidean distance to measure the difference between before and after factorization for convenience and simplicity. However, limitations of the Euclidean distance can lead to inflexibilities. In addition, failure to consider orthogonality of the decomposed features and sparsity of the data representation can also lead to degraded performance of the algorithm. In order to overcome the above shortcomings, we propose a novel β-divergence-based NMF with biorthogonal regularization (BO-βNMF). Our BO-βNMF method uses generalized β-divergence instead of Euclidean distance to measure the similarity between matrices, and selects an appropriate β for each type of data to obtain a more flexible way of measuring similarity. In addition, we also incorporate biorthogonal constraints into the minimized objective function, which ensures both orthogonality of the decomposed features and sparsity of the data representation. Furthermore, we use trace rather than Euclidean distance to measure the orthogonality of the decomposed matrices, which reduces execution time. Finally, clustering experiments on image datasets show that the overall clustering effect of BO-βNMF is better than state-of-the-art methods.

Performance Analysis of a 10 MW Ocean Thermal Energy Conversion Plant Using Rankine Cycle in Malaysia

Ocean thermal energy conversion (OTEC) is a solution for environmental and climate change issues in the tropics. The OTEC potential in Malaysia using ocean conditions and bathymetry data has been previously studied and demonstrated. Following this, it is vital to perform a basic performance analysis of a 10 MW Rankine Cycle OTEC plant using the Malaysian ocean conditions. In this paper, the results of heat and mass balance will be reported for a 10 MW Rankine cycle OTEC plant which uses heat exchangers of plate-type and anhydrous ammonia as its working fluid. The value of a minimum objective function (γ) is derived by total heat surface area (AT) divided by the net power (PN). γ decreases when the inlet temperature difference (inlet temperature of warm seawater (TWSWI)—inlet temperature of cold seawater (TCSWI)) increases. PN is clarified to be approximately 70–80% of the PG (gross power) using Malaysian ocean conditions.

An Optimization Model for Electric Motorcycle Battery Swapping Station in Indonesia: A Case Study

Battery Electric Vehicle (BEV) has become a new technological innovation that effectively accelerates electrification due to their short charging and swapping processes. On the other hand, developing charging infrastructure, such as charging stations, still needs to be improved in Indonesia. The absence of government policies regulating charging station design has led each electric motorcycle company to innovate with their own standards. This research aims to implement a proposed Battery Swap Station (BSS) model to minimize swapping costs by optimizing the charging schedule for each exchanged battery based on a case study of one electric motorcycle service provider in Solo. Three factors are considered in searching for the objective function: the number of batteries taken from the stock during daily operations, battery degradation resulting from high charging scheme usage, and the electricity cost used at the station. Genetic Algorithms are proposed to determine the optimal charging scheduling, resulting in the minimum objective function. A series of battery swapping demand case studies are simulated to assess the feasibility of the proposed model, which can serve as a policy reference for the government and companies.

Airfoil smoothing using unconditional optimization taking into account aerodynamic criteria

The smoothing of airfoils in sections of the surface of an aircraft wing is considered. The issue of using the distribution of pressure and Mach number along the chord of an airfoil as criteria for smoothing efficiency is being studied. Smoothing is considered as a problem of unconditional minimization of a quadratic objective function. The arguments of the objective function are the second derivatives of the tabular function interpolating the contour of the airfoil. Minimization is performed using the gradient descent method.

Long short-term memory (LSTM) model-based reinforcement learning for nonlinear mass spring damper system control

The Neural Networks (NN) model which is incorporated in the control system design has been studied, and the results show better performance than the mathematical model approach. However, some studies consider that only offline NN model learning and does not use the online NN model learning directly on the control system. As a result, the controller's performance decreases due to changes in the system environment from time to time. The Reinforcement Learning (RL) method has been investigated intensively, especially Model-based RL (Mb-RL) to predict system dynamics. It has been investigated and performs well in making the system more robust to environmental changes by enabling online learning. This paper proposes online learning of local dynamics using the Mb-RL method by utilizing Long Short-Term Memory (LSTM) model. We consider Model Predictive Control (MPC) scheme as an agent of the Mb-RL method to control the regulatory trajectory objectives with a random shooting policy to search for the minimum objective function. A nonlinear Mass Spring Damper (NMSD) system with parameter-varying linear inertia is used to demonstrate the effectiveness of the proposed method. The simulation results show that the system can effectively control high-oscillating nonlinear systems with good performance.

