Nonlinear Programming Model Research Articles

A Mathematical Programming Approach for Joint Optimization of Wind Farm Layout and Cable Routing Based on a Three‐Dimensional Gaussian Wake Model

ABSTRACTWind energy is currently one of the most promising alternative energy sources. The optimization of the wind farm layout and the cable layout are two important elements in the design of wind farms. Since increasing the distance between turbines can reduce wake loss but increase cable cost, these two optimizations are coupled and jointly affect the revenue of wind farms. In this paper, we propose a novel nonlinear mathematical programming model based on the 3D Gaussian wake model and use a mathematical programming approach to optimize the layout of the wind farm and the cable layout together, considering both power generation and cable cost. In this method, some of the constraints were linearized to facilitate the solution process. The optimization results show that profit increased by 9.07% when using annual economic efficiency as the objective function, compared with using energy production as the objective function.

Multi-Period Operational Modelling and Optimization for Large-Scale Natural Gas Networks Considering Linepack Functions in Long-Distance Transmission Pipelines

As a promising energy resource, offshore natural gas is primarily used for power generation. The comprehensive offshore gas-to-power system, which includes extraction, treatment, compression, pipeline transmission, and power generation, is extensive and operates within various regulatory, operational, and financial constraints. This complexity offers opportunities to optimize one or more system operations to enhance profitability while fulfilling user demands and environmental considerations. In this research, we present a model-based, computer-aided framework that intuitively connects upstream natural gas operations with downstream power generation and distribution. We develop a multi-period Mixed-Integer Nonlinear Programming (MINLP) model that integrates gas treatment, compression, and long-distance transmission with power generation. The model combines first-principle mechanistic process models with a linepack model that calculates the gas volume storable in long-distance pipelines for transmission. The linepack model facilitates gas storage and withdrawal across different periods to accommodate demand scheduling. We apply this framework using the MINLP model in three scenarios: profit maximization, cost minimization, and supply-demand balancing using linepack. The results demonstrate improved economic performance for offshore natural gas-based power generation in China under varying periodic power demands.

Optimizing Modular Vehicle Public Transportation Services with Short-Turning Strategy and Decoupling/Coupling Operations

In public transportation systems, the passenger demand during peak hours is characterized by over-saturation at intermediate stops and directional imbalances, and the traditional single scheduling strategy and fixed capacity cannot solve the contradiction between the demand and capacity mismatch. In order to accurately match demand and capacity, this paper proposes a method to optimize the service of a public transportation system by using a short-turning strategy combined with decoupled/coupled operation of modular vehicles (MVs). The short-turning strategy is used to alleviate the heavy passenger flow at intermediate stations, and the decoupling/coupling operations of MVs are employed to flexibly adjust the capacity levels in different directions. Considering urban space limitations, depots for storing modular units (MUs) are only set up at the starting and ending stations of bidirectional lines. MVs can not only adjust the departure capacity at the starting station but also consider whether to decouple/couple at turnaround stations for short-turning trips to achieve a more effective supply–demand match, with the decoupled/coupled MUs being deadheaded from or provided by the depot. We formulated this problem as an integer nonlinear programming (INLP) model, jointly optimizing the departure intervals of each trip, the capacity of MVs, the turnaround scheme for short-turning trips, and the decoupling/coupling scheme for MVs at turnaround stations, with the aim of minimizing passenger waiting time costs and vehicle operating costs. To facilitate a solution, we equivalently transformed some nonlinear terms in the model, which was then solved by the commercial solver Gurobi. The numerical study shows that, compared with the traditional full-length strategy combined with conventional buses, the model proposed in this paper can reduce the total system cost by about 19.59%. In particular, it can achieve precise matching between passenger demand and transport capacity, thereby reducing the passenger waiting time cost by about 29.99%. Compared with the full-length strategy combined with MVs, the total system cost is also reduced by about 14.65%. The research results contribute to enhancing the service quality and efficiency of public transportation systems, which is of great significance to the sustainable development of these systems.

