Nonlinear Optimization Model Research Articles

Optimal allocation of agricultural water and land resources integrated with virtual water trade: A perspective on spatial virtual water coordination

Agricultural production consumes the majority of global freshwater resources. The worsening water scarcity has imposed significant stress on agricultural production when regions seek food self-sufficiency. To seek optimal allocation of spatial agricultural water and land resources in each water function zone of the objective region, a multi-objective optimization model was developed to tackle the trade-offs between the water-saving objective and the economic benefit objective considering virtual water trade (VWT). The cultivated area of each crop in each water function zone was taken into account as the decision variable, while a set of strong constraints were used to restrict land resources and water availability. Then, a decomposition-simplex method aggregation algorithm (DSMA) was proposed to solve this nonlinear, bounding-constrained, and multi-objective optimization model. Based on the quantitative analysis of the spatial blue and green virtual water in each agricultural product, the proposed methodology was applied to a real-world, provincial-scale region in China (i.e., Jiangsu Province). The optimized results provided 18 Pareto solutions to reallocate the land resources in the 21 IV-level water function zones of Jiangsu Province, considering four major rainy-season crops and two dry-season crops. Compared to the actual scenario, the superior scheme increased by 7.95% (5.6 × 109 RMB) for economic trade and decreased by 1.77% (2.0 × 109 m3) for agricultural water consumption. It was mainly because the potential of spatial blue and green virtual water in Jiangsu was fully exploited by improving spatial land resource allocation. The food security of Jiangsu could be guaranteed by achieving self-sufficiency in the superior scheme, and the total VWT in the optimal scheme was 2.2 times more than the actual scenario. The results provided a systematic decision-support methodology from the perspective of spatial virtual water coordination, yet, the methodology is widely applicable.

Joint Optimal Train Rescheduling and Passenger Flow Control for Speed Limit and High-Demand Scenarios of Urban Rail Transits

In the operation of urban rail transits, train delays occur frequently, and emergency management is one of the key factors to ensure the service quality. For speed limit scenarios with high demand, this paper takes the train running in the restricted manual (RM) mode in the speed limit zone as an example and discusses a coping method by jointing train rescheduling and passenger flow control. With the goal of maximizing the number of passengers served and minimizing total train delay, a nonlinear optimization model is constructed by taking the train operation-related requirements and passenger flow control-related indicators as constraints, and the model is reformulated to a mixed-integer programming (MIP) model with quadratic constraints, which can be solved by the Gurobi solver. In order to obtain effective solutions faster, a two-stage approach is discussed, which first obtains a rescheduling timetable and then dynamically adjusts the requirement of boarding equalization to obtain the passenger flow control scheme. The validity of the model and the solution approach are discussed with the help of numerical experiments. The results suggest that the model and solution approach are feasible. When the number of trains is fixed, the reasonable implementation of passenger flow control will help to increase the number of passengers served, and the pursuit of a higher equalization of boarding is not conducive to the number of passengers served and the full utilization of transport capacity. The two-stage approach has certain advantages over the direct computing method. The methods in this paper have a guiding value for emergency decision-making in similar delay scenarios.

RETRACTED ARTICLE: Sustainable regional rail system pricing using a machine learning-based optimization approach

AbstractRegional transport pricing is indeed very vital in urban settings where the transportation network is spread out across large areas and can influence travel behavior and the sustainability of cities. Therefore, in addition to existing pricing systems, such as flat fare, distance-based fare, and zonal pricing, this study proposes a sustainable approach to regional rail system pricing using rent prices and a transportation affordability index. The proposed model aims to reduce commuters' overall travel distance in order to reduce air pollution and maintenance costs for public transportation vehicles. Rent-based pricing encourages people to rent houses in regions that shorten their travel distances and fill a gap in the literature on regional rail system pricing by dealing with the decentralization of the cities. A two-step clustering and non-linear optimization modeling approach are proposed based on face-to-face surveys with regional rail system passengers. For various clusters of stations, rent per income rates and rental-based ticket prices were obtained. Furthermore, a sensitivity analysis is conducted to evaluate different conditions of the affordability index and rent prices in the studied regions. Compared to the current pricing system, ticket revenues increased by 3.88% and 1.68% in rent-based pricing.

