Nonlinear Programming Optimization Research Articles

Economic predictive control-based sizing and energy management for grid-connected hybrid renewable energy systems

Hybrid renewable energy systems (HRES) comprise a group of different energy sources and storage units that feed a specific load, efficiently. This research paper aims to develop a new methodology that provides the optimal size of the proposed HRES and runs it efficiently. Bi-level mixed-integer nonlinear programming (BMINLP) optimization approach is used to combine the sizing task and the energy management strategy (EMS) established utilizing the economic model predictive control (EMPC) method. The sizing task (upper layer) is formulated as mixed integer nonlinear programming (MINLP) optimization that has been implemented by the solver: multi-objective genetic algorithm (MOGA). EMS task (lower layer) is represented as a constraint embedded within the upper layer and executed as mixed integer linear programming (MILP) per each applied solution of the sizing task. The principal findings indicate that the total cost of the system is about 114,224 $. In detail, the annual fixed operation and maintenance, investment, and operating costs are 15,090 $, 28,351 $, and 70,783 $, correspondingly. Furthermore, around 90 % of the overall produced power is imported from the grid, while the load power represents about 95 % of the total demanded power.

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.

False data injection in distribution system: Attacker's perspective

The distribution system is digitizing and occupying cyberspace with the help of information and communication technologies (ICTs). It is vulnerable to cyber-attacks like false data injection (FDI) and denial-of-services (DoS). However, limited research on cyber-attacks in the distribution system is reported in the literature, and these attacks are of serious concern to distribution system operators (DSOs). The DSO's primary challenge is to understand the attacker's perspective for FDI attack construction. Thus, the work presented in this paper aims to provide an in-depth insight for DSO to apprehend the attacker's perspective, attack flow, and the nature of the FDI attack vector. The prior knowledge of attack flow to DSO can help to protect critical infrastructures from cyber-attacks. Thus, this work comprehends the attacker's behaviour for deploying the optimal budget to disrupt the distribution system operation therein by injecting a stealthy FDI vector. The attacker is resource-constrained in terms of budget and network information. Therefore, the optimal budget for attack initiation is proposed and formulated as a multi-objective optimization problem to minimize the investment and maximize the economic loss for the DSO. Constructing the attack vectors for the attacker is challenging in the limited network information. It is complex because of network characteristics such as multi-phase configurations & an unbalanced nature, and higher resistance to reactance (r/x) ratio. Thus, the FDI attack vector construction is proposed based on non-linear programming optimization and sensitivity analysis considering partial information from the distribution system. The simulation results are presented and compared with available methods in the literature to validate the efficacy of the proposed methods.

OPTIMAL SINGLE-STORY STEEL BUILDINGS UNDER HIGH LOADS

This paper presents the parametric optimization of single-story steel buildings subjected to high loads. In the parametric study, high loads of snow and wind are determined for different altitudes up to 3000 meters above sea level. The Alpine region and the Eurocode 1 standard are considered. The discrete mixed-integer non-linear programming optimization is performed for different altitude alternatives. The optimization model for the steel structure is developed and used. The mass objective function of the structure is subjected to dimensioning and deflection constraints defined by the Eurocode standards. The modified outer-approximation and equality-relaxation algorithm is applied. The optimal results obtained include the minimal possible mass of the structure, the optimal topology, the steel sections and the steel grade. In the case of a medium-sized single-story steel building, it was found that the structural mass increases by 2.7 times and the number of main portal frames increases by 80 % when the altitude of the building site is increased from 500 to 3000 meters above sea level. The optimal results clearly show how the structural mass and cross-sections increase with increasing load.

Multiple objectives dynamic VM placement for application service availability in cloud networks

Ensuring application service availability is a critical aspect of delivering quality cloud computing services. However, placing virtual machines (VMs) on computing servers to provision these services can present significant challenges, particularly in terms of meeting the requirements of application service providers. In this paper, we present a framework that addresses the NP-hard dynamic VM placement problem in order to optimize application availability in cloud computing paradigm. The problem is modeled as an integer nonlinear programming (INLP) optimization with multiple objectives and constraints. The framework comprises three major modules that use optimization methods and algorithms to determine the most effective VM placement strategy in cases of application deployment, failure, and scaling. Our primary goals are to minimize power consumption, resource waste, and server failures while also ensuring that application availability requirements are met. We compare our proposed heuristic VM placement solution with three related algorithms from the literature and find that it outperforms them in several key areas. Our solution is able to admit more applications, reduce power consumption, and increase CPU and RAM utilization of the servers. Moreover, we use a deep learning method that has high accuracy and low error loss to predict application task failures, allowing for proactive protection actions to reduce service outage. Overall, our framework provides a comprehensive solution by optimizing dynamic VM placement. Therefore, the framework can improve the quality of cloud computing services and enhance the experience for users.

