Nonlinear Programming Optimization Problem Research Articles

Uso do programa Scilab na resolução de problemas da resistência dos materiais com a função fmincon

he subject of Resistance of Materials is fundamental to the training of engineers, as it provides theoretical and practical knowledge about the behavior of materials under different types of loading. Traditionally, the teaching of this subject has focused on analytical approaches. However, the creation of pedagogical practices that stimulate the ability to analyze, solve problems, and interpret results is crucial. In this context, the aim of this article is to present a novel approach to solving problems in Resistance of Materials by employing structural optimization using the open-source software Scilab. Computer codes for the numerical solution of case studies are developed using the fmincon function. This function is a tool used to solve nonlinear programming optimization problems, where the objective is to minimize or maximize a function subject to both equality and inequality constraints. With the integration of computers into the classroom, students will have the opportunity to enhance their ability to comprehend and apply the theoretical knowledge acquired, which in turn improves the learning process. The application of the proposed methodology in the classroom can serve as a starting point for future research related to the potential of educational technologies in other engineering fields. Keywords: Engineering Education. Structural Optimization. Fmincon.

A Dispersed Federated Learning Framework for 6G-Enabled Autonomous Driving Cars

Sixth-Generation (6G)-based Internet of Everything applications (e.g. autonomous driving cars) have witnessed a remarkable interest. Autonomous driving cars using federated learning (FL) has the ability to enable different smart services. Although FL implements distributed machine learning model training without the requirement to move the data of devices to a centralized server, it its own implementation challenges such as robustness, centralized server security, communication resources constraints, and privacy leakage due to the capability of a malicious aggregation server to infer sensitive information of end-devices. To address the aforementioned limitations, a dispersed federated learning (DFL) framework for autonomous driving cars is proposed to offer robust, communication resource-efficient, and privacy-aware learning. A mixed-integer non-linear programming (MINLP) optimization problem is formulated to jointly minimize the loss in federated learning model accuracy due to packet errors and transmission latency. Due to the NP-hard and non-convex nature of the formulated MINLP problem, we propose the Block Successive Upper-bound Minimization (BSUM) based solution. Furthermore, the performance comparison of the proposed scheme with three baseline schemes has been carried out. Extensive numerical results are provided to show the validity of the proposed BSUM-based scheme.

A centralized EMPC scheme for PV-powered alkaline electrolyzer

Photovoltaic (PV)-powered alkaline electrolyzer system (PVPAES) is an advanced technique to convert the off-grid and intermittent PV-based solar energy into storable and transportable electrolyzer-based hydrogen energy with zero carbon emissions. However, it is difficult to realize the coordinated control of the off-grid PV module and the alkaline electrolyzer, due to the multiple timescale dynamics. To address this challenge, the PVPAES is decomposed into the slow part and fast part based on the dynamic time scale. Exploiting the decomposed subsystems, the slow one is assumed to be managed well by the auxiliary controller. For the fast one, a centralized economic model predictive control (CEMPC) scheme is constituted. This CEMPC integrates the energy management system and local feedback control into a single optimal control framework. A mathematical model of the PVPAES is established, on the basis of which the CEMPC directly adopts the economic indices as the cost function to realize the flexible power point tracking, power supply-demand balance, and dynamic economic optimization. Moreover, the inherent strong nonlinearity of PVPAES results in the nonconvex mixed-integer nonlinear programming optimization problem in the CEMPC. The exhaustive search algorithm utilizing finite converter switching states is adopted to achieve the global economic optimum. The effectiveness of the proposed CEMPC controller is illustrated through simulations under varying irradiance conditions.

