Nonlinear Programming Optimization Research Articles

Water Resources Quality Indicators Monitoring by Nonlinear Programming and Simulated Annealing Optimization with Ensemble Learning Approaches

Water Resources Quality Indicators Monitoring by Nonlinear Programming and Simulated Annealing Optimization with Ensemble Learning Approaches

Optimization of transport sustainability index to conserve resources: A case study of Delhi, India

The objective of the study is to propose a methodology for optimization of Transport Sustainability Index (TSI) of National Capital Territory (NCT) of Delhi since maximum value of TSI i.e. 1.0 will occur when all the sustainability indicators attain their extremum values simultaneously, which is highly improbable. TSI is estimated using 29 most appropriate transport sustainability indicators under four pillars of sustainability, viz. environmental, social, economic, and technological. Optimization of TSI involves following steps, viz. identification of three independent variables, i.e. fuel consumption (X1), registered vehicles (X2) and population (X3) which influence all the indicators, data collection in respect of indicators and influencing variables for 30-year time period (from year 2000 to 2030), evolution of regression equations between indicators and influencing variables, and formulation of TSI as a multi-variate non-linear expression in terms of influencing variables, which is used for optimization. The generalized reduced gradient non-linear programming optimization technique is used to solve for the optimum values of influencing variables (X1opt, X2opt, X3opt) as 0.0988, 0.4709 & 0.0 respectively and optimum value of TSI (TSIopt) as 0.71, which is 25% higher than the TSI of 0.59 for the year 2023–24. The knowledge of optimum value of TSI would help the city transport policy planners to allocate, only that much quantum of infrastructural and financial resources so as to reach optimum rather than extremum values, which leads to potential savings or conservation of resources. An overall notional savings of 58% has been estimated by the study.

Optimization of the pipe diameters and the dynamic operation of a district heating network using a robust initialization strategy

District heating networks (DHN) are systems offering a substantial solution for the decarbonization of heat production. As these systems involve significant costs, the development of digital tools for their optimization becomes a necessity. In the literature, there is a lack of studies optimizing the sizing of the DHN while considering a dynamic operation of the system with a detailed physics. In this work, we developed a Non-Linear Programming (NLP) optimization used in a case study of a DHN where the pipe sizing and the operation are optimized with a precise modeling of the distribution network. The method of Orthogonal Collocation on Finite Elements (OCFE) was employed to discretize the partial differential equation (PDE) governing the temperature evolution in the pipes. In addition, the pressure drops were modeled using the Darcy–Weisbach equation. Three optimization criteria were used: investment cost of the pipes, operational cost, and the global cost. The optimization provided the pipe diameters that best fit each optimization criterion. Furthermore, several initializations were tested to verify if the obtained optimum was a confidence optimum and if the resolution was robust. Finally, the optimization provided a coherent response to the variation in the cost of heat production.

Inferred attractiveness gravity-based models for estimating realized access at rural hospitals

Operating obstetric units in rural America is financially challenging in part due to low birth volume. Birth volume at a hospital decreases when birthers bypass it to go to a farther hospital. Beyond financial considerations, it is important from a healthcare equity perspective for hospitals to know whether certain subgroups of birthers avoid utilizing the hospital’s services. This can better inform resource allocation decisions targeting those subgroups. In this paper, we use a nonlinear programming optimization model, inferred attractiveness gravity-based model (GBM), to estimate realized access to obstetric care at hospitals in Montana. We compare three variations of GBM and benchmark our results to a regression-based conditional logit model. Results indicate that hospital attractiveness varies across the level of obstetric care provided and depends on the subgroup of birthers considered. While all GBMs produced smaller errors for hospitals with higher birth volumes, our novel variant was more accurate for low-volume hospitals. Bootstrapping analyses and resolving the models for population subgroups indicated large variations in hospital attractiveness. Research findings contribute to new knowledge about equity in access to obstetric care, the importance of considering population heterogeneity in GBMs, and the benefit of using hospital demand-based thresholds for GBMs in rural settings.

Waste management optimization with NLP modeling and waste-to-energy in a circular economy

This work presents a methodology integrating Non-Linear Programming (NLP) for multi-objective and multi-period optimization, addressing sustainable waste management and energy conversion challenges. It integrates waste-to-energy (WtE) technologies such as Anaerobic Digestion (AD), Incineration (Inc), Gasification (Gsf), and Pyrolysis (Py), and considers thermochemical, technical, economic, and environmental considerations through rigorous non-linear functions. Using Mexico City as a case study, the model develops waste management strategies that balance environmental and economic aims, considering social impacts. A trade-off solution is proposed to address the conflict between objectives. The economical optimal solution generates 1.79M$ with 954 tons of CO2 emissions while the environmental one generates 0.91M$ and reduces emissions by 54%, where 40% is due to gasification technology. Moreover, the environmentally optimal solution, with incineration and gasification generates 9500 MWh/day and 5960 MWh/day, respectively, demonstrates the capacity of the model to support sustainable energy strategies. Finally, this work presents an adaptable framework for sustainable waste management decision-making.