Fractional Transformation-Based Intelligent H-Infinity Controller of a Direct Current Servo Motor

Direct current (DC) servo motors are central to many complex systems, such as electrical, electro-mechanical, and electro-hydraulic frameworks. In practice, these systems can have nonlinear characteristics and parameter variations. Accurate model representation and position tracking of DC motors are the main issues in many real systems, such as twin rotors, aircraft, airships, and robot manipulators. The precise position tracking of these systems has already been achieved using conventional H-infinity (H∞) controllers. However, the order and structure become more intricate when employing complex weights to shape the closed-loop system, which limits the current proposals. To overcome the above-mentioned limitations, in this article, we provide a precise angular position tracking of a DC servo motor utilizing an intelligent, robust linear controller based on a fixed-structure linear fractional transformation. The conventional H∞ controllers are based on the minimization of an unstructured linear fractional transformation objective function that leads to a complex design of these controllers. The main advantage of the proposed intelligent H∞ synthesis is the fixed and simple structure that increases its practical implementation. The methodology is formulated in the MATLAB software for the robust design of the proposed synthesis based on an intelligent fixed-structure H∞ optimization. Simulation results are compared with conventional H∞ and proportional-integral-derivative controllers. The results are also validated experimentally.

Pareto optimality based PID controller design for vehicle active suspension system using grasshopper optimization algorithm

In this paper, a Pareto multiobjective and grasshopper optimization algorithm (GOA) based optimum proportional–integral–derivative (P–I–D) controller design is proposed for improving the vehicle active suspension system dynamics under road disturbance conditions. The Pareto objectives considered are minimization of sprung mass suspension deflection, tyre deflection, sprung mass acceleration minimization and eigenvalue-based objective function. State space model for quarter vehicle active suspension system with P–I–D controller is developed for analyzing the stability and dynamic performance of the system. The sinusoidal-based bump road disturbances are used for testing the robustness of the proposed control technique. Simulation results have been presented to show the advantage of the proposed Pareto multiobjective and GOA-based P–I–D controller over the weighted multiobjective and genetic algorithm-based P–I–D controller in terms of stability and dynamics of the active suspension system.

Railway car routing optimization based on the coordinated utilization of station‐line capacities

AbstractTo optimize railway car routing based on balanced station‐line capacities, thereby improving railway freight traffic organization efficiency, and reducing transportation costs, a railway car routing optimization model based on the coordinated utilization of station‐line capacities was developed. Based on the theory of the membership function in fuzzy mathematics, the level of railway station‐line coordination based on capacity utilization was presented. The occupancy of a railway line by each car was taken as a binary decision variable. Using a set of deviation constraints, the deviation between the station‐line flow of the railway network and the utilization of a certain level was expressed in the form of decision variables that were then penalized to different degrees in the objective function. The total transportation cost and the penalty cost were taken as the objective function for minimization. Based on the characteristics of the fuzzy membership degree, the relationship between the penalty for capacity deviation and the membership function in the optimization model was analyzed, and the calculation method of the penalty for the capacity deviation considering the membership function was presented. An adaptive large‐scale neighbourhood search (ALNS) algorithm was designed to solve the model, and its effectiveness was verified. An actual 36‐station railway network was used to validate the proposed railway car routing optimization model through comparison with existing models. The optimization results showed that, at the expense of increasing the transportation cost by 1.05%, the coordination penalty cost was reduced by 11.24%, the overall cost was reduced by 3.21%, and most of the situation with 90% utilization rate of stations and lines in the railway network was eliminated. The model proposed in this paper can help reduce the pressure on lines and stations with tight capacity in the network, improve the utilization of virtual lines and stations and coordination of station‐line capacities.