A Novel Active Anti-Disturbance Control Strategy for Unmanned Aerial Manipulator Based on Variable Coupling Disturbance Compensation

Inspired by the kangaroo’s active tail wagging to stabilize its body posture while jumping, this paper proposes an active anti-disturbance control strategy for unmanned aerial manipulators based on variable coupling disturbance compensation (AADCVCD), which can achieve the active and energy-saving anti-disturbance performance of “using the enemy’s strength against the enemy” to keep the UAM stable under disturbances. First, the goal of using the coupling disturbance generated by the active swing of the manipulator as a control input signal for active anti-disturbance is clarified. Then, based on the proposed variable coupling disturbance model, this goal is formulated as a nonlinear programming optimization problem under specific physical constraints and solved. Finally, the coupling disturbance torque generated when the manipulator executes an active swing to the solved desired joint angles can be used to compensate and suppress other disturbances of the UAM, thereby achieving active anti-disturbance. The effectiveness and superiority of the proposed AADCVCD were validated through two simulations in Simscape. The simulation results demonstrated that our approach achieved a good active anti-disturbance and energy-saving performance, significantly reducing the position offset of the UAM caused by disturbances and improving the UAM’s ability to maintain stability.

A Modified Davidon-Fletcher-Powell Method for Solving Nonlinear Optimization Problems

One of the quasi-Newton update formulae, namely the Davidon-Fletcher-Powell method, is crucial for resolving nonlinear programming optimization problems. In order to achieve a Newton-like condition that depends on the function values and gradient vectors at each iteration, we construct an alternative positive-definite Hessian approximation in this study. The essential theorems are established to study algorithm convergence. The proposed approach is then tested on well-known test problems and then compared to the standard DFP method. The numerical outcomes demonstrate the effectiveness of the newly developed method.

Sizing of a Scattered Housing Microgrid in a Remote Rural Area

Power solutions for remote rural regions are mainly based on generator sets or individualized generation systems per household. These solutions have low reliability and high financial and environmental costs, especially those involving fossil fuels. However, current solutions incorporate hybrid systems with renewable energy sources to reduce pollutant gas emissions and costs and increase the reliability and robustness of power generation. These hybrid systems can be considered micro-grid (MG) and could contribute to energizing remote non interconnected areas. However, implementing MGs in these regions must challenge energizing dispersed households. Thus, both the sizing of the generation and distribution systems must be considered to guarantee the correct operation of the MG and a low cost. This paper explores coordinated sizing between the power sources and the distribution system to address the challenges of energizing remote areas with dispersed loads through MG. It presents a literature review on energization strategies for remote regions and proposes coordinated MG sizing. Finally, it applies coordinated sizing to a case study in Colombia. The sizing is approached as a mixed-integer nonlinear integer programming optimization problem and is solved by a particle swarm optimization (PSO) algorithm.

Contextual Bayesian optimization of congestion pricing with day-to-day dynamics

Congestion pricing is a common approach to alleviate urban traffic congestion. The design of second-best congestion pricing schemes is typically formulated as non-linear programming and bi-level optimization problems, where the lower-level problem involves either a static or dynamic network equilibrium model. The complexity of these bi-level toll optimization problems increases considerably when incorporating day-to-day dynamic models of travel behavior and dynamic models of network congestion. These models are often operationalized using simulation, and consequently, the toll design problem is a computationally challenging simulation-based optimization problem where the evaluation of a single candidate pricing scheme involves simulating the day-to-day model until convergence. In order to circumvent this issue, we propose a contextual Bayesian optimization (BO) framework, where the BO scheme is embedded within the day-to-day dynamic model by using temporal contextual information. The framework implicitly incorporates the relationship between the objective function across days and uses past days’ observations (function evaluations) as weak priors when constructing the Gaussian process underlying the BO algorithm for the current day’s toll optimization problem, resulting in gains in computational efficiency.The contextual BO approach is applied to the design of distance-based pricing schemes for the morning commute problem. We demonstrate numerically that the scheme converges to the system optimum, and moreover, utilizes a significantly smaller number of simulation evaluations (ten-fold reduction) than the standard approach wherein each function evaluation involves simulating the day-to-day model until convergence. From a policy perspective, we find that the distance-based schemes yield significant welfare gains relative to area-based schemes and show that the design of the distance-based tariff scheme can significantly affect distributional impacts. A suitably designed two-part tariff structure can partially offset the relatively large welfare losses of travelers with longer commute distances while maintaining overall welfare. The proposed contextual BO scheme is also extended to incorporate context specific demand and supply information, which can be of value to policy-makers when evaluating optimal toll design schemes under a wide range of scenarios in a computational tractable manner.

