Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (11)

Search Parameters:
Keywords = non-linear population shrinking

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 4777 KB  
Article
Nonlinear Impact of Population Shrinkage on Urban Ecological Resilience: A Threshold Effect Analysis Based on City-Level Panel Data from the Yangtze River Economic Belt, China
by Xuan Chen, Yuluan Zhao, Chunfang Zhou and Yonglong Cai
Land 2026, 15(2), 261; https://doi.org/10.3390/land15020261 - 3 Feb 2026
Viewed by 441
Abstract
In the context of rapid urbanization and demographic transition, the implications of population shrinkage for urban sustainable development have attracted increasing scholarly attention. Nevertheless, empirical evidence on the relationship between population change and urban ecological resilience remains limited. Drawing on the Pressure–State–Response (PSR) [...] Read more.
In the context of rapid urbanization and demographic transition, the implications of population shrinkage for urban sustainable development have attracted increasing scholarly attention. Nevertheless, empirical evidence on the relationship between population change and urban ecological resilience remains limited. Drawing on the Pressure–State–Response (PSR) framework, this study constructs a comprehensive indicator system to assess urban ecological resilience in 110 cities along the Yangtze River Economic Belt (YEB) over the period of 2012–2021. Furthermore, a panel threshold regression model is employed to examine the nonlinear effects of population shrinkage on urban ecological resilience. The findings indicate that urban ecological resilience exhibits an overall upward trend in YEB, characterized by pronounced spatial disparities. Eastern cities have a higher level of resilience than cities in the western region in YEB. The number of cities with shrinking populations is gradually increasing, and these shrinking cities are mainly small and medium-sized cities. The empirical results show that the impact of population shrinkage on urban ecological resilience is distinctly nonlinear, and regional economic development plays a moderating role in this nonlinear relationship. At lower levels of economic development, population shrinkage does not significantly moderate urban ecological resilience. As the economy reaches a moderate stage, population shrinkage exerts a stronger modulatory effect on ecological resilience. When economic development advances to a higher level, however, population shrinkage tends to inhibit ecological resilience. Overall, this study provides a scientific basis for the population–ecological policies tailored to local conditions and offers valuable insights to promote urban sustainable development under conditions of population shrinkage. Full article
(This article belongs to the Topic Advances in Urban Resilience for Sustainable Futures)
Show Figures

Figure 1

34 pages, 1728 KB  
Article
Time Left to Critical Climate Feedback/Loops: Annual Solar Geoengineering-PLUS, Pathways to Planetary Self-Cooling
by Alec Feinberg
Climate 2026, 14(2), 37; https://doi.org/10.3390/cli14020037 - 1 Feb 2026
Viewed by 946
Abstract
Global warming (GW) contributions from feedbacks and feedback loops are projected to rise from ≈54% (loops: 29%) in 2024 to ≈71% (loops: 50%) under faltering RCP pathways without Solar Geoengineering (SG) by about 2100. A critical threshold, RCP_Critical, defined as the point at [...] Read more.
Global warming (GW) contributions from feedbacks and feedback loops are projected to rise from ≈54% (loops: 29%) in 2024 to ≈71% (loops: 50%) under faltering RCP pathways without Solar Geoengineering (SG) by about 2100. A critical threshold, RCP_Critical, defined as the point at which feedback loops account for more than half of GW, is projected to occur between 2075 and 2125. Beyond this point, reversing warming becomes severely constrained, and climate tipping points become more likely. From these trends, an average mitigation difficulty and cost increase rate (MDCR) of ≈1.33–1.5% per year is estimated. By 2100, absent mitigation, the effort required to offset global warming would roughly double relative to today, approaching an unsustainable mitigation critical threshold. Current feedback levels may already be driving nonlinear warming behavior. These diagnostic estimates align with three key indicators: a minimum-feedback baseline from 1870, an equilibrium climate sensitivity (ECS) range of 3.1 °C–4.3 °C (potentially reached by ≈2082), and consistency with IPCC AR6 confidence bounds. In response, this study proposes Annual Solar Geoengineering-PLUS pathways (ASG+Ps) as supplemental measures. These include Earth Brightening, targeted Arctic Stratospheric Aerosol Injection (SAI), and feasible L1 Space Sunshade systems designed to reduce feedback amplification and extend mitigation timelines. The “PLUS” component refers to the use of increased mitigation levels with a focus on high-amplification regions, particularly the Arctic and the tropics, to help reverse local feedbacks and promote negative feedback loops. These moderate ASG+P pathways directly address AR6 concerns while avoiding many governance challenges of full-scale SG. ASG+Ps are less controversial and provide ≈14× stronger cooling potential per Wm−2 than Carbon Dioxide Removal (CDR), while allowing variable regional targeting. Meanwhile, RCP2.6 has already been missed, placing RCP4.5 and RCP6 at risk. In 2024, atmospheric CO2 rose by ≈23 Gt (≈3 ppm), while forest tree losses exceeded afforestation gains by 2×, yielding a 2 GtCO2 sink loss, further diminishing CDR’s effectiveness. Declines in planetary albedo since 1998 continue to amplify warming. Urbanization accounts for roughly 13% of total surface GW, affecting 60% of the population, underscoring the mitigation potential of urban Earth Brightening. New results here also show major Space Sunshading area reductions, at ≈32× less than prior flawed estimates (detailed here) and ≈1600× less under the ASG+P method, substantially improving feasibility and the importance of space agencies’ needed mitigation role. A coordinated global ASG+P strategy, supported by IPCC working groups and space agencies like NASA/SpaceX, are needed to provide a critical supplemental pathway for climate stabilization. Given the shrinking intervention window, rising MDCR, and the escalating risks to civilization, prioritizing timely work in this area is essential; the investment is minor compared to the trillions in climate financial damages that could be avoided. Full article
Show Figures

