Mixed Integer Nonlinear Programming Research Articles

Optimizing Route and Speed under the Sulfur Emission Control Areas for a Cruise Liner: A New Strategy Considering Route Competitiveness and Low Carbon

In order to reduce pollution caused by ship emissions, the International Maritime Organization (IMO) implemented sulfur emission control areas (SECAs). In comparison to ordinary vessels, cruise ships with dual attributes of transportation and tourism generate a greater amount of marine pollution, which poses a significant threat to the marine environment in both berthing ports and the sailing area. In light of the fierce competition of the cruise tourism market, cruise lines are looking for strategies, such as designing more attractive cruise routes, to maintain their core competencies under the emission control policy. In order to achieve this goal, this paper presents a mixed-integer non-linear programming (MINP) model with two objectives and is derived from the traditional route optimization problem. The primary objective is to optimize the route and speed of a cruise liner, while simultaneously enhancing route competitiveness and minimizing carbon emissions both within and outside the SECAs. Subsequently, the multi-objective particle swarm optimization (MOPSO) algorithm was used to reach the objective, and simulations were carried out to verify the effectiveness of the model and method. The results show that speed and sailing route optimization can affect carbon emissions. This paper has a certain application value and guiding significance for cruise line decision makers that will be beneficial for the environment.

Lyapunov-guided Deep Reinforcement Learning for service caching and task offloading in Mobile Edge Computing

With the development of Internet of Things (IoT) networks and Mobile Edge Computing (MEC), many computing-intensive applications have been developed in large quantities. Due to the heterogeneity of tasks, different application services are required to perform each task. Caching application services and related data in edge servers is challenging. Hence, we study the service cache placement and task offloading problem in IoT networks. Since IoT devices and edge servers with limited storage resources can only cache a few services at the same time, we formulate the service cache placement and task offloading of IoT devices problem to minimize task service delay with long-term energy constraint of IoT devices, which is a mixed integer nonlinear programming problem. To solve this problem, an online Deep Reinforcement Learning guided by the Lyapunov optimization framework algorithm (LYADRL) is proposed. We first build a virtual queue model to decouple the problem by Lyapunov optimization technique to transform the problem into a single time slot optimization problem. Then, we use Deep Reinforcement Learning techniques to find the optimal edge service caching and task offloading policies for each time slot. Simulation results show that our algorithm can reduce the service delay compared with other benchmark algorithms.

Full-Duplex Unmanned Aerial Vehicle Communications for Cellular Spectral Efficiency Enhancement Utilizing Device-to-Device Underlaying Structure

Unmanned aerial vehicle (UAV) communications have gained recognition as a promising technology due to their unique characteristics of rapid deployment and flexible configuration. Meanwhile, device-to-device (D2D) and full-duplex (FD) technologies have emerged as promising methods for enhancing spectral efficiency and offloading traffic. One significant advantage of UAVs is their ability to partition suitable D2D pairs to increase cell capacity. In this paper, we present a novel network model in which UAVs are considered D2D pairs underlaying cellular networks, integrating FD into the communication links between UAVs to improve spectral efficiency. We then investigate a resource allocation problem for the proposed FD-UAV D2D underlaying structure model, with the objective of maximizing the system’s sum rate. Specifically, the UAVs in our model operate in full-duplex mode as D2D users (DUs), allowing the reuse of both the uplink and downlink subcarrier resources of cellular users (CUs). This optimization challenge is formulated as a mixed-integer nonlinear programming problem, known for its NP-hard and intractable nature. To address this issue, we propose a heuristic algorithm (HA) that decomposes the problem into two steps: power allocation and user pairing. The optimal power allocation is solved as a nonlinear programming problem by searching among a finite set, while the user pairing problem is addressed using the Kuhn–Munkres algorithm. The numerical results indicate that our proposed FD-MaxSumCell-HA (full-duplex UAVs maximizing the cell sum rate with a heuristic algorithm) scheme for FD-UAV D2D underlaying models outperforms HD-UAV underlaying cellular networks, with improved access rates for UAVs in FD-MaxSumCell-HA compared to HD-UAV networks.

