Nonlinear Optimization Model Research Articles

Designing a multi-purpose network of sustainable and closed-loop renewable energy supply chain, considering reliability and circular economy

Since renewable energy systems have a limited lifespan and cannot be used after a while, it seems imperative to pay attention to recycling and sustainability in the supply chain network design of these systems. Also, modern power systems have high complexity and a large number of problems that affect the reliability of electricity supply to consumers. Therefore, organizations should consider broader goals, including the maximum use of resources and the minimization of waste, which is known as lean economy. In this research, a multi-objective non-linear forward optimization model has been considered for the design of the supply chain network of photovoltaic and wind systems based on the aspects of stability and taking into account the reliability. Also, adding the reverse flow, in addition to the forward flow, is also considered, which, in addition to economic advantages, also pays attention to environmental and social issues. The objective function includes minimizing all costs and negative environmental effects as well as increasing reliability. In order to convert the multi-objective planning model into a single-objective one, the epsilon method of the enhanced constraint is used. Uncertainty has been considered for all variables (except binary variables) and parameters of demand, intensity of sun radiation and amount of wind speed. Then, the efficiency of the model has been investigated through its implementation on a case study and the results have been obtained. Eventually, the model's efficiency is illustrated by discussing a real-world case, through which prominent managerial results are acquired.

Risk-based dynamic inoperability input-output and non-linear optimisation models to analyse resilience in the construction industry

ABSTRACT Pakistan has faced significant economic losses due to catastrophes, specifically floods. This study aims to assess the ripple effects of the 2022 floods, focusing on the Construction Industry, which has been gaining importance in the national economy, and on the resilience of economic sectors absorbing the negative shocks from floods. The study uses the Asian Development Bank's (ADB) Input-Output database for Pakistan using the Dynamic Inoperability Input-Output Model (DIIM) with the Fuzzy Full Consistency Method (F-FUCOM). The analysis revealed that the Construction Industry’s weak resilience resulted in a prolonged recovery period and that the lack of flood risk mitigation infrastructure was identified as the most critical. The results suggest that policymakers prioritise such infrastructures, like dams, early warning systems, and transportation infrastructure, to enhance the resilience of the overall economy.

Second‐order cone programming models for the unitary weighted Weber problem and for the minimum sum of the squares clustering problem

AbstractIn this work, new mixed integer nonlinear optimization models are proposed for two clustering problems: the unitary weighted Weber problem and the minimum sum of squares clustering. The proposed formulations are convex quadratic models with linear and second‐order cone constraints that can be efficiently solved by interior point algorithms. Their continuous relaxation is convex and differentiable. The numerical experiments show the proposed models are more efficient than some classical models for these problems known in the literature.

An assessment of numerical and geometrical quality of bases on surface fitting on Powell–Sabin triangulations

It is well known that the problem of fitting a dataset by using a spline surface minimizing an energy functional can be carried out by solving a linear system. Such a linear system strongly depends on the underlying functional space and, particularly, on the basis considered. Some papers in the literature study the numerical behavior and processing of the above-mentioned linear systems in specific cases. The bases that have local support and constitute a partition of unity have been shown to be interesting in the frame of geometric problems. In this work, we investigate the numerical effects of considering these bases in the quadratic Powell–Sabin spline space. Specifically, we present a direct approach to explore different preconditioning strategies and assess whether the already known ‘good’ bases also possess favorable numerical properties. Additionally, we introduce an inverse optimization approach based on a nonlinear optimization model to identify new bases that exhibit both good geometric and numerical properties.

A novel solution methodology for electrical vehicles charging schedule in coordinated with full flexible resources in microgrid