Learning and forgetting interactions within a collaborative human-centric manufacturing network

Learning and forgetting (LaF) phenomena are characteristic of labor-intensive production and service industries. To mitigate the effects of LaF in a human-centric manufacturing system integrated with outsourcing, managers need to coordinate their decisions with partners for assigning operations and scheduling processes following a hierarchy. A model that addresses this should consider the expected latency of various tasks across assignments and production sequences and similarities among jobs as that affects learning. This paper develops a novel bi-level LaF model to help determine the leader-follower decisions in a decentralized network. It models the learning concept as a factor of task execution order and task variety. The mixed-integer non-linear optimization model determines the best order coordination and scheduling scheme by minimizing the processing, operating, and holding costs and penalties for missing deadlines. This study also develops an efficient column-and-constraint generation algorithm based on the duplication method, which enables solving bi-level models in which the lower-level model includes integer variables. This study also provides an illustrative real-sized example to validate the model and prove the efficiency of our resolution method. The results indicate that adopting compromise solutions enables preoccupied workers to be released earlier than expected, reducing the costs associated with learning and forgetting (due to latency). Despite the effects of LaF and the decentralized structure of the supply chain, which includes rising network costs, the schedules become more precise, and the cost balance among actors effectively increases.

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method.

Operation Optimization Adapting to Active Distribution Networks Under Three-Phase Unbalanced Conditions: Parametric Linear Relaxation Programming

Asymmetric phase distributed generation, which is widely used in distribution systems, aggravates the severity of the intrinsic three-phase unbalanced condition of distribution systems. To overcome these problems, operation optimization formulas of the three-phase unbalanced active distribution network (ADN) are established considering soft open point (SOP) and belong to a nonconvex quadratic programming (NQP) problem. However, in conventional methods, either approximations that are not valid for an unbalanced distribution system are used or convex relaxation methods are applied to primitive nonlinear optimization models. However, these methods do not guarantee a feasible optimization solution. Therefore, determining the solution to the NQP problem is challenging. In this article, we propose a parametric linear relaxation algorithm to obtain the optimal feasible solution by solving the operation optimization problem of the three-phase unbalanced ADN with the SOP. The parametric linear relaxation technique is constructed based on the properties of quadratic functions and the mean value theorem, and the NQP is converted to a series of parametric linear relaxation programming problems. The results revealed that the proposed algorithm can achieve the optimal and feasible solution and considerably reduce the computation time compared with an equivalent NLP optimization model for the same distribution system.

Research on Pilot Control Strategy and Workload for Tilt-Rotor Aircraft Conversion Procedure

This paper studies the pilot control strategy and workload of a tilt-rotor aircraft dynamic conversion procedure between helicopter mode and fixed-wing mode. A nonlinear flight dynamics model of tilt-rotor aircraft with full flight modes is established. On this basis, a nonlinear optimal control model of dynamic conversion is constructed, considering factors such as conversion corridor limitations, pilot control, flight attitude, engine rated power, and wing stall effects. To assess pilot workload, an analytical method based on wavelet transform is proposed, which examines the mapping relationship between pilot control input amplitude, constituent frequencies, and control tasks. By integrating the nonlinear optimal control model and the pilot workload evaluation method, an analysis of the pilot control strategy and workload during the conversion procedure is conducted, leading to the identification of strategies to reduce pilot workload. The results indicate that incorporating the item of pilot workload in the performance index results in a notable reduction in the magnitude of collective stick inputs and longitudinal stick inputs. Moreover, it facilitates smoother adjustments in altitude and pitch attitude. Additionally, the conversion of the engine nacelle can be achieved at a lower and constant angular velocity. In summary, the conversion and reconversion procedures are estimated to have a low workload (level 1~2), with relatively simple and easy manipulation for the pilot.

Approximating Linear Programming by Geometric Programming and Its Application to Urban Planning

In this study, we approximated linear programming by geometric programming; the developed method converts linear programming to geometric programming. We applied the developed method to Neighbourhood planning, a vital aspect of urban planning, and obtained the optimal cost of Neighbourhood designs. The method demonstrated that geometric programming is a robust non-linear optimization model that can be extended to approximate linear optimization problems. This method has obvious advantages in the sense that it allows every decision variable to contribute to the optimal objective function. This is not the case with the known regular Simplex method and the Interior Point Algorithm of solution to linear programming which assign zeros to some variables when the matrix of the non-basic variables is rectangular or when some of the non-basic variables did not enter the basis. The developed method was used to find the global optimal solution, optimal primal and dual decision variables. The solution was better compared to the linear programming method via Simplex method or Interior Point Algorithm because it achieved the global optimal solution. We observed that in addition to achieving the global optimal solution, we obtained the optimal dual decision variables which was absent in the other methods and all the primal decision variables have value against the other methods that assigned some of the variables with zeroes.