Mathematical Program with Vanishing Constraints for Optimal Pressure Control in Water Distribution Systems

Optimizing pressure management to reduce water leakage in water distribution systems (WDSs) is one of the major tasks for water utilities. By regulating the operation of pressure reducing valves (PRVs) installed in WDSs, the pressure in WDSs can be kept under control and thus the water leakage amount can be decreased. Mathematically, the problem of pressure management to water leakage reduction can be formulated as a nonlinear optimization program. To make the optimization model proper for practice, the model of PRVs should be accurate and can describe all its operation modes in practice: active, fully opened, and check valve modes. In the literature, the model can be represented either by a non-smooth equation with low accuracy or by several complicated constraints. This research developed a highly accurate PRV model based on vanishing constraints. The idea comes from the fact that the model equation representing operations of PRVs in active mode will be vanished as PRVs operate in the check valve mode. The formulated mathematical program with vanishing constraints (MPVCs) can be solved efficiently by using the regularization approach. Several WDSs have evaluated the new PRV model which shows that accurate solutions are obtained with less computation time.

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.

Exploring optimal pathways of the high-CO2 content natural gas source to chemicals and fuels using superstructure multi-objective optimization

This study aims to develop a mathematical formulation of superstructure multi-objective optimization to find optimal pathways of high-CO2 natural gas and PV-hydrogen to chemicals and fuels integrated with CO2 sequestration. A mixed-integer nonlinear programming optimization model is used to compete along 56 pathways in the superstructure optimization network. The model was developed with the general algebraic modeling system and computed with the standard branch and bound (SBB) solver to maximize annual net profit and minimize annual net CO2 emissions. The result shows the selected products in 2020 are liquefied natural gas, methanol, dimethyl ether, formic acid, and acetic acid, with annual net profits and net CO2 emissions of 38.17 million $/year and −8.47 million tons of CO2/year, respectively. In the projection analysis, the annual net profit growth results at a compounding annual growth rate of 7.85% per year between 2020 and 2060, while annual net CO2 emissions decrease until −16.37 million tons of CO2/year in 2060. In 2030, blue acetic acid will be selected via all separation processes. For 2050, the synfuel via partial membrane separation is selected. The other products, formic acid, methanol, and acetic acid via membrane separation (full and partial), will always be selected between 2020 and 2060. Therefore, this could be a future strategy for monetizing high–CO2–content natural gas sources with low-carbon process development.

Global optimization of mixed-integer nonlinear programs with SCIP 8

AbstractFor over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

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.

Polyethylene gasification for sustainable plastic waste management with respect to energy, exergy, and environmental considerations: A non-linear programming optimization

Plastic waste poses a significant threat to the environment and plays a substantial role in contributing to climate change. One possible solution for addressing the issue of plastic waste is through plastic waste gasification, which involves converting plastic waste into a valuable gas that can be utilized as an energy source. Numerous reports have investigated the optimization procedures for converting plastic waste into syngas. Nevertheless, all of these reports have concentrated on improving the performance of the gasification process by adjusting processing variables, and none have examined how to optimize plastic waste gasification performance considering material characteristics. To improve the efficiency of polyethylene gasification, this research was undertaken with a focus on energy, exergy, and environmental factors in relation to the material conditions. Various regression models were created to forecast the energy, exergy, and environmental aspects of polyethylene gasification based on material characteristics. These models were then optimized using a general algebraic modeling system. The results indicate that the ideal conditions consist of 84.40 % carbon content, 15 % hydrogen content, and no oxygen or nitrogen content. The optimal criteria include an energy efficiency of 65.9 %, an exergy efficiency of 81.5 %, and an emission level of 28.0 kg/MWh.

Integrating reaction pathways and downstream separation network for optimal sustainable process route selection

Reducing the environmental impact of chemical production has become a critical objective due to carbon emission regulations and the challenges the carbon market poses. Downstream separation network optimization, which can improve process sustainability by using complex heat exchanger networks, applying advanced separation techniques, optimizing the design/operating parameters, etc., has been researched for many years. However, most optimization work focuses solely on downstream separation sections without considering the selection of raw materials and different reaction pathways. This work aims to develop a mixed integer nonlinear programming (MINLP) optimization model, which integrates reaction pathway selection and downstream separation optimization, to select the optimal sustainable process route for utilizing raw materials or producing products. The objective is to maximize/minimize the process profit/cost. Decision variables such as binary variables, which represent the selection of separation task, key component, heating utility, and continuous variables, which influence the separation mass/energy balance, are considered. By giving parameters like reaction conversion rate, selectivity, and raw material/product price, this optimization model can identify the optimal process route for producing a target product or utilizing a raw material. The optimization model was applied to two case studies: one-step isobutylene and methanol utilization and two-step 1,4-butanediol (BDO) production. The process routes, using isobutylene for pivalic acid production and methanol for gasoline production, have the highest process profit per carbon emission. And the process route, which uses acetylene for BDO production, leads to minimum process cost.