Optimisation of Embodied Carbon and Thermal Performance of Roof Material Selections for Australian Residential Housing

This research is responding to the latest sustainable development policy for residential housing in Australia, which mandates a minimum R6.0 for roof insulation and a requirement of reporting the embodied carbon footprint for new build residential houses before obtaining development approval. The requirement of thermal resistance (R-value) results in thicker roof material to be used, and inevitably increases the total embodied carbon. This condition has drawn the need for an optimised design to balance the embodied carbon with the required thermal performance. In this paper, a multi-objective, mixed-integer, non-linear mathematical programming model is adopted to perform the optimisation. While mathematical programming is a well-established method in optimisation, a research gap has been observed in its application in optimising roof material selection under the simultaneous constraints of the R-value and volumetric heat capacity (thermal mass). Using a common conventional pitched roof with a timber frame, the study demonstrates how the model identifies material combinations that minimise the total embodied carbon within the specified thermal performance ranges. The unique contribution of this research is integrating thermal mass into the optimisation of roof material selections alongside thermal resistance, and embodied carbon. The findings provide practical recommendations for sustainable material selections across varying R-value and thermal mass ranges, offering a new perspective on roof material selections.

Valorization of Biomass Through Anaerobic Digestion and Hydrothermal Carbonization: Integrated Process Flowsheet and Supply Chain Network Optimization

Utilization of biomass through anaerobic digestion and hydrothermal carbonization is crucial to maximize resource efficiency. At the same time, supply chain integration ensures sustainable feedstock management and minimizes environmental and logistical impacts, enabling a holistic approach to a circular bioeconomy. This study presents an integrated approach to simultaneously optimize the biomass supply chain network and process flowsheet, which includes anaerobic digestion, cogeneration, and hydrothermal carbonization. A three-layer supply chain network superstructure was hence developed to integrate the optimization of process variables with supply chain features such as transportation modes, feedstock supply, plant location, and demand location. A mixed-integer nonlinear programming model aimed at maximizing the economic performance of the system was formulated and applied to a case study of selected regions in Slovenia. The results show a great potential for the utilization of organic biomass with an annual after tax profit of 23.13 million USD per year, with the production of 245.70 GWh/yr of electricity, 298.83 GWh/yr of heat, and 185.08 kt/yr of hydrochar. The optimal configuration of the supply chain network, including the selection of supply zones, plant locations and demand locations, transportation links, and mode of transportation is presented, along with the optimal process variables within the plant.

Models and methods for forming service packages for solving of the problem of designing services in information systems of providers

Today, in the telecommunications industry, service is one of the fundamental concepts. Building a service architecture is a key stage in the service life cycle. Information systems of telecommunications providers are designed, implemented and supported by IT companies based on the End-to-End model. This requires the IT company to solve a number of complex problems. In these conditions, building a service architecture, implementing and providing a service are divided into subproblems. Solutions to subproblems must be integrated to determine the coordinated activities of both the IT company and the provider. In this case, it is necessary to take into account the goals of IT companies, providers and their customers in such a way that it is beneficial to all parties. One of such subproblems is the formation of service packages that the IT company offers to providers. The article proposes formal models for the subproblem of forming service packages that allow taking into account the interests of the IT company and providers. These are multi-criteria nonlinear mathematical programming models. To solve the subproblem of forming service packages, a two-stage algorithm and a modified version of the guided genetic algorithm are proposed. The use of these methods allows us to take into account the interests of the IT company and providers. Also, such important factors that affect the formation of packages as the base price of the service, service dependency, discount system, resource and other constraints of the IT company and providers are taken into account. The two-stage algorithm at the first stage uses classical algorithms for solving the knapsack problem, and at the second stage implements a compromise scheme to improve the solution. The second of the proposed methods uses three types of tools in combination. The first tool controls the convergence of the genetic algorithm. The second tool determines the choice of the best solutions taking into account the features of the multi-criteria problem. The third tool allows to obtain the best solutions to the optimization problem with the simultaneous choice of a discount strategy. Experimental studies have confirmed the effectiveness of the proposed methods. Their ability to form the basis of the technology of forming service packages as a component of the platform for supporting the life cycle of services is also confirmed.