Figure 1

15 pages, 2700 KB  
Article
Research on Mobile Robot Path Planning Using Improved Whale Optimization Algorithm Integrated with Bird Navigation Mechanism
by Zhijun Guo, Tong Zhang, Hao Su, Shilei Jie, Yanan Tu and Yixuan Li
World Electr. Veh. J. 2025, 16(12), 676; https://doi.org/10.3390/wevj16120676 - 17 Dec 2025
Viewed by 470
Abstract
In order to solve the problems of slow convergence speed, insufficient accuracy, and easily falling into the local optimum of the traditional whale optimization algorithm (WOA) in mobile robot path planning, an improved whale optimization algorithm (IWOA) combined with the bird navigation mechanism [...] Read more.
In order to solve the problems of slow convergence speed, insufficient accuracy, and easily falling into the local optimum of the traditional whale optimization algorithm (WOA) in mobile robot path planning, an improved whale optimization algorithm (IWOA) combined with the bird navigation mechanism was proposed. Specific improvement measures include using logical chaos mapping to initialize the population to enhance the randomness and diversity of the initial solution, designing a nonlinear convergence factor to prevent the algorithm from prematurely entering the shrinking surround phase and extending the global search time, introducing an adaptive spiral shape constant to dynamically adjust the search range to balance exploration and development capabilities, optimizing the individual update strategy in combination with the bird navigation mechanism, and optimizing the algorithm through companion position information, thereby improving the stability and convergence speed of the algorithm. Path planning simulations were performed on 30 × 30 and 50 × 50 grid maps. The results show that compared with WOA, MSWOA, and GA, in the 30 × 30 map, the path length of IWOA is shortened by 3.23%, 7.16%, and 6.49%, respectively; in the 50 × 50 map, the path length is shortened by 4.88%, 4.53%, and 28.37%, respectively. This study shows that IWOA has significant advantages in the accuracy and efficiency of path planning, which verifies its feasibility and superiority. Full article
(This article belongs to the Special Issue Research on Intelligent Vehicle Path Planning Algorithm)
Show Figures