Mixed integer programming with kriging surrogate model technique for dispersion control of photonic crystal fibers

In this paper, mixed integer nonlinear programming (MINLP) optimization algorithm integrated with kriging surrogate-model is newly formulated to optimize the dispersion characteristics of photonic crystal fibers (PCFs). The MINLP is linked with full vectorial finite difference method (FVFDM) to optimize the modal properties of the PCFs. Through the optimization process, the design parameters can take real and/or integer values. The integer values can be used to selectively fill the PCF air holes to control its dispersion characteristics. However, the other optimization techniques deal with real design parameters where the PCF can be optimized using none or predefined infiltrated air holes. The MINLP algorithm is used to obtain an ultra-flat zero dispersion over a broadband of wavelength range from 1.25 to 1.6 μm using silica PCF selectively infiltrated with Ethanol material. To show the superiority of the proposed algorithm, nematic liquid crystal selectively infiltrated PCFs are also designed with high negative flat dispersion over wide range of wavelengths from 1.25 to 1.6 μm for the quasi transverse magnetic (TM) and the quasi transverse electric (TE) modes. Such designs have negative flat dispersions of − 163 ± 0.9 and − 170 ± 1.2 ps/Km nm, respectively over the studied wavelength range. Therefore, the MINLP algorithms could be used efficiently for the design and optimization of selectively filled photonic devices.

Enhancing energy efficiency and comfort with a multi-domain approach: Development of a novel human thermoregulatory model for occupant-centric control

Occupant Centric Control (OCC) strategies aims to achieve a more personalized and comfortable indoor environment, translating occupants' comfort requirements into real environmental conditions. This strategy relies on a multilevel non-linear programming optimization procedure to determine optimal thermo-hygrometric setpoints. The objective is to minimize space heating and cooling requirements while addressing multi-domain comfort concerns related to individual thermal sensations and perceived air quality. To facilitate this process, this study adopts a novel Personal Comfort Model (PCM), incorporating physiological factors to predict occupants' thermal sensations and CO2 intakes. The PCM's reliable predictive capabilities are confirmed through validation with real experimental data from a test room at the University of Perugia. For detailed energy analyses, considering occupants' subjective comfort preferences, the PCM is seamlessly integrated into DETECt, an in-house building energy performance simulation tool developed by the University of Naples Federico II, for the design of advanced control algorithms and energy efficiency strategies. To effectively manage the HVAC system, a model predictive control is implemented, using the determined setpoints to ensure mechanical ventilation and maximize cost savings. The proof of concept for the developed methodology involves simulating experimental tests using the thermal model of the human body and the new facility management system, to be simulated and optimized by means of the enhanced building energy performance simulation tool, exploited for the design and operation of more occupant-centric and sustainable buildings. The proposed study demonstrates that through the developed OCC strategy enables a significant reduction in thermal discomfort (40 % and 60 % less than the occupation time for test 1 and test 2, respectively) compared to reference scenarios. Additionally, energy analysis reveals high efficiency, achieving savings of 12.8 % and 7.8 % of electricity consumed for HVAC system operation.

Train rescheduling and platforming in large high-speed railway stations

To deal with train delays in large high-speed railway stations, a multi-objective mixed-integer nonlinear programming (MO-MINLP) optimization model was proposed. The model used the arrival time, departure time, track occupation, and route selection as the decision variables and fully considered the station infrastructure layout, train operational requirements, and time standards as limiting factors. The optimization objective was to minimize train delays and reduce track and route adjustments. To realize the large-scale and rapid solution of the MO-MINLP model, this study proposed a rolling horizon optimization algorithm that used “half an hour” as a time interval and solved the rescheduling and platforming problem of each time interval step-by-step. In numerical experiments, 227 train movements under delay circumstances in Hangzhoudong station were optimized by using the proposed model and solution algorithm. The results show that the proposed MO-MINLP model could resolve route conflicts, compress unnecessary dwell times, and reduce train delays; the solution algorithm could efficiently increase the computational speed. The maximum solution time for optimizing the 227 train movements is 15 min 24 s.

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.

A second-order conic approximation to solving the optimal power flow problem in bipolar DC networks while considering a high penetration of distributed energy resources

This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language.

Strategic investment planning for the hydrogen economy – A mixed integer non-linear framework for the development and capacity expansion of hydrogen supply chain networks

This work presents a novel Mixed-Integer Nonlinear Programming (MINLP) modeling and optimization framework for the investment planning of large-scale hydrogen economy envelopes. The scope of the model includes the design, synthesis, and long-term capacity expansion of hydrogen supply chain networks (HSCN) that include hydrogen production, purification, storage, transportation, and distribution, subject to environmental sustainability considerations. Production and carbon capture units are represented using surrogate models derived from rigorous simulations to capture important process non-linearities. This framework provides an optimal roadmap for the 10-year plan of hydrogen infrastructure development in the state of California, that demonstrates the important trade-offs between investment decisions, economic incentives, and regulatory carbon emissions constraints. It is shown that the development of the hydrogen production and distribution networks can be achieved over a 10-year horizon in an economically profitable way, while achieving a 90 % reduction in carbon emissions and satisfying all state regulatory mandates.