Mixed-integer Nonlinear Programming Optimization Research Articles

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 the 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 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.

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.

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.

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.

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.

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.

Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO2 Emissions

District heating systems are gaining global recognition as an essential tool for reducing greenhouse gas emissions and transitioning to a low-carbon-energy future. In this context, heat pumps are becoming an important technology, providing an effective solution for improving energy efficiency and reducing the reliance on fossil fuels in heating systems. Therefore, this study is focused on the optimal selection of heat pump systems for different types of buildings considering technical, economic, environmental, and social factors. This paper proposes a novel methodology based on mixed-integer nonlinear programming and multi-objective optimization that minimizes total costs and reduces CO2 emissions for heat production and supply systems over a desired period. The methodology is applied to various building types, including renovated and unrenovated apartment buildings, schools, kindergartens, and a supermarket. The study analyzes various types of heat pumps and electric heaters for space heating and domestic hot water production. Optimization results showed that the optimal heating system includes air-to-water heat pumps and electric heaters. Furthermore, for schools and a supermarket, these systems are combined with hybrid heat pumps. The goal of making the heating system neutral in terms of CO2 emissions was achieved for eight out of eleven buildings analyzed. The most profitable investments were in the heating systems of renovated five-story and unrenovated nine-story apartment buildings due to their low energy costs (0.0831 EUR/kWh), short payback periods, and high returns on investment.

Novel Reactive Distillation Process for Cyclohexyl Acetate Production: Design, Optimization, and Control.

A side-reactor column (SRC) configuration, comprising a vacuum column coupled with atmospheric side reactors, is proposed to overcome the thermodynamic restriction in the esterification of cyclohexene with acetic acid to produce cyclohexyl acetate. Meantime, this configuration can avoid the utilization of the high-pressure steam and provide enough zone for catalyst loading. In order to obtain the minimum total annual cost (TAC), the process is optimized by a mixed-integer nonlinear programming optimization method based on the improved bat algorithm. The results indicate that the optimized SRC configuration saves about 44.81% of the TAC compared to the reactive distillation process. Based on the optimized SRC process, dynamic control is carried out. The dual-point temperature and temperature-composition control structures are proposed to reject throughput and feed composition disturbances. The dynamic performances demonstrate that the temperature-composition control structure is better in maintaining product purity.

A Superstructure Mixed-Integer Nonlinear Programming Optimization for the Optimal Processing Pathway Selection of Sludge-to-Energy Technologies

The perception of sewage sludge has increasingly changed from being a waste, which is a burden to the environment and society, to a useful resource of materials and renewable energy. There are several available technologies at different stages of maturity that aim to convert sludge to energy in the form of electricity and/or fuels. In this paper, a decision-making support tool is proposed to help in choosing the optimal pathway for the sludge-to-energy conversion from a techno-economic perspective. The conversion technologies under study are: (1) anaerobic digestion, (2) pyrolysis, (3) gasification, (4) incineration, (5) supercritical water oxidation, (6) supercritical water gasification, as well as the corresponding dewatering and drying methods for each technology. Different synergies between the available technologies are compared by the formulation of a superstructure optimization problem expressed in a mixed-integer non-linear program (MINLP) model. The applicability of the proposed model is explored via a case study for a hypothetical sludge treatment plant with a capacity of 100 tons of dry solids (tDS) per day. The model is solved via the BARON solver using GAMS software within a reasonable processing time. According to the obtained results, the fast pyrolysis technology, coupled with filter press dewatering and thermal drying as pre-treatment steps, show the most promising outcomes with the minimum treatment cost of USD 180/tDS. Fast pyrolysis converts the sludge to bio-oil, which can be used as an alternative fuel after further refining, and biochar, which can be used for soil amendment or adsorption purposes. The model parameters are subject to uncertainty that is addressed in the sensitivity analysis section of this paper. Moreover, the pyrolysis pathway shows a high degree of robustness in most of the sensitivity analysis scenarios. Meanwhile, anaerobic digestion coupled with fast pyrolysis demonstrates the best energy recovery performance upon increasing electricity prices.

OPTIMAL ENERGY CONSUMPTION AND COST PERFORMANCE SOLUTION WITH DELAY CONSTRAINTS ON FOG COMPUTING

Cloud computing plays an essential role in development of the Internet of Things, which provides data processing and storage services. Fog computing is the evolution of cloud computing, which helps provide solutions to cloud computing challenges such as latency, location awareness, and real-time mobility support. Fog computing fills the gap between the cloud and IoT devices within the close vicinity of IoT devices. So, computation, networking, storage, data management, and decision making occur along the path between the cloud and IoT devices. The automatic and intelligent management of fog node resources and achieving an effective scheduling policy in the computing model is a necessary requirement and will lead to the improvement of the overall performance of fog computing. Some optimization problems are modeled by mixed-integer nonlinear programming (MINLP). In this paper, a model, i.e. an MINLP optimization problem on fog computing, is designed. Our model has two goals: to increase Cost Performance as well as to reduce energy consumption. Cost Performance is the price, users are charged as benefit/revenue. In other words Cost Performance is defined as the ratio of the average data rate of each user to its cost. Then the exact mathematical method with the GAMS program was used to prove its logical process. In the next step, we solved the model with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing+GA (SA+GA), Teaching–Learning-Based Optimization (TLBO), Grey Wolf Optimizer (GWO), Grasshopper Optimization Algorithm (GOA), and random method. According to the TOPSIS comparison, the SA+GA method with a value of 0.23 is the best compared to other methods. Then GWO, GA, TLBO, PSO, and GOA methods are better, respectively.