Figure 1

31 pages, 21973 KB  
Article
Spatial–Temporal Characteristics and Influencing Factors of Shrinking County Towns’ Resilience in China
by Chang Liu, Qing Yuan and Hong Leng
Land 2025, 14(11), 2202; https://doi.org/10.3390/land14112202 - 6 Nov 2025
Cited by 1 | Viewed by 1189
Abstract
Enhancing shrinking county towns’ resilience (SCTR) is crucial for fostering high-quality development and supporting China’s new urbanization strategy. However, research on resilience in shrinking areas remains limited, particularly at the county level—characterized as an “urban-rural intermediary”. In this study, we develop an evaluation [...] Read more.
Enhancing shrinking county towns’ resilience (SCTR) is crucial for fostering high-quality development and supporting China’s new urbanization strategy. However, research on resilience in shrinking areas remains limited, particularly at the county level—characterized as an “urban-rural intermediary”. In this study, we develop an evaluation framework based on a coupled human–environment perspective. Using this framework, we assess SCTR across various regions and levels of shrinkage in China from 2013 to 2022, while analyzing the coupling coordination degree among subsystems. To address challenges such as nonlinearity, spatial heterogeneity, and interpretability in attribution analysis, we integrate the Geographically Weighted Random Forest (GWRF) model with the SHapley Additive exPlanation (SHAP) model. The results show a gradual increase in resilience throughout the study period. Spatially, a distinct East–West disparity emerges, with higher resilience in the East and lower resilience in the West, as delineated by the Hu Line. For extreme-shrinking counties, population decline has become a paramount constraint on their resilience. Key factors, including local fiscal revenue, GDP, the Gini coefficient, and urbanization levels, have a significant impact on SCTR. Notably, in counties undergoing severe or extreme shrinkage, population decline has become a critical barrier to resilience. This study provides scientific insights and policy recommendations for the development of a sustainable and resilient county-town system in China. Full article
(This article belongs to the Special Issue Planning for Sustainable Urban and Land Development, Second Edition)
Show Figures

Figure 1

25 pages, 1657 KB  
Review
Control Algorithms for Intelligent Agriculture: Applications, Challenges, and Future Directions
by Shiyu Qin, Shengnan Zhang, Wenjun Zhong and Zhixia He
Processes 2025, 13(10), 3061; https://doi.org/10.3390/pr13103061 - 25 Sep 2025
Cited by 5 | Viewed by 2357
Abstract
Facing global pressures such as population growth, shrinking arable land, and climate change, intelligent agriculture has emerged as a critical pathway toward sustainable and efficient agricultural production. Control algorithms serve as the core enabler of this transition, finding applications in crop production, pest [...] Read more.
Facing global pressures such as population growth, shrinking arable land, and climate change, intelligent agriculture has emerged as a critical pathway toward sustainable and efficient agricultural production. Control algorithms serve as the core enabler of this transition, finding applications in crop production, pest management, agricultural machinery, and resource optimization. This review systematically examines the performance and applications of both traditional (e.g., PID, fuzzy logic) and advanced control algorithms (e.g., neural networks, model predictive control, adaptive control, active disturbance rejection control, and sliding mode control) in agriculture. While traditional methods are valued for simplicity and robustness, advanced algorithms better handle nonlinearity, uncertainty, and multi-objective optimization, enhancing both precision and resource efficiency. However, challenges such as environmental heterogeneity, hardware limitations, data scarcity, real-time requirements, and multi-objective conflicts hinder widespread adoption. This review contributes a structured, critical synthesis of these algorithms, highlighting their comparative strengths and limitations, and identifies key research gaps that distinguish it from prior reviews. Future directions include lightweight algorithms, digital twins, multi-sensor integration, and edge computing, which together promise to enhance the scalability and sustainability of intelligent agricultural systems. Full article
(This article belongs to the Section Automation Control Systems)
Show Figures