A new hybrid approach for cold load restoration using deep learning

After an extended outage in a power system, restoration of feeders with high penetration levels of thermostatically controlled loads (TCLs) will be a challenging problem. By restoring these feeders, the demand will increase several times the normal conditions which is called the cold load pick-up (CLPU) phenomenon. This can lead to overload of equipment such as power transformers in transmission substations. In order to increase the reliability of network load supply, in transmission substations, usually several transformers are used which can be operated in parallel by closing circuit breakers on the secondary side called bus section (BS). When the restoration process is long and the loads are cold, more loads can be restored by closing the BSs and paralleling the transformers. On the other hand, it is not possible to close all the BSs simultaneously because paralleling all the transformers at the same time increases the short circuit level on the secondary side. Furthermore, in power systems, some loads are voltage-dependent and by reducing the voltage, their demand can be decreased and therefore the restoration process is expedited. Due to the increase in demand caused by CLPU, additional stress is applied to the power system, which can lead to operational constraints violation and even long-term voltage instability. Therefore, at the time of restoration of each feeder, the settings of voltage control devices are updated to avoid the violation of operational constraints and the occurrence of wider events. In this paper, in order to reduce cold load restoration time, closing the bus sections and voltage reduction are used simultaneously. Also, short circuit and operational constraints are considered. The cold load restoration problem is formulated as a mixed integer nonlinear programming and is solved using the pattern search algorithm. Since there are many decision variables and solving the problem is time-consuming, a combination of deep learning networks, pattern search algorithm and parallel computing is used to accelerate the computations.

Incorporating decentralized facilities into the food waste treatment infrastructure in Megacity: A locational optimization in Beijing

Food waste management has emerged as a pivotal issue with the acceleration of urbanization. Inappropriate treatment of food waste causes environmental contamination, resource squandering, and land occupation. This research explores optimal strategies in Beijing with an experimental case study on the bioconversion technology using black soldier fly larvae (BSFL), comparing centralized and decentralized approaches. We studied waste sorting behaviors influenced by community characteristics, employing an Agent-Based Model (ABM) and a mixed integer non-linear programming (MINLP). Results indicate that 29 % of Beijing's food waste could be suitably managed through decentralized methods with BSFL, particularly in outlying areas and densely populated suburbs. Decentralized treatment exhibits the potential to boost waste separation participation in medium-sized, close- knit communities. However, this approach encounters hurdles related to technological implementation, public perception, and urban planning. This study underscores the need for community-specific strategies and a concerted effort from communities, government, and the private sector in advancing sustainable urban food waste management.

Joint optimization of deployment, user association, channel, and resource allocation for fairness‐aware multi‐UAV network

AbstractThis paper studies the problem of joint deployment, user association, channel, and resource allocation in unmanned aerial vehicle‐enabled access network. Since different user equipments performing different tasks and have different data rate requirements, the priority‐based traffic fairness problem is investigated. This problem, however, is a mixed integer nonlinear programming problem with NP‐hard complexity, making it challenging to be solved. To address this issue, a self‐organized and distributed framework “sense‐as‐you‐fly” based on the decomposition process, which divides the original problem into several subproblems, is proposed. Assuming without central controller, we derive the closed‐form resource allocation scheme and propose distributed many‐to‐one matching to optimize user association subproblem. Considering the coupled characteristics, the multi‐unmanned aerial vehicle deployment and channel allocation subproblems are modelled as a local altruistic game. The existence of Nash equilibrium is proved with the aid of exact potential game and efficient best response learning‐based algorithm is proposed. The original problem is finally addressed by solving the sub‐problems alternately and iteratively. Simulation results verify its effectiveness. By jointly optimizing multidimensional variables, the proposed algorithm unlocks network performance gains, especially in resource‐limited regimes.

Recovery Scheduling of Road Networks Considering Day-to-Day Flow Evolution

Natural disasters can lead to substantial disruptions in road networks, making many critical links unusable. It is important to timely repair the damaged links as they allow transportation of emergency services, relief materials, and so forth, after disasters. Many existing studies that focus on optimal recovery of damaged links after disasters assume that only a single agency is available for repair. Moreover, most of the existing studies do not consider travel time on links to be a function of traffic flow passing through the links and assume that the traffic flow gets distributed based on user equilibrium each time a link is repaired. However, such a traffic distribution is unrealistic as it assumes that the traffic flow remains the same across all the days for which a link is repaired and the traffic distribution gets suddenly modified whenever a link is fully repaired. The goal of this paper is to address these gaps in the literature of disaster recovery. We study the problem of determining the optimal repair scheduling of damaged links to minimize the sum of the total system travel time over the repair duration given that multiple repair agencies are available for recovery. Also, we consider a day-to-day traffic flow evolution where the route choices of travelers depend on the travel conditions of the previous day. We formulate this problem as a mixed-integer non-linear program. We proposed two solution methodologies to solve the problem: a genetic algorithm and a greedy algorithm. We tested these methodologies under different settings.

Cluster-Based Strategy for Maximizing the Sum-Rate of a Distributed Reconfigurable Intelligent Surface (RIS)-Assisted Coordinated Multi-Point Non-Orthogonal Multiple-Access (CoMP-NOMA) System.