Energy-Efficient Federated Edge Learning in Multi-Tier NOMA-Enabled HetNet

We propose a novel multi-tier (top, intermediate, and bottom tiers) architecture at the edge of a heterogeneous network (HetNet) where non-orthogonal multiple access (NOMA) provides access to user equipment (UE) to participate in federated edge learning (FEL). The HetNet consists of a macro base station (MBS) and several small base stations (SBSs) where each BS is equipped with an edge server (ES). SBSs use the same system bandwidth to increase the system capacity. The top tier consists of the MBS-ES which works as the global model aggregator while ESs of SBSs and UEs connected with MBS reside in the intermediate tier. Similarly, UEs connected with an SBS-ES of the intermediate tier occupy the bottom tier. ESs of SBSs work as the intermediate model aggregators between the ES of the top tier and the UEs of the bottom tier. To minimize the total energy consumption (EC) for local computing (LC) and uplink transmission (UT) of UEs, we formulate a non-linear programming (NLP) optimization problem, present our solution by decomposing the problem into sub-problems, and propose two sequential algorithms to estimate EC for both LC and UT with less complexity. Our extensively simulated results demonstrate the viability of our proposed work.

Resource Allocation for NOMA-Enabled Cognitive Satellite–UAV–Terrestrial Networks With Imperfect CSI

Recently, non-orthogonal multiple access (NOMA)-enabled cognitive satellite-unmanned aerial vehicle (UAV)-terrestrial networks have attracted extensive attention for the advantages of enhancing spectrum efficiency and coping with the exponential growth of access users. In this paper, we propose a joint subchannel assignment and power allocation algorithm for NOMA-enabled cognitive satellite-UAV-terrestrial networks to further enhance the transmission performance, where imperfect channel state information is taken into consideration. Specifically, we formulate a mixed integer non-linear programming resource allocation problem to optimize the sum rate of the secondary network, in which the demands of the interference temperature constraint for primary users, the minimum transmission rate of each secondary user, the maximal transmitter power of the UAV, and the maximal number of secondary users that each subchannel can serve are satisfied. To tackle this tough non-convex problem, we first decouple it into two subproblems, namely, subchannel assignment and power allocation. Next, a heuristic subchannel assignment algorithm and a Taylor series and successive convex approximation-based power allocation algorithm are designed to solve the above subproblems, respectively. By alternately optimizing the sum rate of the secondary network, we finally solve the mixed integer non-linear programming optimization problem. Numerical results reveal the impacts of key parameters on system performance and indicate that our proposed scheme outperforms benchmarks in large-scale networks.

Data-driven multi-period modeling and optimization for the industrial steam system of large-scale refineries

Steam system modeling and optimization contributes toward low energy consumption for large-scale industrial refineries. However, formidable challenges have been generated by steam demand variation, the optimization of CO2 emissions and outsourced steam, the uncertainty of sudden equipment failures, and the introduction of new equipment. To address this issue, this work presents a novel steam system model with periodic process steam demand. The multiple cost factors of CO2 emission treatment and outsourced steam are considered and formulated as a mixed integer nonlinear programming optimization problem. A strategy to discretize the uncertainty of equipment failure into three main scenarios is proposed. The proposed model, strategy, and introduction of new equipment are demonstrated on three cases of industrial refinery steam systems. In case 1, the optimized operating costs have reduced by 1.5%. In case 2, the optimized average operating cost is 1,135,402 CNY/h. In case 3, with the introduction of the aromatics turbocharged turbine (ATT) and the letdown valve, the optimized operating costs are 1,292,182 CNY/h and 1,316,227 CNY/h respectively, confirming the feasibility of introducing ATTs.