Figure 1

22 pages, 2215 KB  
Article
Energy Implications of Urban Shrinkage in China: Pathways of Population Dilution, Industrial Restructuring, and Consumption Inertia
by Xiu Yi, Hong Yi, Yaru Liu and Ming Wang
Sustainability 2025, 17(16), 7248; https://doi.org/10.3390/su17167248 - 11 Aug 2025
Cited by 2 | Viewed by 1293
Abstract
The structural responsiveness of urban energy systems has emerged as a central challenge in the governance of shrinking cities. Urban shrinkage entails more than a redistribution of resources—it reflects deep tensions embedded in population spatial configuration, functional redundancy, and institutional inertia. To investigate [...] Read more.
The structural responsiveness of urban energy systems has emerged as a central challenge in the governance of shrinking cities. Urban shrinkage entails more than a redistribution of resources—it reflects deep tensions embedded in population spatial configuration, functional redundancy, and institutional inertia. To investigate the evolutionary trajectory and driving mechanisms of urban energy consumption (UEC) under the context of urban shrinkage, this study focuses on China, a country undergoing rapid internal regional transformation. Drawing on panel data from 281 cities between 2008 and 2021, the study integrates two-way fixed effects (TWFE) models, mediation analysis, and spatial econometric models to ensure the scientific rigor and robustness of the quantitative analysis. Contrary to the intuitive assumption that declining population leads to reduced energy loads, the results reveal a non-linear and asymmetric trajectory wherein per capita energy consumption increases alongside continued demographic decline. Mechanism decomposition further shows that declines in population density and the share of secondary industry suppress UEC through spatial dispersal and the retreat of energy-intensive sectors, respectively. In contrast, fiscal contraction and institutional path dependency collectively elevate the share of traditional energy consumption, reinforcing the structural inertia of UEC. This study illuminates the non-linear dynamics of energy system evolution under urban shrinkage and argues for a shift away from linear and target-driven governance paradigms toward governance frameworks that emphasize structural adaptation, distributive equity, and systemic resilience—thereby offering a theoretical and empirical foundation for multi-objective sustainable urban transitions. Full article
Show Figures

Figure 1

22 pages, 618 KB  
Article
Dynamics of a Symmetric Seasonal Influenza Model with Variable Recovery, Treatment, and Fear Effects
by Rubayyi T. Alqahtani, Abdelhamid Ajbar and Manal Alqhtani
Symmetry 2025, 17(6), 803; https://doi.org/10.3390/sym17060803 - 22 May 2025
Cited by 1 | Viewed by 1247
Abstract
This study proposes and examines the dynamics of a susceptible–exposed–infectious–recovered (SEIR) model for the spread of seasonal influenza. The population is categorized into four distinct groups: susceptible (S), exposed (E), infectious (I), and recovered (R) individuals. The symmetric model integrates a bilinear incidence [...] Read more.
This study proposes and examines the dynamics of a susceptible–exposed–infectious–recovered (SEIR) model for the spread of seasonal influenza. The population is categorized into four distinct groups: susceptible (S), exposed (E), infectious (I), and recovered (R) individuals. The symmetric model integrates a bilinear incidence rate alongside a nonlinear recovery rate that depends on the quality of healthcare services. Additionally, it accounts for the impact of fear related to the disease and includes a constant vaccination rate as well as a nonlinear treatment function. The model advances current epidemiological frameworks by simultaneously accounting for these interrelated mechanisms, which are typically studied in isolation. We derive the expression for the basic reproduction number and analyze the essential stability properties of the model. Key analytical results demonstrate that the system exhibits rich dynamic behavior, including backward bifurcation (where stable endemic equilibria persist even when the basic reproduction number is less than one) and Hopf bifurcation. These phenomena emerge from the interplay between fear-induced suppression of transmission, treatment saturation, and healthcare quality. Numerical simulations using Saudi Arabian demographic and epidemiological data quantify how increased fear perception shrinks the bistability region, facilitating eradication. Healthcare capacity improvements, on the other hand, reduce the critical reproduction number threshold while treatment accessibility suppresses infection loads. The model’s practical significance lies in its ability to identify intervention points where small parameter changes yield disproportionate control benefits and evaluate trade-offs between pharmaceutical (vaccination/treatment) and non-pharmaceutical (fear-driven distancing) strategies. This work establishes a versatile framework for public health decision making and the integrated approach offers policymakers a tool to simulate combined intervention scenarios and anticipate nonlinear system responses that simpler models cannot capture. Full article
(This article belongs to the Special Issue Three-Dimensional Dynamical Systems and Symmetry)
Show Figures