Modeling a Carbon-Efficient Road–Rail Intermodal Routing Problem with Soft Time Windows in a Time-Dependent and Fuzzy Environment by Chance-Constrained Programming

This study explores a road–rail intermodal routing problem. To improve the carbon efficiency of transportation, reducing CO2 emissions is considered by the routing. Soft time windows are incorporated into the routing to optimize the timeliness of the first-mile pickup and last-mile delivery services in intermodal transportation. The routing is further modeled in a time-dependent and fuzzy environment where the average truck speeds of the road depend on the truck departure times and are simultaneously considered fuzzy along with rail capacities. The fuzzy truck speed leads to the fuzziness of three aspects, including speed-dependent CO2 emissions of the road, a timetable-constrained transfer process from road to rail, and delivery time window violation. This study formulates the routing problem under the above considerations and carbon tax regulation as a combination of transportation path planning problem and truck departure time and speed matching problem. A fuzzy nonlinear optimization model is then established for the proposed routing problem. Furthermore, chance-constrained programming with general fuzzy measure is used to conduct the defuzzification of the model to make the problem solvable, and linearization techniques are adopted to linearize the model to enhance the efficiency of problem-solving. Finally, this study presents an empirical case to demonstrate the effectiveness of the designed approach. This case study evaluates the performance of carbon tax regulation by comparing it with multi-objective optimization. It also focuses on sensitivity analysis to discuss the influence of the optimistic–pessimistic parameter and confidence level on the optimization results. Several managerial insights are revealed based on the case study.

Studying the effects of Türkiye earthquake disaster and its impact on real estate industry: A risk analysis based on input-output & non-linear optimization models

The real estate industry of Türkiye is highly susceptible to seismic activity. The recent earthquakes have severely impacted the industry and the country's economy. This study examines Türkiye's real estate resilience during earthquakes using the Dynamic Inoperability Input-Output Model (DIIM) and a non-linear optimization technique. According to the findings of DIIM, specific industries, including those dealing with the supply of electricity and gas, chemicals, non-metallic minerals, and financial and insurance intermediaries, suffer significant financial losses. The levels of inoperability are highest in the mining and quarrying industries, followed by the chemical and non-metallic mineral product industries, and then by mining support activities. The top nine most inoperable industries account for approximately $9.5 billion in economic losses, with real estate alone accounting for $27.4 billion. The Fuzzy-FUCOM technique was used to identify significant risk factors related to technological, political, and social hazards, assisting policymakers in making more informed decisions. The novelty of this study is in its application of the DIIM model and a non-linear optimization technique to the challenge of seismic hazard mitigation in Türkiye's real estate market. In conclusion, this study's findings provide insight into Türkiye's affected sectors' risks, recovery time, and adaptability.

A method for economic expansion planning of transmission networks using heuristic rules and non-linear optimization model

A method for economic expansion planning of transmission networks using heuristic rules and non-linear optimization model

Carbon footprint of residents' online consumption in China

Although China boasts the largest online consumption market, there has been no prior case study addressing the carbon footprint of online consumption. The rapid expansion of online consumption has posed a challenge to China's carbon neutrality pledge. This paper aims to fill this crucial gap by conducting a pioneering study based on survey data collected from 6000 households. To achieve this goal, this study has combined provincial Multi-Regional Input-Output (MRIO) tables with residents' online consumption calculated by the Non-Linear Optimization model, and applied the Environmental Input-Output Life Cycle Assessment (EIO-LCA) model to calculate the carbon footprint of residents' online consumption. Result indicated that the average carbon footprint of residents' online consumption was 0.46 tCO2e in 2016, accounting for 12.30% of the total consumption carbon footprint. Notably, high-emission regions include Beijing-Tianjin, Jiangsu-Zhejiang-Shanghai, and Hubei. Moreover, the dominant sources of the online consumption carbon footprint were electricity, food, clothing, and beauty products. Furthermore, we found that the carbon footprint of online consumption tends to increase with income, with differential income elasticities observed for various products and income groups. We also quantified the average expenditure-based life-cycle carbon coefficient for parcel delivery (0.22 kgCO2e/yuan) and conducted two scenario analyses to assess its impact. From a policy perspective, our research on measuring the carbon footprint of residents' online consumption can provide valuable insights for designing future policies and decisions related to e-commerce and key sectors along the supply chains. Additionally, it will further encourage Chinese residents to adopt low-carbon lifestyles.