This paper proposes a new model for the day-ahead Electric Vehicle charging schedule in Microgrids (MGs) with flexible resources such as Wind Turbine (WT) and Photovoltaic (PV) electrical power, Combined Heat and Power (CHP), Energy Storage Source (ESS), and load Demand Responses (DR). The proposed Mixed Integer Nonlinear Multi-Objective Optimization (MINMO) model considers uncertainty properties with optimal operation objects. The cost function, and power loss minimization are the proposed model's objects for considering optimal operation objects. This model is solved by a three-level decomposition method in master-sub problem presentation and Binary-Continues PSO algorithm (BC PSO) to quickly calculate the optimal solution. In the first layer, the main constraint of electric vehicle aggregators (EVAs) is satisfied by the binary PSO algorithm. According to the top-layer solution, flexible recourses are managed to satisfy the operation objects by the Bi-level Continues PSO algorithm in the second layer. Then, after converging to the optimum solution of these two layers, Electric Vehicles (EVs) charging stations are solved at the last layer by algebraic equations. Finally, the efficiency of the proposed method is illustrated via its application in IEEE 33-bus MG system. The numerical results show that the proposed solution methodology reduces the runtime of the problem up to 95 % compared to intelligence-based and full Newton–Raphson AC power flow method. Also, numerical results illustrate that considering CHP and DR in addition to the other flexible resources reduces the operation cost and power loss up to 21 % and 5 % respectively. In top of that the minimum total cost for day-ahead EV charging schedule by the proposed model and solution methodology is 578,312.7$.

Joint determination of nurse and patient bed positions in an inpatient unit considering equity in visibility

Layout design is considered a crucial aspect of healthcare architecture and its goal is to allow easy access to essential hospital services and effective patient care. Literature suggests that modifying or redesigning the inpatient unit layout is one of the ways to maximize patient visibility in an inpatient layout. However, prior work has been descriptive in nature and limited in their ability to derive optimal layouts. To fill this gap, we propose a non-linear optimization model that optimizes both equity and effectiveness in visibility by jointly determining the optimal location of two nurses and patient bed positions in multiple rooms. The bi-objective model is then converted into a single objective model utilizing the ε-constrained method, with equity in the objective function and effectiveness as a constraint. Patient visibility is estimated using a ray-casting algorithm that also considers nurses’ line of sight, door positions, and obstruction levels. A progressive refinement algorithm embedded in the Particle Swarm Optimization framework is proposed to efficiently solve this model. Our results suggest that optimizing bed position in conjunction with nurse position can enhance equity by over 45.2% compared to just optimizing the nurse position. Similarly, angular layouts are superior to linear layout by up to 53% in patient equity. We also notice that increasing spatial distance between nurses in angular layouts can further increase equity. Our approach provides valuable insights and can serve as a benchmark tool for hospitals looking to improve the design of their inpatient units that promote patient safety and high-quality care.

Fast loop closure detection using probabilistic integration of pose and appearance similarity

Loop closure detection is a key technique for robots to minimize the accumulated localization and mapping errors after long-time explorations of simultaneous localization and mapping. However, the requirement for efficiency and accuracy performance for mobile robot applications is not well satisfied. In this article, we propose a fast and accurate loop closure detection method by exploiting both pose-based and appearance-based information in a probabilistic manner, inspired by the complementarity between the pose-based and the appearance-based information. Our approach formulates a probability framework combing the pose-based loop closure detection probability and the appearance-based loop closure detection probability. In the proposed framework, the pose-based loop closure detection model is firstly derived from the nonlinear optimization model of odometry. Then the appearance-based loop similarity and the pose-based loop similarity are combined into a joint framework to improve the loop closure detection performance. We implemented our approach using C++ and ROS and thoroughly tested it on the publicly available datasets. The experiments presented in this article suggest that the proposed method can achieve high efficiency and accuracy performance on loop closure detection.

Optimization of Integrated Energy System Considering Electricity and Hydrogen Coordination in the Context of Carbon Trading

In order to improve the consumption of renewable energy and reduce the carbon emissions of integrated energy systems (IESs), this paper proposes an optimal operation strategy for an integrated energy system considering the coordination of electricity and hydrogen in the context of carbon trading. The strategy makes full use of the traditional power-to-gas hydrogen production process and establishes a coupling model comprising cogeneration and carbon capture equipment, an electrolytic cell, a methane reactor, and a hydrogen fuel cell. Taking a minimum daily operating cost and minimal carbon emissions from the system as objective functions, a mixed-integer nonlinear optimal scheduling model is established. This paper designs examples based on MATLAB R2021b and uses the GUROBI solver to solve them. The results show that compared with the traditional two-stage operation process, the optimization method can reduce the daily operation cost of an IES by 26.01% and its carbon emissions by 90.32%. The results show that the operation mode of electro-hydrogen synergy can significantly reduce the carbon emissions of the system and realize a two-way flow of electro-hydrogen energy. At the same time, the addition of carbon capture equipment and the realization of carbon recycling prove the scheduling strategy’s ability to achieve a low-carbon economy of the scheduling strategy.