Layout Planning of a Basic Public Transit Network Considering Expected Travel Times and Transportation Efficiency

Urban transit systems are crucial for modern cities, providing sustainable and efficient transportation solutions for residents’ daily commutes. Extensive research has been conducted on optimizing the design of transit systems. Among these studies, designing transit line trajectories and setting operating frequencies are critical components at the strategic planning level, and they are typically implemented in an urban integrated transportation network. However, its computational complexity grows exponentially with the expansion of urban integrated transportation networks, resulting in challenges to global optimization in large-scale cities. To address this problem, this study investigates the layout planning of a basic public transit network (BPTN) to simplify the urban integrated transportation network by filtering out road segments and intersections that are unattractive for both users and operators. A non-linear integer programming model is proposed to maximize the utility of the BPTN, which is defined as a weighted sum of expected travel times (from a user perspective) and transportation efficiency (from an operator perspective). An expected transit flow distribution (ETFD) analysis method is developed, combining different assignment approaches to evaluate the expected travel time and transportation efficiency of the BPTN under various types of transit systems. Moreover, we propose an objective–subjective integrated weighting approach to determine reasonable weight coefficients for travel time and transportation efficiency. The problem is solved by a heuristic solution framework with a topological graph simplification (TGS) process that further simplifies the BPTN into a small-scale graph. Numerical experiments demonstrate the efficacy of the proposed model and algorithm in achieving desirable BPTN layouts for different types of transit systems under variable demand structures. The scale of the BPTN is significantly reduced while maintaining a well-balanced trade-off between expected travel time and transportation efficiency.

Drawdown minimization in asset portfolio selection: MINLP models and efficient cross‐entropy algorithm

AbstractPortfolio management is an important research topic in finance and optimization. Drawdown as one of the measures in evaluating portfolios indicates the relative difference between the portfolio value in the current moment and its maximum value during a given time interval in the recent past. In this paper, first, the importance of this measure is discussed and then two mixed‐integer nonlinear programming (MINLP) models with the objectives of minimizing the expected drawdown and the maximum drawdown under real‐world constraints are presented. Due to the NP‐hardness of this problem, by utilizing the problem structure, an efficient cross‐entropy‐based algorithm is presented to solve it. An effective mechanism is suggested to calibrate the algorithm parameters. Computational results confirm the performance of the proposed algorithm from both solution quality and running time in comparison with MINLP solvers.

Modeling a Green and Reliable Intermodal Routing Problem for Food Grain Transportation Under Carbon Tax and Trading Regulations and Multi-Source Uncertainty

This study addresses an intermodal routing problem encountered by an intermodal transportation operator fulfilling the food grain transportation order of an agri-food company. To enhance the environmental sustainability of food logistics, carbon tax and trading regulations have been employed to reduce the carbon emissions associated with transportation. Multi-source uncertainties, including the company’s demand for food grains and various parameters related to the intermodal transportation activities, are modeled via trapezoidal fuzzy numbers to optimize the comprehensive reliability of the solution. This work incorporates wastage reduction by lowering the wastage costs and formulating a wastage threshold constraint in intermodal routing. Accordingly, a fuzzy mixed-integer nonlinear programming model for a green and reliable intermodal routing problem for food grain transportation is proposed. To overcome the model’s insolvability and the difficulty in finding the global optimum solution to a nonlinear optimization model, a two-stage solution method is developed, employing chance-constrained programming and linearization technique to reformulate the initial model. A numerical case study is given to verify the feasibility of the proposed methods. Sensitivity analysis reveals the influence of confidence levels and wastage threshold, providing insights for the agri-food company to balance economics, reliability, and wastage reduction in food grain transportation. The numerical case study also analyzes the feasibility of carbon tax and trading regulations in reducing carbon emissions, concluding that carbon tax regulations consistently achieve greater reductions and are universally feasible. In contrast, the feasibility of carbon trading regulations depends on confidence levels and wastage threshold. The findings of this work could provide strong quantitative support for intermodal transportation operators and agri-food companies seeking to implement sustainable food grain transportation.