Strong Tracking UKF-Based Hybrid Algorithm and Its Application to Initial Alignment of Rotating SINS With Large Misalignment Angles

In this paper, the fast and precise initial alignment of the low-cost rotary strapdown inertial navigation system under mooring conditions is investigated. The unscented Kalman filter (UKF) is used to address model nonlinearity and to achieve fast alignment for large misalignment angles. A generalized multi-fading strong tracking UKF (GSTUKF) is proposed to effectively compensate for the kinematic model errors caused by mooring and rotary motions. The performance of the standard strong tracking UKF cannot be optimal because only a portion of the fading factors associated with the directly observable state variables can be obtained approximately using the analytical method. By contrast, using the iteration method to calculate the full-dimension fading factors precisely, the GSTUKF has greater robustness and adaptability. To find out the optimal fading factors in real time, the multivariate nonlinear optimization model is first designed, and then the iteration approach based on a hybrid algorithm consisting of particle swarm optimization and beetle antennae search is developed, which has no risk of falling into a local minimum. Simulations and experiments are conducted to validate the GSTUKF's effectiveness. The experiments demonstrate that the proposed method reduces the yaw error by 47.2% compared with the standard strong tracking UKF.

A Calibration Algorithm of 3-D Laser Scanner Based on KMPE Loss Function

Aiming at solving the estimation problem of measurement model parameters of 3D laser scanner, a kernel mean p-power error (KMPE) loss function-based calibration algorithm is proposed in this paper. The KMPE loss function is robust to measurement noise and outliers. Thus, a KMPE loss function-based nonlinear optimization model of measurement model parameters of 3D laser scanner is firstly established according to the distance constraint between each laser scanning point on the calibration sphere and the center of the calibration sphere. Then, to conduct calibration of the model parameters, the optimization model is solved by combining the success-history based parameter adaptation for differential evolution (SHADE) algorithm with the Levenberg-Marquardt (LM) algorithm. Experimental results show that the proposed algorithm can achieve high calibration accuracy of the measurement model parameters of the 3D laser scanner by effectively suppressing the influence of measurement noise and outliers.

A multi-objective solution framework for the assembly inventory routing problem considering supply risk and carbon offset policies

This study aims to provide novel insights into the multi-objective optimisation of an inbound assembly inventory routing problem (IRP) by considering customer demand uncertainty, stochastic supply failure risks, and a carbon offset policy. An inbound IRP network generally comprises several geographically dispersed suppliers, vehicle depots, and assembly plants. In this study, a new mixed-integer nonlinear optimisation model is formulated considering two objective functions: (i) minimising the total supply network cost and (ii) maximising a low-risk supplier priority function with practical constraints. A hybrid non-dominated sorting genetic algorithm-II was developed to obtain near-optimal Pareto solutions for various small, medium, and large IRP instances. The Pareto solutions were compared with the efficient solution obtained using the ε-constraint method. Finally, the best Pareto solution was obtained using the multi-criteria decision-making technique. The results indicate that implementing supply risk-mitigation strategies leads to higher overall supply network costs and carbon emissions. However, a sensitivity analysis based on factorial simulation experiments indicates that a supply risk-mitigation strategy is advantageous if component prices are low and supply capacity, fuel price, and demand variations are high. In addition, the lower the demand variation, the lower the expected overall network cost and carbon emissions.

Uncertainty analysis and optimization of laser thermal pain treatment

Uncertainty in operating parameters during laser thermal pain treatment can yield unreliable results. To ensure reliability and effectiveness, we performed uncertainty analysis and optimization on these parameters. Firstly, we conducted univariate analysis to identify significant operational parameters. Next, an agent model using RBNN regression determined the relationship between these parameters, the constraint function, and the target function. Using interval uncertainty analysis, we obtained confidence distributions and established a nonlinear interval optimization model. Introducing RPDI transformed the model into a deterministic optimization approach. Solving this with a genetic algorithm yielded an optimal solution. The results demonstrate that this solution significantly enhances treatment efficacy while ensuring temperature control stability and reliability. Accounting for parameter uncertainties is crucial for achieving dependable and effective laser thermal pain treatment. These findings have important implications for advancing the clinical application of this treatment and enhancing patient outcomes.