Linear precoder design for peak‐to‐average power ratio reduction of generalized frequency division multiplexing signal using gradient descent methods

AbstractThis article addresses linear precoder design for the peak‐to‐average power ratio (PAPR) reduction of the generalized frequency division multiplexing (GFDM) scheme. This design relies on minimizing various statistical parameters of the instantaneous power of the GFDM signal—including variance, second and third moments—using gradient‐based optimization methods. In this regard, a general framework of four different scenarios, which employs the steepest descent and conjugate‐gradient methods and utilizes two different approaches of fixed and dynamic step‐sizing, is proposed. In the case of fixed step‐sizing, the results demonstrate that the algorithm diverges in some scenarios and provides low‐speed convergence for the others due to its inability in meeting the terminating threshold regarding minimizing objective function to a desirable level. However, dynamic step‐sizing using the Wolf line search rule circumvents these drawbacks, outperforms the existing research, and converges in all scenarios to a precoder providing advantages in terms of design speed and achievable PAPR, while keeping the symbol error rate and out‐of‐band emissions at the ranges of the un‐precoded GFDM systems. Moreover, the results confirm the comprehensiveness of the proposed framework in adapting to various GFDM statistical parameters and gradient methods.

A theoretical demonstration for reinforcement learning of PI control dynamics for optimal speed control of DC motors by using Twin Delay Deep Deterministic Policy Gradient Algorithm

To benefit from the advantages of Reinforcement Learning (RL) in industrial control applications, RL methods can be used for optimal tuning of the classical controllers based on the simulation scenarios of operating conditions. In this study, the Twin Delay Deep Deterministic (TD3) policy gradient method, which is an effective actor-critic RL strategy, is implemented to learn optimal Proportional Integral (PI) controller dynamics from a Direct Current (DC) motor speed control simulation environment. For this purpose, the PI controller dynamics are introduced to the actor-network by using the PI-based observer states from the control simulation environment. A suitable Simulink simulation environment is adapted to perform the training process of the TD3 algorithm. The actor-network learns the optimal PI controller dynamics by using the reward mechanism that implements the minimization of the optimal control objective function. A setpoint filter is used to describe the desired setpoint response, and step disturbance signals with random amplitude are incorporated in the simulation environment to improve disturbance rejection control skills with the help of experience based learning in the designed control simulation environment. When the training task is completed, the optimal PI controller coefficients are obtained from the weight coefficients of the actor-network. The performance of the optimal PI dynamics, which were learned by using the TD3 algorithm and Deep Deterministic Policy Gradient algorithm, are compared. Moreover, control performance improvement of this RL based PI controller tuning method (RL-PI) is demonstrated relative to performances of both integer and fractional order PI controllers that were tuned by using several popular metaheuristic optimization algorithms such as Genetic Algorithm, Particle Swarm Optimization, Grey Wolf Optimization and Differential Evolution.

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.

Artificial intelligence-enabled probabilistic load demand scheduling with dynamic pricing involving renewable resource

Residential demand response is one of the key enabling technologies which plays an important role in managing the load demand of prosumers. However, the load scheduling problem becomes quite challenging due to the involvement of dynamic parameters and renewable energy resources. This work has proposed a bi-level load scheduling mechanism with dynamic electricity pricing integrated with renewable energy and storage system to overcome this problem. The first level involves the formulation of load scheduling and optimization problems as optimal stopping problems with the objective of energy consumption and delay cost minimization. This problem involved the real-time electricity pricing signal, customers load scheduling priority, machine learning (ML) based forecasted load demand, and renewable & storage unit profiles, which is solved using mathematical programming with branch-and-cut & branch-and-bound algorithms. Since the first-level optimization problem is formulated as a stopping problem, the optimal time slots are obtained using a one-step lookahead rule to schedule the load with the ability to handle the uncertainties. The second level is used to further model the load scheduling problem through the dynamic electricity pricing signal. The cost minimization objective function is then solved using the genetic algorithm (GA), where the input parameters are obtained from the first-level optimization solution. Furthermore, the impact of load prioritization in terms of time factor and electricity price is also modeled to allow the end-users to control their load. Analytical and simulation results are conducted using solar-home electricity data, Ausgrid, AUS to validate the proposed model. Results show that the proposed model can handle uncertainties involved in the load scheduling process along with a cost-effective solution in terms of cost and discomfort reduction. Furthermore, the bi-level process ensures cost minimization with end-user satisfaction regarding the dynamic electricity price signal.