Figure 1

45 pages, 1703 KB  
Article
NLAPSMjSO-EDA: A Nonlinear Shrinking Population Strategy Algorithm for Elite Group Exploration with Symmetry Applications
by Yong Shen, Jiaxuan Liang, Hongwei Kang, Xingping Sun and Qingyi Chen
Symmetry 2025, 17(2), 153; https://doi.org/10.3390/sym17020153 - 21 Jan 2025
Cited by 2 | Viewed by 1585
Abstract
This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA [...] Read more.
This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA and APSM-jSO. Firstly, in the linear population reduction strategy, the number of individuals eliminated in each generation is insufficient. This results in a higher number of inferior individuals remaining, and since the total number of iterations is fixed, these inferior individuals will also consume iteration counts for their evolution. Therefore, it is essential to allocate more iterations to the elite population to promote the emergence of superior individuals. The nonlinear population reduction strategy effectively addresses this issue. Secondly, we have introduced an Estimation of Distribution Algorithm (EDA) to sample and generate individuals from the elite population, aiming to produce higher-quality individuals that can drive the iterative evolution of the population. Furthermore, to enhance algorithmic diversity, we increased the number of individuals in the initial population during subsequent experiments to ensure a diverse early population while maintaining a constant total number of iterations. Symmetry plays an essential role in the design and performance of NLAPSMjSO-EDA. The nonlinear population reduction strategy inherently introduces a form of asymmetry that mimics natural evolutionary processes, favoring elite individuals while reducing the influence of inferior ones. This asymmetric yet balanced approach ensures a dynamic equilibrium between exploration and exploitation, aligning with the principles of symmetry and asymmetry in optimization. Additionally, the incorporation of EDA utilizes probabilistic symmetry in sampling from the elite population, maintaining structural coherence while promoting diversity. Such applications of symmetry in algorithm design not only improve performance but also provide insights into balancing diverse algorithmic components. NLAPSMjSO-EDA, evaluated on the CEC 2017 benchmark suite, significantly outperforms recent differential evolution algorithms. In conclusion, NLAPSMjSO-EDA effectively enhances the overall performance of APSM-jSO, establishing itself as an outstanding variant combining jSO and EDA algorithms. The algorithm code has been open-sourced. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
Show Figures

Figure 1

22 pages, 4752 KB  
Article
Spatio-Temporal Patterns of County Population Shrinkage and Influencing Factors in the North–South Transitional Zone of China
by Tong Wu, Beibei Ma and Yongyong Song
Int. J. Environ. Res. Public Health 2022, 19(23), 15801; https://doi.org/10.3390/ijerph192315801 - 27 Nov 2022
Cited by 1 | Viewed by 2567
Abstract
Population is the foundation of socio-economic development. However, continued population shrinkage has made the problem of unbalanced and insufficient regional development more prominent, threatening human well-being. How to solve the contradiction between population shrinkage and regional development has become an urgent scientific problem. [...] Read more.
Population is the foundation of socio-economic development. However, continued population shrinkage has made the problem of unbalanced and insufficient regional development more prominent, threatening human well-being. How to solve the contradiction between population shrinkage and regional development has become an urgent scientific problem. Therefore, taking a typical underdeveloped mountainous region, the North–South Transitional Zone of China, as an example, we analyzed the spatial and temporal evolution of regional population shrinkage from 2000 to 2020, classified the types of regional population shrinkage, and revealed the key influencing factors and driving mechanisms for the formation of population shrinkage patterns in poor mountainous counties. The results showed that: (1) From 2000 to 2020, the number of counties in the North–South Transitional Zone of China with population shrinkage grew, and the degree of shrinkage increased. The shrinking counties were mainly municipal counties, and the shrinkage types were mainly continuous shrinkage and expansion followed by shrinkage. (2) Spatially, the shrinking counties had significant and strengthening spatial autocorrelation, with obvious characteristics of the contiguous shrinkage of county units, and the shrinkage center of gravity and shrinkage agglomeration areas showed an evolutionary trend of shifting from east to west. The shrinking counties had obvious divergence in both the “east–west” and “north–south” directions. (3) Natural factors had an endogenous rooting role, while human factors had a strong driving role, and the impact of different influencing factors varied significantly. (4) The formation and evolution of the spatial pattern of county population shrinkage was subject to the synergistic effect of natural factors and human factors. The interaction between natural and human factors had a non-linear enhancement effect and a two-factor enhancement effect. The results of this study are expected to provide a scientific basis for coordinating regional human–land relations in order to optimize population-flow governance and sustainable regional development in the North–South Transitional Zone and less-developed regions of China. Full article
(This article belongs to the Special Issue Research in Ecological Economy and Regional Sustainable Development)
Show Figures