Carbon-oriented energy system planning using forest carbon sink

More than 130 countries and regions have put forward various climate goals, which makes carbon-oriented energy system planning a heated topic. However, these planning studies do not consider the carbon fixation role played by forest carbon sinks (FCSs). To take advantage of the carbon fixation role of FCSs, this paper will develop a carbon-cycle integrated energy hub (CC-EH) model to quantify the economic advantages of FCSs in planning a zero-carbon energy system, where energy flow and carbon flow are both analyzed. A total planning and operating costs minimization with the constraints of CO2 emissions is proposed as a mixed integer nonlinear programming (MINLP) optimization model and the overall problem is solved based on commercial solver. The proposed model is validated by case studies on six medium to large-size cities in different geographical locations in China. Results indicate that the typical cities in China can fulfill their carbon-neutral commitments by 2060. Throughout the entire planning period, FCSs can offset up to 55.31 % of the total carbon dioxide emissions from urban energy systems. Besides, FCSs achieved by forestation will help the energy system to reduce up to 36 % of the planning cost compared to the case without using FCSs.

Core allocation to minimize total flow time in a multicore system in the presence of a processing time constraint

Data centers are a vital and fundamental infrastructure component of the cloud. The requirement to execute a large number of demanding jobs places a premium on processing capacity. Parallelizing jobs to run on multiple cores reduces execution time. However, there is a decreasing marginal benefit to using more cores, with the speedup function quantifying the achievable gains. A critical performance metric is flow time. Previous results in the literature derived closed-form expressions for the optimal allocation of cores to minimize total flow time for a power-law speedup function if all jobs are present at time 0. However, this work did not place a constraint on the makespan. For many diverse applications, fast response times are essential, and latency targets are specified to avoid adverse impacts on user experience. This paper is the first to determine the optimal core allocations for a multicore system to minimize total flow time in the presence of a completion deadline (where all jobs have the same deadline). The allocation problem is formulated as a nonlinear optimization program that is solved using the Lagrange multiplier technique. Closed-form expressions are derived for the optimal core allocations, total flow time, and makespan, which can be fitted to a specified deadline by adjusting the value of a single Lagrange multiplier. Compared to the unconstrained problem, the shortest job first property for optimal allocation is maintained; however, a number of other properties require revising and other properties are only retained in a modified form (such as the scale-free and size-dependence properties). It is found that with a completion deadline the optimal solution may contain groups of simultaneous completions. In general, all possible patterns of single- and group-completion need to be considered, producing an exponential search space. However, the paper determines analytically that the optimal completion pattern consists of a sequence of single completions followed by a single group of simultaneous completions at the end, which reduces the search space dimension to being linear. The paper validates the Lagrange multiplier approach by verifying constraint qualifications.

Optimal fare and headway for a demand adaptive paired-line hybrid transit system in a rectangular area with elastic demand

Demand adaptive paired-line hybrid transit systems that integrate fixed- and flex-route transit have emerged in the last decade and attracted increasing attention because of their potential to improve accessibility for passengers. To facilitate the operation of such a hybrid transit system, this study develops a model to determine the optimal fare and headways associated with fixed- and flex-route transit along a rectangular corridor. Compared with existing literature, the novelty of this study lies in designing the fare structure while simultaneously considering demand elasticity and passenger behaviour. A continuous approximation modelling approach is employed to derive the agency’s and travellers’ cost components. Using these, a nonlinear programming optimisation model is formulated to minimise the total user cost subject to the agency’s nonnegative revenue constraints and passengers’ route choice behaviour, which is characterised as a path-size logit model. Numerical experiments are performed using a stylised network to examine the properties of the model, in which the solution is obtained by combining a brute force method that enumerates headway and fare combinations and an iterative method that determines equilibrated passenger choices. The results show that as potential demand density increases, fare and headway fluctuate and drop, while the percentage of passengers choosing to ride on flex-route transit increases. In addition, there may be an optimal maximum offset distance, which is defined as the width of the corridor to be covered by the transit system, when the potential demand density is low, leading to minimum user cost and maximum travel demand within the service area.

Water quality constrained adjustment planning for regional breeding management with nonlinear programming model under uncertainty in Wenchang City, China

Basin water pollution caused by livestock, poultry and fish breeding is still a serious problem for remote villages, however, reliable regional breeding management programming have the potentials to improve pollution status. This paper focuses on the optimal model design and water quality analysis of the livestock, poultry and fish breeding system for Wenchang City, China. Methods of multi-objective programming (MOP), interval parameter programming (IPP), fuzzy-stochastic parameter programming (FSPP), and chance constrained programming (CCP) were incorporated into the developed model to tackle multi uncertainties described by interval values, probability distributions, fuzzy membership function. Based on the estimation of local breeding potential and current situation of surface water section, a multi-objective mixed fuzzy-stochastic nonlinear programming optimization model is presented with one-dimensional water quality model. In order to evaluate the environmental carrying capacity of livestock, poultry and fishery manure, predict its development trend and investigate the implementation effect of different emission reduction policies, this paper designs quantization system of the urban water environmental carrying capacity for the model. The results indicated that the water environment pollutant absorption capacity and carrying capacity of Wenchang city have approached the limit especially the towns in the northeast of City which limited the overall development space of the City. The modeling results are valuable for supporting the adjustment of the existing livestock, poultry and fish breeding schemes within a complicated system benefit and surface water quality situation under uncertainty.

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.

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.