Optimization of cargo distribution for high-speed freight trains to overcome strong wind conditions

The high-speed freight train (HSFT) is an emerging freight transportation mode that can play a significant role in the development of remote cities. In this study, we propose an optimization method for cargo distribution to prevent HSFT from overturning in strong winds. The multibody dynamics (MBD) HSFT model is built and imposed with aerodynamic loads derived through the computational fluid dynamics method. Based on the MBD simulation results, the prediction model of overturning safety for HSFT is established using gradient-boosting decision tree to make the value of cargo height continuous. Consequently, a nonlinear programming model for the cargo distribution problem is built and solved. The MBD simulation results reveal that the outer side crosswind is good for large vehicle velocity and the vehicle in the rear position of HSFT is safer. The case study demonstrates that the proposed optimization method can decrease the overturning risk for HSFT by more than 10% compared with the even distribution scheme. This research will contribute to making the loading plan for the rail company, ensuring the operational safety of HSFT in the windy area.

Optimal structural and functional assemblies in additive manufacturing using the African buffalo-inspired part segregation algorithm

In multilevel or additive production, reduction of the total manufacturing duration is crucial. This may be achieved by harmonizing assembly and production time and by simultaneous collaboration with component manufacturers, thus incurring fewer delays. Here, a novel approach, the African buffalo-inspired part segregation algorithm, is proposed for optimal structural and functional assemblies in additive manufacturing. A mixed-integer nonlinear programming model is developed to assess the near-term optimum criteria area and dispersed materials in a computational manufacturing context. The number of support substances, total production period and total assembly costs are reduced in the time-reduction approach. A specific swarm intelligence-part-based segregation strategy is used to choose the appropriate number of element assemblages, and a part division strategy that complies with the criteria for transverse effect, dimensions and elevations is applied. The proposed approach is evaluated for structures with conventional and free-form borders using two real-size three-dimensional representations. The results indicate that this method may reduce overall production time compared to the time spent constructing one component, under all investigated circumstances.

Integrated optimization of flexible train timetable, stop plan and exogenous passenger assignment under demand responsive condition

Demand responsive bus has been put into practice widely in recent decades. However, implementing this concept in railway transportation poses considerable challenges. One of the main obstacles is how to synchronize train timetable, stop plan, and passenger assignment to guarantee the interests of the operators and passengers. Additionally, it is crucial to fulfill various operational requirements under resource constraints and address the issue of supply-demand mismatch. This paper introduces an integrated optimization model incorporating a flexible train timetable, stop plan, and exogenous passenger assignment based on demand responsiveness. Realistic situations, such as overtaking, no preset train departure time window, and allowing passengers’ requests to be rejected, are considered. Leveraging data from the trip reservation system (TRS), we aim to maximize enterprise operating profit while minimizing passenger travel costs. To achieve this, we embed the train stop plans and passenger assignment constraints into the train timetable, introduce the reservation rolling horizon, and establish a multi-objective mixed-integer nonlinear programming (MINLP) model. We employ the GUROBI optimization solver to obtain optimal or near-optimal solutions for our proposed model. Numerical and real-world cases are conducted to demonstrate the performance of the proposed method. The experimental results show that, even for the real-world Xiamen-Shenzhen railway corridor, the GUROBI solver efficiently generates integrated solutions within acceptable computational times, highlighting the effectiveness of our proposed model.

A joint work package sizing and scheduling problem considering resource constraints with a look-ahead heterogeneous reinforcement learning method

Effective work package sizing and project scheduling are crucial for construction project management. However, existing studies often address them as separate optimisation problems, neglecting the interactive nature of these processes. In practical scenarios with limited resources, there is an increasing demand for integrating work package sizing and project scheduling to enhance project management efficiency. This research aims to bridge this gap by developing an integer non-linear programming model that incorporates work package sizing and project scheduling while considering their interaction within a resource-constrained environment. Moreover, we introduce a novel look-ahead heterogeneous reinforcement learning approach that dynamically adjusts work package sizes and project schedules based on observed information at each decision step. A look-ahead sequential decision mechanism is proposed to effectively address the interdependencies and constraints inherent in the joint model. We extend the heterogeneous agent mirror learning technique to our problem to improve sample efficiency and ensure progressive enhancement of the joint policy. To evaluate our approach's effectiveness, we conduct experiments using datasets of 15, 30, 60, 90, and 120 tasks from Rangen and PSPLIB and validate our method in a real-world modular integrated construction project. The experimental results reveal that a joint model integrating work package sizing and project scheduling offers a more comprehensive understanding of their interplay, leading to better resource utilisation and improved project schedules. A comparative analysis against existing state-of-the-art reinforcement learning and priority rule-based methods further substantiates the superior effectiveness of our proposed approach, yielding an approximate 5% reduction in total project cost.