Long-term planning of wind and solar power considering the technology readiness level under China's decarbonization strategy

To address climate change, the Chinese government has committed to achieving carbon peaking by 2030. Projecting the wind power and photovoltaic installed capacity is essential for China's low carbon transition as these renewables have been widely recognized as the major energy sources in future. This study proposes a long-term strategic planning approach for wind power and photovoltaic by simulating multiple policies and market scenarios for the national-level energy transitions and incorporating the feedback effects of market development on technology readiness level. The proposed approach simulates the national energy consumption and energy mix under various transition scenarios based on the Long-range Energy Alternatives Planning System (LEAP). The dynamics of market development, technology readiness level, and future renewable costs are further incorporated into a nonlinear optimization model to generate economically optimal planning solutions for wind power and photovoltaic under different policy and market scenarios. Valuable insights are obtained from three perspectives, i.e., (1) the economic and emission reduction co-benefits under different scenarios, (2) the evolution of the Levelized Cost of Energy, and (3) the impact on the transition of power sector. In particular, the simulation and optimization results reveal that appropriate acceleration of wind power and photovoltaic development can promote technology readiness level, reduce overall transition costs, and effectively reduce the peak value of emissions. The maximum peak reduction in carbon dioxide emissions is 16.06%, and the maximum cumulative reduction in carbon dioxide emissions is 14.54%. The total project cost can be reduced by a maximum of 3.23%. Thus, more active supporting policies for renewables can further enhance long-term economic and environmental co-benefits under current conditions.

A non-linear optimal control model for illicit drug use and terrorism dynamics in developing countries with time-dependent control variables

The burden of illicit drug use and terrorism has become a significant health and social problem in many developing countries. Illicit drug use and terrorism have negatively affected the economy and development of some nations because the death rate due to these two phenomena is increasing daily, particularly among the young generation. Implementing preventive and control measures for illicit drug use and terrorism requires considerable government spending. This study aims to formulate and critically examine a non-linear optimal control problem based on an existing non-linear compartmental model of illicit drug use and terrorism dynamics. The existing seven-dimensional deterministic model is modified to capture four time-dependent control variables denoting public awareness, empowerment rate, detention rate of illicit drug users, and rehabilitation rate of illicit drug users. The non-linear optimal control model is rigorously analyzed to explicitly prove its existence and characterize the optimal control quadruple using optimal control theory. Effects of different combinations of at least two control variables in minimizing illicit drug use and terrorism are evaluated through simulations. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy required for preventing and controlling the burden of illicit drug use and terrorism with limited resources in the population.

Nested loop approach for topology and shape optimization of crash-loaded deep-drawn components using contact forces for the inner loops

In this paper a new method for the optimization of deep-drawn shell components in crash by using substitute load cases in established sensitivity based static optimization is presented. The optimization process is split into an inner and an outer loop. In the outer loop the contact forces during crash are determined. These contact forces are used as substitute load cases in a static topology optimization, which builds the inner loop of the method. The presented method was inspired by the Equivalent Static Loads Method, but differs primarily in two aspects. These are the use of the contact forces as alternative to equivalent static loads in the linear static topology optimization and the extraction of a shell model that represents the voxel result obtained from topology optimization. A manufacturing constraint is applied in the topology optimization so that the results are shell components. This manufacturing constraint is enabling the mentioned extraction of a shell model. Two examples are presented where the method is applied to minimize the intrusion. The first example is a cantilever, the second example is a structure that is twisted. In both examples a rigid body impacts the structure. The method has shown to be numerical stable and suitable for the shown examples when the intrusion is the objective of the optimization. The intrusion was reduced significantly in both examples. The key novelty of the presented method is the ability to perform a static topology optimization of a voxel design space for a non-linear dynamic optimization model with the result being a shell model that can be analyzed for crash.

Negative carbon optimal scheduling of integrated energy system using a non-dominant sorting genetic algorithm

An integrated energy system, as a system where multiple energy sources coexist, is important for achieving energy conservation and emission reduction and upgrading the energy structure. In this study, a regional integrated energy system capable of absorbing CO2 emissions is proposed. The system can absorb 38.24% of the CO2 generated in the system by using the alkaline solution produced by electrolysis of water for hydrogen production. At the same time, the system can recover the waste heat generated by electrolysis of water and fuel cells, which can meet 42.42% of the heat demand. In order to better achieve efficient utilization between energy sources of the integrated energy system, a nonlinear mixed integer dynamic scheduling optimization model is constructed with multiple objectives of minimizing economic operating costs, CO2 emissions, and energy consumption. The model is solved using a non-dominated ranking genetic algorithm, and the optimal scheduling scheme is determined by combining compromise schemes. Meanwhile, the system can spontaneously select the most appropriate scheduling strategy based on the proposed scheduling model. The results show that it saves 7.23% of operation cost, 33.04% of CO2 emission, and 9.94% of energy consumption compared with the conventional cooling, heating, and power triple-supply system. The system is not only a stable source of energy such as electricity and hydrogen, but also achieves energy saving and emission reduction.