Figure 1

22 pages, 791 KB  
Article
The Characteristics, Influencing Factors, and Push-Pull Mechanism of Shrinking Counties: A Case Study of Shandong Province, China
by Min Wang, Shuqi Yang, Huajie Gao and Kahaer Abudu
Sustainability 2021, 13(4), 2402; https://doi.org/10.3390/su13042402 - 23 Feb 2021
Cited by 8 | Viewed by 5163
Abstract
To analyze the characteristics, influencing factors, and microscopic mechanisms of county-level city shrinkage, this paper uses a quantitative push-pull model to explore the shrinking counties of Shandong Province between 2000 and 2018. The measurement method formulates three research objectives. First, the shrinking intensity [...] Read more.
To analyze the characteristics, influencing factors, and microscopic mechanisms of county-level city shrinkage, this paper uses a quantitative push-pull model to explore the shrinking counties of Shandong Province between 2000 and 2018. The measurement method formulates three research objectives. First, the shrinking intensity and characteristics are analyzed according to statistics about the average annual rate of population growth, the primary production proportion, and public expenditure. Second, the influence factors are explored. Living standards, industrial development, social input, and public resource indicators are selected to quantitatively identify the push factors and pull factors and the correlated relationship of how the factors influence the population decline using ridge regression. Finally, the circular feedback mechanism and push-pull effect of multiple factors are explained. How do the factors affect each other and which is the decisive factor shaping county shrinkage? The push-pull mechanism is analyzed using dynamic relationship testing and the Granger causality test. The results show that the shrinkage of county-level cities faces common problems, including lack of resources, slowing down of the economy, and declining cityscape quality of life, which are the push factors for the population decline. There are differentiated characteristics of shrinkage. There has not yet been a full-scale recession in Shandong Province in terms of the degree of shrinkage. The towns with population loss accounted for only 15.4%, and the loss of population was less than 10% in ten years. In terms of impact mechanisms, county economic strength has a nonlinear correlation to population migration. Some counties tend to shrink in population and society. The degradation of the cultural environment, quality of life, and social welfare highlight social shrinkage signs in counties. A healthy living environment, equal public services, and a slowing down of relative deprivation have become essential pull factors for migration. County governments should shift from economic growth to people’s well-being, balancing government governance, economic growth, cultural development, environmental protection, and improving the livability level, as they are important directions for improving shrinking counties’ resilience. Full article
Show Figures

Figure 1

16 pages, 1817 KB  
Article
Optimizing a Bi-Objective Mathematical Model for Minimizing Spraying Time and Drift Proportion
by Muhammad Nadeem, Claver Diallo, Tri Nguyen-Quang, Uday Venkatadri and Peter Havard
AgriEngineering 2019, 1(3), 418-433; https://doi.org/10.3390/agriengineering1030031 - 12 Aug 2019
Cited by 4 | Viewed by 4697
Abstract
The global agriculture sector faces many challenges in its mission to meet the increasing demand for food and fiber. Climate change, increasing population growth, emergence of crop diseases, damage to crops from rodents and critters, and shrinking farming land in some regions are [...] Read more.
The global agriculture sector faces many challenges in its mission to meet the increasing demand for food and fiber. Climate change, increasing population growth, emergence of crop diseases, damage to crops from rodents and critters, and shrinking farming land in some regions are among these challenges. Application of agrochemicals has proven to be an efficient answer to some of these challenges. However, the impacts of these products on human health and the environment combined with the increased requirement for sustainable farming requires the development of optimal spraying practices that would balance out all interests and concerns. In this paper, a mathematical model is developed to jointly minimize spraying time and drift losses. The obtained bi-objective mixed integer nonlinear programming model is solved for a case study example published in the crop protection literature. Optimal solutions are obtained using the weighted sum method and the epsilon-constraint approach. The results showed that valid and reasonable solutions can be obtained by selecting the appropriate combination of boom height, nozzle spacing, nozzle type, and tractor travel speed. Useful insights are obtained through various computational experiments. Full article
Show Figures

Figure 1

Back to TopTop