Optimizing Batch Scheduling of Multiproduct Pipelines Using a Smooth Modeling Approach

Summary The main method of delivering oil products is by the sequential operation of pipelines. Scheduling oil batches efficiently, considering intricate constraints, is typically a challenging problem that is not readily solvable. The present work developed a systematic approach for the optimization of batch scheduling. The model utilized a continuous-time representation with the objective of minimizing the total costs related to energy and oil mixing loss. The analysis included multiple constraints, including time frame, oil download, flow rate, and fluctuations in pressure caused by friction at various batch interface locations. By applying the penalty function approach, the original model was transformed into an unconstrained model. Smoothing was applied to the noncontinuous variables using the Dirac delta function and the maximum entropy function. A novel nonlinear programming (NLP) model was successfully devised to enhance the efficiency of oil product scheduling. A successive function approximation algorithm was used to solve the model, and the decision variables were modified to decrease the number of model decision variables and enhance the system’s capacity to surpass the local optimum. Subsequently, the model was calculated to address a practical multiproduct pipeline scheduling problem. The model presented in this study identified 74 decision variables, which account for around 1% of the typical mixed integer linear programming (MILP) model. The method presented in this work has the capability to accurately obtain an enhanced solution, making it useful for real applications.

Two non-linear programming models for the multi-stage multi-cycle smart production system with autonomation and remanufacturing in same and different cycles to reduce wastes

Two non-linear programming models for the multi-stage multi-cycle smart production system with autonomation and remanufacturing in same and different cycles to reduce wastes

Electric airport ferry vehicle scheduling problem for sustainable operation

This study discusses the challenges and solutions surrounding the scheduling of electric airport ferry vehicles (EAFVs) in the aviation industry. With the rise of electric vehicle technology and the push for sustainability, the adoption of EAFVs presents a significant opportunity for reducing emissions in airport ground transportation. However, scheduling EAFVs involves integrated considerations of operational scheduling and charging scheduling. To address these challenges, this study proposes a mixed-integer nonlinear programming (MINLP) model aimed at minimizing total costs associated with EAFV utilization while adhering to flight time window constraints and ensuring electric power availability. Furthermore, we transform the proposed MINLP model into a solvable mixed-integer linear programming model, facilitating its solution using off-the-shelf commercial solvers. To meet the requirements of the large international airport, we propose a stabilization approach for solving the large-scale instances. Finally, we further analyze the influence of crucial parameters, including the number of EAFVs deployed, the number of flights for servicing, and the charging power of charging facilities. Managerial policies are proposed for the airport managers based on the findings. This research addresses both theoretical and practical aspects, offering valuable policy recommendations for the effective EAFV management and providing a foundation for further exploration in EAFV scheduling. The findings contribute to the advancement of sustainable transportation practices in the aviation industry.

Design and optimization of steam power systems in industrial parks based on the distributed steam turbine system

Steam power systems (SPSs) in industrial parks are the typical utility systems for heat and electricity supply. In SPSs, electricity is generated by steam turbines, and steam is generally produced and supplied at multiple levels to serve the heat demands of consumers with different temperature grades, so that energy is utilized in cascade. While a large number of steam levels enhances energy utilization efficiency, it also tends to cause a complex steam pipeline network in the industrial park. In practice, a moderate number of steam levels is always adopted in SPSs, leading to temperature mismatches between heat supply and demand for some consumers. This study proposes a distributed steam turbine system (DSTS) consisting of main steam turbines on the energy supply side and auxiliary steam turbines on the energy consumption side, aiming to balance the heat production costs, the distance-related costs, and the electricity generation of SPSs in industrial parks. A mixed-integer nonlinear programming model is established for the optimization of SPSs, with the objective of minimizing the total annual cost (TAC). The optimal number of steam levels and the optimal configuration of DSTS for an industrial park can be determined by solving the model. A case study demonstrates that the TAC of the SPS is reduced by 220.6 k$ (2.21%) through the arrangement of auxiliary steam turbines. The sub-optimal number of steam levels and a non-optimal operating condition slightly increase the TAC by 0.46% and 0.28%, respectively. The sensitivity analysis indicates that the optimal number of steam levels tends to decrease from 3 to 2 as electricity price declines.