This article proposes a distributed intelligent Coordinated Multi-Point Non-Orthogonal Multiple-Access (CoMP-NOMA) collaborative transmission model with the assistance of reconfigurable intelligent surfaces (RISs) to address the issues of poor communication quality, low fairness, and high system power consumption for edge users in multi-cellular networks. By analyzing the interaction mechanisms and influencing factors among RIS signal enhancement, NOMA user scheduling, and multi-point collaborative transmission, the model establishes RIS-enhanced edge user grouping and coordinates NOMA user clusters based on this. In the multi-cell RIS-assisted JT-CoMP NOMA downlink transmission, joint optimization of the power allocation (PA), user clustering (UC), and RIS phase-shift matrix design (PS) poses a challenging Mixed-Integer Non-Linear Programming (MINLP) problem. The original problem is decomposed by optimizing the formulas into joint sub-problems of PA, UC, and PA and PS, and solved using an alternating optimization approach. Simulation results demonstrate that the proposed scheme effectively reduces the system's power consumption while significantly improving the system's throughput and rates.

A Bayesian optimization approach for data‐driven mixed‐integer nonlinear programming problems

AbstractThe optimization of process systems within the field of Chemical Engineering often confronts uncertainties that can exert significant influences on the performance and dependability of the obtained solutions. This research endeavors to investigate the application of Bayesian optimization in the realm of constrained mixed integer nonlinear problems. A comparative analysis was conducted, exploring different surrogate models, and evaluating diverse kernel functions and acquisition functions. Furthermore, a sampling strategy was devised to assess the enhancement achieved by the acquisition function. The findings of this article reveal the superior performance of sparse Gaussian processes in conjunction with computationally inexpensive acquisition functions, thereby highlighting their suitability for addressing mixed integer nonlinear programming problems characterized by noisy functions and stochastic behavior. Consequently, this article presents a computationally efficient approach to effectively tackle the challenges associated with data‐driven mixed integer nonlinear programming problems within the domain of Process System Engineering.

Multi-objective location-routing model and algorithm study of material reserve bases for large-scale railway engineering construction projects

Material supply is an important support for engineering construction and an important factor affecting the progress and quality of engineering construction. A multi-objective mixed-integer nonlinear programming model is proposed for the location routing problem of the material reserve base of large-scale railway engineering construction projects, considering realistic factors like the construction period, the cycle of the material reserve, the variety of materials, the heterogeneous fleet, and demand splitting. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA- II) is developed for solving this model. This paper optimises obtaining the initial population based on the linear feature of railway engineering, improves the fitness function, and designs a two-stage crossover operator. In addition, the algorithm is compared with the augmented ϵ-constraint method with the help of a practical example. Three metrics are used to assess the performance of the algorithm's outputs, and two metrics are used to assess the similarity of the Pareto fronts obtained by the two algorithms. The results show that the proposed algorithm performs better in terms of ‘quantity’ and ‘spacing’, that the Pareto solutions obtained are accurate, and that the speed of solution is almost 10 times that of the augmented ϵ-constraint (AUGMECON) method.

A MINP model and hybrid heuristic algorithm for railway cold chain service network design problem: a case study of China

Railway Cold Chain Service Network Design (RCC-SND) aims to optimise resource allocation and utilisation to ensure the efficient transportation of perishable foods. In this study, we propose a Mixed Integer Nonlinear Programming (MINP) model to solve the hub selection, service frequency determination, wagon flow organisation and routing problems in RCC-SND. The application of the model is illustrated using the real network comprising 163 cities in China. The PSO-GA algorithm is proven effective in solving the problem. Furthermore, we introduce two future scenarios to assess the carbon reduction potential and economic costs of railway cold chain operations. There are some main findings: as the hub number increases from 30 to 40, the total cost decreases, as the hub continues to rise, this reduction is offset by the increased hub operational costs. Increasing hubs can enhance direct train frequency while causing railway capacity redundancy, this redundancy can be addressed by freight volume increase, as demonstrated in this study, 4.5 times increase in freight volume can boost train utilisation by up to 12.5%. By 2030, railway cold chain carbon emissions are projected to exceed 1.1 million tons, the adoption of hydrogen as alternative energy is an economically viable solution for emission reduction.

Shared e-bike operational planning under different relocation schemes: A smart campus case

Major urban centers are grappling with challenges related to urban mobility and elevated greenhouse gas emissions. Shared electric bicycles (e-bikes) present a potential solution to these issues. Nonetheless, many ventures of this nature have previously faltered due to high operational costs. This paper aims to assess the optimal decisions for a shared e-bike company serving a university community. To this end, we consider two relocation strategies: one led by the operator and another by the user. Additionally, we examine elements inherent to a smart campus, such as photovoltaic systems and advanced energy tariffs, like time-of-use and real-time tariffs. We modeled the optimization problem as a mixed-integer nonlinear program, further linearized to a mixed-integer linear program using the Big-M method. Our case study focuses on the academic community at Universidade Federal Fluminense in Niterói, Brazil. Findings suggest a trade-off between operator and user relocation tariffs. They also underscore an enhancement in meeting demand, from 51 % to 69 %, when both mechanisms are employed. Lastly, the smart campus influences the operator's decisions, highlighting the importance of considering the interplay between energy and rental tariffs during planning.