Hybrid Multiple Access for Network Slicing Aware Mobile Edge Computing

Meeting huge traffic demand with resource constraints imposes a significant challenge for future generation wireless networks. In this work, we propose to utilize limited resources in a dense mobile edge computing (MEC) network to compute user equipment (UE) tasks through a novel hybrid multiple access (HYMA) scheme that employs both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA). The main purpose of using HYMA is to reduce the co-channel interference incurred in NOMA by selectively deploying OMA while maintaining the required signal-to-interference ratio. We adopt partial offloading of computing tasks in the MEC network. We also employ network slicing to efficiently utilize the resources of the MEC network to meet different types of application requirements. We prioritize NOMA to increase spectral efficiency as well as energy efficiency. We first formulate a mixed integer nonlinear programming (MINLP) optimization problem to minimize the total energy consumption for both local computing and wireless transmission of the MEC network and propose an algorithm consisting of three parts (UE association, computing resource allocation, and wireless resource and uplink transmission power allocation) to solve the MINLP problem with less computational complexity. We demonstrate the viability of our solution via extensive simulations.

Kinetic resolution of thermal runaway for lithium-ion batteries: A Gaussian surrogate-assisted separate optimization approach

Accurate kinetic resolution of thermal runaway (TR) for lithium-ion batteries (LIBs) plays a central role in battery safety design and early warning. However, simultaneous extraction of the number and kinetic parameters of TR reactions from multi-peak overlapping differential scanning calorimetry (DSC) profiles is a complicated nonlinear programming optimization problem. A Gaussian surrogate-assisted separate optimization framework is proposed to address the kinetic resolution problem. First, an offline equivalent kinetic database, based on the geometric similarity of heat flow peaks and Gaussian functions, is designed to provide initial parameter estimations for multiple reactions. Second, an adaptive range division method, based on priori local extrema, is proposed to divide the DSC profile into separate ranges of fitting (ROF) to assist the key mechanism selection. Third, divisional kinetic resolution is performed for each ROF where kinetic models initialized by the above database are utilized to fit sub-range profiles and then potential solutions are searched based on a posteriori error-based criterion. Finally, Bayesian information criterion is utilized for the optimal solution selection among the combinations of potential solutions for multiple ROFs. The proposed framework is validated through experimental data from the DSC tests of types of LIBs. The results illustrate the applicability and efficiency of the proposed framework.

Joint terminal-AP association and power allocation for NOMA-enabled space–air–ground integrated networks

This paper considers a space–air–ground integrated network (SAGIN) to provide network access services for aerial and terrestrial terminals. The non-orthogonal multiple access (NOMA) is used for improving spectral efficiency in the uplink transmission between terminals and access points (APs) in SAGIN. A sum rate maximization optimization problem is formulated by optimizing terminal-AP association and power allocation, while simultaneously satisfying the constraints of transmit power, network coverage characteristics, and quality-of-service (QoS) requirements of both aerial and terrestrial terminals. To deal with the formulated mixed integer nonlinear programming (MINLP) optimization problem, we first decouple it into separated terminal-AP association and power allocation problems. Then, we adopt the Q-learning algorithm to solve the terminal-AP association subproblem. Based on the obtained terminal-AP association solution, an iterative power allocation algorithm is developed by exploiting the Lagrange dual method. Moreover, the computational complexity of the proposed algorithm is further analyzed. Simulation results demonstrate that, compared with other schemes, our proposed algorithm can achieves a better performance in terms of the achievable sum rate, average achievable rate, and outage probability.

Optimal design-for-control of self-cleaning water distribution networks using a convex multi-start algorithm

The provision of self-cleaning velocities has been shown to reduce the risk of discolouration in water distribution networks (WDNs). Despite these findings, control implementations continue to be focused primarily on pressure and leakage management. This paper considers the control of diurnal flow velocities to maximize the self-cleaning capacity (SCC) of WDNs. We formulate a new optimal design-for-control problem where locations and operational settings of pressure control and automatic flushing valves are jointly optimized. The problem formulation includes a nonconvex objective function, nonconvex hydraulic conservation law constraints, and binary variables for modelling valve placement, resulting in a nonconvex mixed integer nonlinear programming (MINLP) optimization problem. Considering the challenges with solving nonconvex MINLP problems, we propose a heuristic algorithm which combines convex relaxations (with domain reduction), a randomization technique, and a multi-start strategy to compute feasible solutions. We evaluate the proposed algorithm on case study networks with varying size and degrees of complexity, including a large-scale operational network in the UK. The convex multi-start algorithm is shown to be a more robust solution method compared to an off-the-shelf genetic algorithm, finding good-quality feasible solutions to all design-for-control numerical experiments. Moreover, we demonstrate the implemented multi-start strategy to be a fast and scalable method for computing feasible solutions to the nonlinear SCC control problem. The proposed method extends the control capabilities and benefits of dynamically adaptive networks to improve water quality in WDNs.