Structural Challenges and a Role Innew Health Policy Management in Future India

Objectives: This paper aims to investigate the evolution of supply chain management (SCM) in the globalization era, which is typified by the focus on global supplier relationship systems and the growth of supply chains across national borders and continents. Methods: The introduction of the mathematical models, which include a broad range of linear, integer, and non-linear programming models, is the first section of this paper. Location modeling and transportation planning are two common applications for heuristic models. Although mathematical and heuristic models are best suited for analytical problem solving, complex real-world issues frequently call for basic assumptions. In simulation models, the intricacies of the problem and the relationships between different variables are represented by equations, and then an attempt is made to discuss a comparative analysis of the results. Results: Once put into place, the system always has a lifespan that is determined by the previously mentioned factors and problems. It would be more accurate to say that all developed systems should be reviewed on a regular basis and any necessary adjustments made to maintain their functionality and effectiveness. Conclusion: According to this paper, the fiercely competitive food production market is largely driven by time-based competition, and a producer's or farmer's ability to offer a customer a flexible and responsive supply determines its competitive edge. These businesses understand that providing creative products and outstanding customer service is essential to retaining clients and opening up new revenue streams.

Joint optimization of overbooking and seat allocation for high-speed railways considering stochastic demand.

To mitigate empty seat loss caused by random passenger no-show behavior, this study extends seat allocation to joint optimization of overbooking and seat allocation for high-speed railways (HSR). Assuming that stochastic passenger demand follows a specific distribution and considering various constraints, including train capacity, demand, and denied boarding rate constraints, a nonlinear stochastic programming model for joint optimization of overbooking and seat allocation for HSR is constructed with the aim of maximizing railway expected revenue. To solve this optimization model, a multi-level optimization algorithm is designed. Based on the sampling averaging approximation method, demand scenarios and passenger no-show scenarios are generated and the optimization problem is decomposed, including the joint optimization of overbooking and seat allocation under a single demand scenario, and the ticket adjustment under other demand scenarios. For the former, it is further divided into two sub-problems according to the stochastic nature of passenger no-show behavior, which is optimized iteratively. Finally, the effectiveness of the proposed model and algorithm is evaluated through numerical studies. The results demonstrate that the proposed joint optimization method effectively addresses the randomness of passenger demand and no-show behavior, thereby improving HSR expected revenue and making up for the empty seat loss resulting from passenger no-show behavior.

Optimal Allocation of Depots for Electric Bus Charging: Cost Minimization and Power System Impact Mitigation Using Mixed Integer Nonlinear Programming

ABSTRACTThis paper proposes a novel approach for the optimal allocation of a depot for electric buses (EBs) charging in a specific transit service, considering the impact on the power system. The main objective is to minimize the total cost, achieved by minimizing the cost of the new cables connecting the depot station to the distribution system and the upgrade cost of existing lines to meet the additional loads. The outcomes are the optimal location of the depot, the optimal electric node bus in the distribution system to supply it, and the required system upgrades. The optimization problem is formulated as a Mixed Integer Nonlinear Programming (MINLP) model and solved using the General Algebraic Modeling System (GAMS). The methodology is tested on the H16 EB service line in Barcelona, Spain, and a typical electrical distribution system. Three case studies are presented in this paper. In the first case, the impact of a single service on the distribution network is analyzed, and in the second case, three H16 EB services are assumed to serve the network. The third case handles a multi‐route, multi‐terminal bus service to allocate and supply a depot capable of accommodating all the routes. This case will also include sensitivity analysis to test the robustness and reliability of the model. Results show that for a single H16 EB service, no line upgrades were needed, and the total cost per phase was $120,000. For three H16 EB services, three lines required upgrades, and the total cost per phase increased to $718,000. In the third case, the sensitivity analysis revealed that higher demand factors lead to increased costs due to more update requirements and voltage deviations. The results demonstrate that the minimum distance between the depot and node is not always the optimal or feasible solution that would prevent the depot load installation at a weak spot and meet the power flow constraints.