Optimizing tensile strength and energy consumption for FDM through Mixed-Integer Nonlinear Multi-objective optimization and design of experiments

This study presents a methodology for optimizing key parameters of a fused deposition modeling (FDM) printer to minimize energy consumption (EC) while exceeding a specified tensile strength (TS) threshold. Employing Design of Experiments (DoE) with Taguchi and Response Surface analysis, we identify influential parameters affecting TS and EC. A Mixed-Integer Nonlinear Multi-Objective Optimization model is then utilized to balance TS and EC, resulting in optimal parameter values. Validation using fabricated specimens demonstrates less than 5 % error in Tensile Strength and less than 2 % error in Energy Consumption, confirming the efficacy of the proposed methodology.

Evidential-Reasoning-Type Multi-Attribute Large Group Decision-Making Method Based on Public Satisfaction

To address public participation-oriented, large group decision-making problems with uncertain attribute weights, we propose a multi-attribute decision-making method considering public satisfaction. Firstly, a large group is organized to provide their opinions in the form of linguistic variables. Public opinions can be categorized into two types based on their content: one reflects the effectiveness of an alternative implementation and the other reflects the public expectations. Secondly, the two types of public opinions are sorted separately by linguistic variables. The evaluation of alternatives and the evaluation of expectations in different attributes are determined, both of which are expressed in the form of linguistic distributions. These two evaluations are then compared to determine the public satisfaction of the attributes in different alternatives. Thirdly, based on the deviation of public satisfaction in different attributes, a weight optimization model is constructed to determine the attribute weights. Fourthly, leveraging the interval credibility of attribute satisfaction for various alternatives, an evidential reasoning non-linear optimization model is established to obtain the comprehensive utility evaluation value for each alternative, which is used for ranking. Finally, a numerical example is employed to validate the feasibility and effectiveness of the proposed approach. According to the results of the numerical example, it can be concluded that the proposed approach can be effectively applied to large group decision-making problems that consider public satisfaction. Based on the comparison of methods, the proposed approach has certain advantages in reflecting public opinions and setting reference points, which can ensure the reliability of the decision results.

Research on Detection System of Intelligent Computer Optimization Algorithm for Concrete Mix Ratio Based on Big Data

PLC is used to complete the control function of the concrete proportioning system. The MCGS (Configuration Software Monitor and Control System) is used to realize the real-time monitoring, data management and fault warning of the whole monitoring system. The material feed and PLC control process in the feed system are emphatically introduced. A concrete proportioning design method based on multiple parameters is proposed. The nonlinear multi-objective optimization model of concrete mix ratio was established by stepwise regression analysis and complex optimization method. The problems of narrow range of variables and single form of objective and constraint in traditional linear optimization methods are solved, which makes the selection of optimal index simpler and more flexible. Through the calculation of examples, it is clear that this method can obtain the mixture that meets the use conditions, and can greatly save the experimental work and construction cost.

Optimizing large-scale hydrogen storage: A novel hybrid genetic algorithm approach for efficient pipeline network design

As hydrogen production technologies continue to advance, efficient and high-capacity hydrogen storage solutions become increasingly crucial. To address the complex optimization challenges in the design of large-scale hydrogen storage pipeline networks, the study introduces a mixed integer nonlinear optimization model inspired by hydrogen pipeline design optimization theory. The model not only focuses on optimizing network design parameters but also aims to minimize investment costs. To achieve this, the study proposes an innovative hybrid genetic algorithm that combines the Modified Feasible Directions Method (MFDM) and Genetic Algorithm Theory (GAT), specifically targeting the optimization of pipeline diameter's discrete distribution challenges. Comparative analyses with SUMT and GA algorithms demonstrate the superiority of the approach. In continuous space, the algorithm achieves a lower convergence cost of 232.4437 × 104 Yuan, while in discrete space, the cost further decreases to 212.1636 × 104 Yuan. Additionally, the study delves into the sensitivity of the HGA-MFDM algorithm to ambient temperature and wellhead temperature in hydrogen storage facilities. The analysis reveals that wellhead temperature has a more significant impact on pipeline network investment, whereas ambient temperature exhibits a more pronounced effect on iteration curves. The findings provide valuable insights for the precise adjustment and optimization of hydrogen storage pipeline networks in practical applications.