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.

Energy-Efficient Resource Allocation for Short Packet Transmission in MISO Multicarrier NOMA

In this article, we investigate energy efficiency (EE) maximization of short packet transmission (SPT) in a downlink multiple-input single-output (MISO) multi-carrier non-orthogonal multiple access (MC-NOMA) communication system. We use the ratio of the effective throughput to the power as a performance metric to formulate a non-convex mixed-integer nonlinear programming (MINLP) problem. Then, a low-complexity three-step optimization framework is proposed for MINLP optimization. Under a given maximum transmit power and channel blocklength of each subcarrier, a block coordinate descent (BCD) based method is proposed to jointly optimize the power allocation coefficient, transmission rate, and transmit power within a single subcarrier. Then, we transform the subcarrier allocation problem into a weighted bipartite graph matching problem and obtain the optimal subcarrier allocation scheme using the Kuhn-Munkres (KM) algorithm. Finally, a dynamic programming (DP) method is proposed to obtain the optimal channel blocklength allocation scheme. The simulation results validate the effectiveness of the proposed three-step optimization framework and indicate that the MC-NOMA system achieves higher EE and higher effective throughput than the orthogonal frequency-division multiple access (OFDMA) system in SPT.

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.

A hybrid modified Bat Algorithm with Dynamic Spiral Method for solving mixed integer non-linear programming optimization

Most optimization problems in engineering are nonlinear, with many constraints. Consequently, finding optimal solutions to such nonlinear problems requires efficient optimization methods. Most of the methods used so far are gradient-based methods. In gradient-based methods, the objective function must be differentiable, and the search for the optimum solution usually starts with a guess-point. For multimodal objectives, the search will likely get stuck at a local optimum. Nowadays, new metaheuristic methods are being developed for solving nonlinear optimization problems. Metaheuristic methods neither require a guess-point nor a derivative of the objective function. Metaheuristic methods, called Bat Algorithm and Spiral Dynamic Method, have been developed for solving optimization problems. Each of the methods has the strength to solve the problem. We propose combining Bat Algorithm (BA) and Dynamic Spiral Method (DSM) for solving mixed integer optimization. The bat Algorithm is used for the exploration stage to find some candidate solutions. Meanwhile, the dynamic spiral method is used in local search to find the best optimum solution. The result obtained by Bat Algorithm-Dynamic Spiral Method (BA-DSM) were more effective than the standard Bat Algorithm in solving the problem.

Simultaneous identification of the number, location and release intensity of groundwater contamination sources based on simulation optimization and ensemble surrogate model

Abstract In most instances, the number, location and release intensity of groundwater contamination sources (GCSs) are all unknown. The 0-1 mixed integer nonlinear programming optimization model (0-1 MINPOM) used previously could only identify the location and release intensity for GCSs. Thus a 0-1 MINPOM was improved and applied to simultaneously identify the number, location and release history of GCSs. In addition, to reduce the time of calling the simulation model for iterative calculation, the deep belief neural network (DBNN), long short-term memory network (LSTM) and Kriging method were applied to establish an ensemble surrogate model of the simulation model to replace the simulation model for iterative calculation. The results show that compared with the three single surrogate models, the ensemble surrogate model has the highest approximation accuracy to the simulation model, and could save 99% of the calculation time when iterative calculation was performed in place of the simulation model. The improved 0-1 MINPOM could identify the number, location, and release history of GCSs simultaneously. The accuracy of identifying the number of GCSs was 100%, and the accuracies of identifying the locations and release history were above 95.12% and 83.51%, respectively.

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 noninterconnected 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.

Cost-based site and capacity optimization of multi-energy storage system in the regional integrated energy networks

The unbalance between the renewable energy sources and user loads reduces the performance improvement of regional integrated energy systems (RIES), in which the multi-energy storage system with battery and heat tank is necessarily integrated. This paper aims to optimize the sites and capacities of multi-energy storage systems in the RIES. A RIES model including renewable wind power, power distribution network, district heating network, multi-energy storage system, and heat pump to convert electricity to heat is constructed. An optimization method combining a mixed-integer nonlinear programming optimization model is proposed to minimize the comprehensive cost of RIES. The second-order cone relaxation method performs convex relaxation of the power flow constraints, and the district heat network is operated under a constant-flow-variable-temperature strategy. The original optimization model is transformed into a mixed-integer second-order cone programming problem to solve. Three solution methods, including enumeration method, improved enumeration method and genetic algorithm, are employed to determine the optimum installation locations, and they are compared in computation time and efficiency. The results demonstrate that the distributed hybrid integration of electricity and thermal energy storages improves the RIES economy by collaborating the power and heat balances and reducing the purchased electricity from the grid. By integrating the hybrid storage system, the curtailed wind is reduced by 53.9%, and the economy is improved by 13.4%.