Machine Learning-Based Uplink Scheduling Approaches for Mixed Traffic in Cellular Systems

The problem of the uplink resource allocation of mixed-traffic types in cellular networks is a challenging problem that has not been addressed sufficiently in the literature. In this paper, we consider the 5G uplink scheduling for Ultra-Reliable and Low Latency Communications and enhanced Mobile Broad-Band (eMBB) traffic types. There are three main scheduling techniques to be considered, namely, the grant-based (GB), the semi-persistent, and the grant-free (GF) techniques. Furthermore, there are three different schemes used in GF scheduling, namely, the reactive, the k-repetitions, and the proactive schemes. We devise a mathematical model for the GF services using the k-repetitions scheme as the first model to define such traffic in a single cell. In addition, the GB scheduling model for eMBB traffic is adapted to fit our problem. We formulate the scheduling problem as a mixed-integer non-linear programming optimization problem. We introduce a complete system model that includes GF and GB subsystems. We introduce a novel mixed scheduler that combines the advantages of two well-known schedulers in the literature. We introduce novel machine-learning-based scheduling algorithms and evaluate them in comparison to well-known algorithms in the literature in addition to the optimal bound that we also derive. The results show that the proposed algorithms produce near-optimal results in real time.

Branch and price for submodular bin packing

The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques.

Estimating and Exploiting the Impact of Photo Layout: A Structural Approach

Host-generated property images as a visual channel reveal substantial information about properties. Selecting proper images to display can lead to higher demand and increased rental revenue. In this paper, we define, estimate, and optimize the impacts of Airbnb photos on customers’ renting decisions. We apply ResNet-50, a convolutional neural network model, to build two separate, supervised learning models to evaluate the image quality and room types posted by Airbnb hosts. Then, we characterize the overall impacts of photo layout by the room type featured in the photo, photo quality, and order of display on the listings’ web pages. To address two estimation challenges in the Airbnb setting, namely, censored demand and changing consideration sets, we propose a novel pairwise comparison model that utilizes customers’ booking sequence data to consistently estimate the impact of photo layout on customers’ renting decisions. Our estimation results suggest that the cover image has a significantly larger impact than noncover photos and a high-quality bedroom cover image leads to the largest increase in demand. Furthermore, we build a nonlinear integer programming optimization problem and develop an algorithm to determine the optimal photo layout. Our counterfactual analysis suggests that a listing’s unilateral adoption of optimal photo layout leads to 11.0% more bookings on average. Moreover, depending on the neighborhood and market size, when listings simultaneously switch to the optimal photo layout, they get booked for two to five additional days in a year on average, which boosts revenue by $500 to $1,100. This paper was accepted by Swaminathan, Jayashankar, operations management. Funding: This research was partially sponsored by the MIT Data Science Lab and also benefited from generous support provided by Zalando. Supplemental Material: The online companion and data are available at https://doi.org/10.1287/mnsc.2022.4616 .