Collaborative optimization of passenger flow control and bus-bridging services in commuting metro lines

With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints

This study models a container routing problem using multimodal transportation to improve its economy, timeliness, and reliability. Pickup and delivery time windows are simultaneously formulated in optimization to provide the shipper and the receiver with time-efficient services, in which early pickup and delayed delivery can be avoided, and nonlinear storage periods at the origin and the destination can be minimized. Furthermore, the capacity uncertainty of the multimodal network is incorporated into the advanced routing to enhance its reliability in practical transportation. The LR triangular fuzzy number is adopted to model the capacity uncertainty, in which its spread ratio is defined to measure the uncertainty level of the fuzzy capacity. Due to the nonlinearity introduced by the time windows and the fuzziness from the network capacity, this study establishes a fuzzy nonlinear optimization model for optimization problem. A chance-constrained linear reformulation equivalent to the proposed model is then generated based on the credibility measure, which makes the global optimum solution attainable by using Lingo software. A numerical case verification demonstrates that the proposed model can effectively solve the problem. The case analysis points out that the formulation of pickup and delivery time windows can improve the timeliness of the entire transportation process and help to achieve on-time transportation. Furthermore, improving the confidence level and the uncertainty level increases the total costs of the optimal route. Therefore, the shipper and the receiver must prepare more transportation budget to improve reliability and address the increasing uncertainty level. Further analysis draws some insights to help the shipper, receiver, and multimodal transport operator to organize a reliable and cost-efficient multimodal transportation under capacity uncertainty through confidence level balance and transportation service and transfer service selection.

A Multi-response Nonlinear Programming Model with an Inscribed Design to Optimize Bioreduction Conditions of (S)-phenyl (pyridin-2-yl)methanol by Leuconostoc pseudomesenteroides N13

AbstractAsymmetric bioreductions have the potential to synthesize chiral alcohols when catalyzed by biocatalysts. Nevertheless, the (S)-phenyl (pyridin-2-yl)methanol ((S)-2) analgesic synthesis poses significant challenges concerning unsatisfactory substrate amount and production method. Thus, this study proposes an inscribed design-focused multi-response nonlinear optimization model for the asymmetric reduction of the phenyl(pyridin-2-yl)methanone (1) with Leuconostoc pseudomesenteroides N13 biocatalyst. From the novel inscribed design-focused multi-response nonlinear optimization model, optimization conditions of the reaction, such as pH = 6, temperature = 29 °C, incubation time = 53 h, and agitation speed = 153 rpm, were found. Also, the reaction conversion was predicted to be 99%, and the product of the enantiomeric excess (ee) was 98.4% under the obtained optimization conditions. (S)-2 was obtained with 99% ee, 99% conversion, and 98% yield while performing a validation experiment using the determined optimized conditions. In addition, 1 with the amount of 11.9 g was converted entirely to (S)-2 (11.79 g, 98% isolated yield) on a high gram scale. Also, this study is noted as the first example of the gram-scale production of (S)-2 using an optimization strategy and biocatalyst. Further, the applicability of the inscribed design-focused optimization model in biocatalytic reactions has been demonstrated and provides an effective process for the analgesic synthesis of (S)-2, which is a green, cost-effective method of producing chiral aryl heteroaryl methanol.

Optimization of Load Distribution Method for Hydropower Units Based on Output Fluctuation Constraint and Double-Layer Nested Model

During the load distribution of hydropower units, the frequent crossing of vibration zones as well as large output fluctuations affect the stability of the power station. A multi-objective double-layer intelligent nesting model that considers the constraint of the output fluctuation of units is proposed to address these problems. The nonlinear constraint unit commitment optimization model layer is built based on outer dynamic programming, and the load distribution optimization model layer is constructed based on the improved biogeography-based optimization algorithm. Simultaneously, the unit output fluctuation constraint is established based on whether the unit combination changes in order to limit the unit output fluctuation. The results of this model indicate that compared with traditional load allocation models, the application of the method proposed in this paper can reduce the fluctuation range of unit output by 85.01%. In addition, except for the inevitable vibration zone crossings during startup and shutdown processes, the unit does not cross the vibration zone during operation, which greatly improves the unit’s vibration isolation and optimization capabilities. The multi-objective double-layer intelligent nested model proposed in this paper has significant advantages in the field of load allocation for hydropower units. It effectively improves the stability and reliability of unit operation, and this method can be applied to practical load allocation processes. It is of great significance for the research on load allocation optimization of hydropower units.