An automatic inversion approach for magnetic data applying the global bat optimization algorithm (GBOA): application to ore deposits and basement rock intrusion

Recently, metaheuristic approaches are frequently used to the potential data inversion (i.e., magnetic data) as a global optimizing approach. In the present study, we proposed a global optimizing bat algorithm (GOBA) that based on bat echolocation behavior to obtain globally optimal solutions (best parameters) of magnetic anomalies. The best determined source parameters were picked at the suggested minimum objective function. The proposed GOBA approach does not require prior information and represents an effective technique of surveying the entire domain of the raw data to evaluate sources optimal parameters. The GOBA approach is employed to magnetic data profiles to determine the characteristic source attributes (i.e. the vertical depths to the center of the anomalous structures, the magnitude of amplitude coefficients, the sources origin, the approximated geometric form factors, and the effective angles of magnetization). The GOBA approach can be applied to single and multiple anomaly structures in the restricted categories of basic geometric shapes (spheres, cylinders, sheets, and dikes). The stability, constancy, and performance of the given GOBA approach are achieved on different purely and contaminated examples for individual and double sources. Besides, the introduced GOBA approach has been fruitfully utilized to three field datasets from Turkey, Canada, and Senegal for ore deposit and basement rock intrusion investigations. Overall, the recovered inversion results from the GOBA approach are in high correlation with the available drill-holes, geologic data, and scholarly articles outcomes. Finally, the provided metaheuristic GOBA approach is a simple, accurate, and powerful technique for magnetic data interpretation.Article highlightsAn automatic approach for magnetic data interpretation to investigate the ore deposits and sustainable resources such as volcanic and basement rock intrusions based on bat echolocation behavior to obtain the global optimal solutions.In this study we built 2D models aims to image of the interior of the subsurface to investigate their natural resources, for example minerals & ore deposits and rock intrusions, helping in understand their concentration and the distribution location, including the depth to their sources.We came to the conclusion that the suggested approach is useful in ore & mineral research, the reconnaissance geological studies and can be extend to the volcanic activity & geothermal exploration studies in the future.

Dynamic Economic Dispatching Considering Time-Coupling Spinning Reserve Response Risk with High Penetration of Wind Power

Aiming at the problem that the current dynamic economic dispatch (DED) fails to consider the response risk of spinning reserve caused by the fluctuation and uncertainty of wind power, we work out a DED problem considering time-coupling spinning reserve response risk while the stochasticity and variability arising from RESs are taken into consideration. The developed framwork unified the response risk of reserve caused by forced shutdown of the unit into the response risk caused by time coupling. The expected customer interruption cost (ECOST) and the expected abandoned wind cost considering this reserve response risk are added to the objective function. While seeking the minimum objective function, the system is automatically configured with suitable reserve to ensure the consistency of the system’s response risk in each period. An improved multi-universe parallel quantum genetic algorithm was used to solve the model. Numerical examples and analysis prove the effectiveness and feasibility of the proposed method.

Distributed Newton Optimization With Maximized Convergence Rate

The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the sum of local functions known at individual nodes. A number of methods, having different advantages, are available for addressing this problem. The goal of this article is to achieve the maximum possible convergence rate. As the first step toward this end, we propose a new method, which we show converges faster than other available options. As the second step toward our goal, we complement the proposed method with a fully distributed method for estimating the optimal step size that maximizes the convergence rate. We provide theoretical guarantees for the convergence of the resulting method in a neighborhood of the solution. We present numerical experiments showing that, when using the same step size, our method converges significantly faster than its rivals. Experiments also show that the distributed step-size estimation method achieves an asymptotic convergence rate very close to the theoretical maximum.