Approximate method of optimization of nonlinear programming problems

Currently, the problem of choosing the optimal solution is one of the most important and urgent problems in industry, economy, agriculture and the military sphere. Methods and approaches of the theory of nonlinear programming are used to solve many applied optimization problems. The main difficulty of nonlinear optimization is the lack of a universal method for solving this class of problems. To solve this problem, special methods are being developed for solving particular nonlinear programming problems, for example, for positive or limited initial data. The paper investigates the problem of analytical optimization of nonlinear programming problems. The purpose of this work is to develop a new approximate method for solving optimization problems of a nonlinear function under nonlinear constraints in the form of equalities. To do this, an approximation (expansion in a series) of the objective function and constraints is performed. All variables are considered bounded at the top and bottom. The objective function and constraints are considered infinitely differentiable by the set of arguments, and all their derivatives are assumed to be limited in absolute value by a given number. In this article, the theorem on the conditional maximum of the objective function under given constraints is proved. the results of which are the justification of the developed method. Since the developed optimization method is approximate, the error of the proposed representation of the objective function and constraint functions is estimated. In problems of an applied nature, the boundaries of variable changes are often set approximately and they can be adjusted. In addition, it is possible to adjust the point relative to which the functions are decomposed into series. Therefore, the article analyzes the sensitivity of the optimal solution of the problem when changing the decomposition point into a series of functions for different values of the coordinates of the left boundaries when searching for the maximum of the objective function. To explain the operation of the method, a specific numerical example is analyzed in detail. Modeling in the MS Excel environment was used to solve it. Graphs of the sensitivity study of the solution of the problem when changing the initial data are constructed. Nonlinear programming models are used, for example, to solve the following practically important issues: minimizing costs in the sale of products, optimizing consumer choice, maximizing production volume, determining the rational behavior of an individual in a given situation, rational use of resources, forming an optimal portfolio of securities.

Plantwide control design using latent variables: An integration between control allocation and a measurement combination approach

This paper presents a plantwide control design methodology based on a novel structure which consists of a decentralized strategy complemented by a control allocation (CA) module and a measurement combination (MC) block. Taking into account a principal components analysis (PCA) selection approach, the CA and MC modules perform a dimensional reduction of the original input–output variable space in order to obtain sets of latent variables (or principal components) as control actions and controlled variables. The use of principal components in the controller design provides several interesting features given that: (i) the conditioning of the subsystem to be controlled can be improved, (ii) when performing combinations of variables, the CA and MC modules act as steady-state decouplers and thus an apparently diagonal process is obtained, which favors the reduction of the variables interaction and the pairing problem is automatically solved, and (iii) they allow to naturally handle nonsquare systems. The proposed design procedure is implemented through a multiobjective bilevel mixed-integer nonlinear programming (BMINLP) optimization problem. The leader problem is based on the minimization of three functional costs: 1- the well-known sum of squared deviations (SSD) index, 2- the number of selected manipulated variables (actuators), and 3- the number of selected measurements (sensors). The inner optimization minimizes the relative gain array number (RGAN). This provides a good trade-off between the degree of conditioning/controllability and the complexity/cost of the resulting system. This problem is efficiently solved through genetic algorithms and allows to perform: (i) the selection of the manipulated variables (actuators) and the measurements (sensors) to be used, (ii) the computation of the matrices that characterize the CA and MC modules, and (iii) the stability analysis of the multivariable control structure. The overall design procedure only requires steady-state models of the process. The Tennessee Eastman case study is considered for the simulation and performance evaluation of the proposed solutions.

Two‐timescale optimization approach for coordinated multi‐point design in unmanned aerial vehicle‐assisted cellular networks

AbstractThanks to their mobility, flexibility, and adaptive altitude, unmanned aerial vehicles (UAVs) have been admitted for several applications in wireless communication systems. In particular, UAVs can function as aerial base stations (BSs) to increase cellular network capacity and provide persistent coverage. Due to the line‐of‐sight channels between UAVs and user equipments (UEs), strong co‐channel interference may be generated in the network. In this article, a joint transmission coordinated multi‐point technique is considered in the downlink cellular network to effectively manage the interference brought by UAVs. A two‐timescale optimization approach is proposed to prevent exchanging absurd messages and channel information between the transmission points. The objective of the proposed method is to maximize the sum rate of the network subject to the constraints on UEs' quality of service as well as per‐ground BS and per‐UAV total transmitted power. The proposed approach is decomposed into long‐term and short‐term problems. The long‐term problem aims to jointly optimize the UEs' clusters, the UAVs' locations, and the initial transmit beamforming vectors based on large‐scale channel gain. This problem is a mixed‐integer nonlinear programming optimization problem, which is nondeterministic polynomial hard. Meanwhile, the short‐term problem requires obtaining the transmit beamforming vectors according to the overall channel vector. This problem is also a non‐convex optimization problem. To address these challenges, two algorithms are proposed based on difference of convex functions programming and successive convex approximation technique to deal with these two problems. Extensive simulations show that the performance of the proposed approach outperforms the comparable algorithms.