Study on the Optimization of Wujiang’s Water Resources by Combining the Quota Method and NSGA-II Algorithm

Recently, the Chinese government has implemented stringent water requirements based on the concept of ‘Basing four aspects on water resources’. However, existing research has inadequately addressed the constraints of water resources on population, city boundaries, land, and production, failing to adequately analyze the interplay between water resource limitations and urban development. Recognizing the interconnectedness between urban water use and economic development, a multi-objective model becomes crucial for optimizing urban water resources. This study establishes a nonlinear multi-objective water resources joint optimization model, aligning with the “Basing four aspects on water resources” requirement to maximize urban GDP and minimize total water use. A genetic algorithm (NSGA-II Algorithm) is applied to solve this complex nonlinear multi-objective model and obtain the Pareto solution set, addressing information loss inherent in the traditional water quota method. The model was tested in Wujiang District, an area located in China’s Jiangsu Province that has been rapidly urbanizing over the past few decades, and yielded 50 non-inferior water resource optimization schemes. The results reveal that the Pareto solution set visually illustrates the competition among objectives and comprehensively displays the interplay between water and urban development. The model takes a holistic approach to consider the relationships between water resources and urban population, land use, and industries, clearly presenting their intricate interdependencies. This study serves as a valuable reference for the rational optimization of water resources in urban development.

Route Optimization for Hazardous Chemicals Transportation under Time-Varying Conditions

Since accidents of hazardous chemicals transportation will cause serious loss to the surrounding environment and lives and properties, this paper studies the transportation route optimization problem of hazardous chemicals under dynamic time-varying conditions. Combined with the goal of green sustainable development, a multiobjective nonlinear optimization model is constructed to minimize the transportation risk, transportation cost, and carbon emissions generated in the transportation. The model is solved by the improved Fast Non-Dominated Sorting Genetic Algorithm with Elite Strategy (NSGA-II) algorithm. The effectiveness of the model and the algorithm are tested on the Sioux Falls network. The experimental results show that under time-varying conditions, a vehicle’s departure at different times will generate different transportation costs and risks. Therefore, enterprises need to rationally arrange the departure time of vehicles according to the time windows of customer nodes and road conditions. In additio, from the relationship between the optimization objectives, in order to achieve green, sustainable and low-risk transportation, enterprises should first reduce their transportation costs.

RC-SLAM: Road Constrained Stereo Visual SLAM System Based on Graph Optimization.

Intelligent vehicles are constrained by road, resulting in a disparity between the assumed six degrees of freedom (DoF) motion within the Visual Simultaneous Localization and Mapping (SLAM) system and the approximate planar motion of vehicles in local areas, inevitably causing additional pose estimation errors. To address this problem, a stereo Visual SLAM system with road constraints based on graph optimization is proposed, called RC-SLAM. Addressing the challenge of representing roads parametrically, a novel method is proposed to approximate local roads as discrete planes and extract parameters of local road planes (LRPs) using homography. Unlike conventional methods, constraints between the vehicle and LRPs are established, effectively mitigating errors arising from assumed six DoF motion in the system. Furthermore, to avoid the impact of depth uncertainty in road features, epipolar constraints are employed to estimate rotation by minimizing the distance between road feature points and epipolar lines, robust rotation estimation is achieved despite depth uncertainties. Notably, a distinctive nonlinear optimization model based on graph optimization is presented, jointly optimizing the poses of vehicle trajectories, LPRs, and map points. The experiments on two datasets demonstrate that the proposed system achieved more accurate estimations of vehicle trajectories by introducing constraints between the vehicle and LRPs. The experiments on a real-world dataset further validate the effectiveness of the proposed system.