Deep reinforcement learning based latency-energy minimization in smart healthcare network

Significant breakthroughs in the Internet of Things (IoT) and 5G technologies have driven several smart healthcare activities, leading to a flood of computationally intensive applications in smart healthcare networks. Mobile Edge Computing (MEC) is considered as an efficient solution to provide powerful computing capabilities to latency or energy sensitive nodes. The low-latency and high-reliability requirements of healthcare application services can be met through optimal offloading and resource allocation for the computational tasks of the nodes. In this study, we established a system model consisting of two types of nodes by considering nondivisible and trade-off computational tasks between latency and energy consumption. To minimize processing cost of the system tasks, a Mixed-Integer Nonlinear Programming (MINLP) task offloading problem is proposed. Furthermore, this problem is decomposed into task offloading decisions and resource allocation problems. The resource allocation problem is solved using traditional optimization algorithms, and the offloading decision problem is solved using a deep reinforcement learning algorithm. We propose an Online Offloading based on the Deep Reinforcement Learning (OO-DRL) algorithm with parallel deep neural networks and a weight-sensitive experience replay mechanism. Simulation results show that, compared with several existing methods, our proposed algorithm can perform real-time task offloading in a smart healthcare network in dynamically varying environments and reduce the system task processing cost.

Heterogeneous joint vaccine allocation and quarantine restriction planning under uncertainty: The COVID-19 pandemic

Once effective vaccines are discovered for a pandemic and initial distribution infrastructure, and mechanisms are implemented, the next concern is an optimal vaccination campaign to stop the disease or minimize the casualties. This paper studies the optimization of a Vaccine Distribution Network (VDN) through a single-objective Mixed-Integer Non-Linear Programming (MINLP) model for minimizing the total cost in terms of governmental aid (to maintain the economy), logistics, vaccination, and hospitalization costs. The proposed model develops the optimal joint vaccination-quarantine strategy under equity considerations to (1) determine the optimal allocation of available vaccine stockpiles to different population classes in different regions and (2) seek to impose quarantine restrictions to different regions optimally. The proposed model was applied to a real case study, the vaccine distribution network in France. Through a comprehensive numerical analysis, the optimal vaccine allocation is calculated, and the impact of equity and quarantine on the performance of the distribution network is investigated. Moreover, fractional dosing on the number of infections is examined. The results show that equity considerations, counter-intuitively, lead to an increased number of infections. Furthermore, it is illustrated that fractional dosing helps policymakers to control the pandemic better under a limited supply of vaccines.

DNN-based algorithm for joint SIC ordering and power allocation in downlink NOMA-enabled heterogeneous networks

In the heterogeneous network (HetNet) employing downlink non-orthogonal multiple access (NOMA), we focus on the non-convex optimization problem to optimize the spectral efficiency (SE) while the users satisfy the quality-of-service (QoS) requirement. In the previous work, the optimal joint successive interference cancellation and power allocation (JSPA) algorithm for maximizing SE is proposed to solve the mixed-integer non-linear programming (MINLP) problem in NOMA-enabled HetNet. However, the optimal solution requires exponential complexity by the number of base stations (BSs). Therefore, we present a deep neural network (DNN)-based algorithm for JSPA to reduce the complexity. In particular, to deal with the MINLP-based JSPA problem, we reformulate it into an equivalently simple problem that optimizes only the power consumption of BSs. Then, we introduce the unsupervised DNN-based method for JSPA to handle the simplified problem. The presented scheme yields improved SE and outage performance compared with traditional DNN-based methods. Additionally, we propose a user selection scheme with low complexity to enhance the SE of the proposed DNN-based power allocation. Through simulations, we illustrate that the suggested DNN-based scheme can attain SE performance similar to that of the optimal scheme.

Model for Intercity Railway Schedule Optimization Incorporating Metrorail Transfers

The promotion of multimodal coordination is of great significance for the joint development of diverse urban transportation systems. Focusing on a comprehensive urban passenger transport hub that converges both intercity modes and multiple inner-city modes, our study aims to incorporate intercity railway and Metrorail coordination into train scheduling optimization to enhance transfer efficiency and provide a seamless service for passengers in urban railway networks. By considering the variety of passenger demands in different transport modes (e.g., rail transit and traditional mainline railway), train loading capacity, and potential disruption scenarios, we specifically developed a mixed-integer nonlinear programming (MINLP) model to simultaneously generate the coordination strategies, arrival/departure times of trains at each station, and the number of carriages in service in the network. To enhance computational efficiency, we proposed several improvement strategies involving the model linearization to reformulate the MINLP model into a mixed-integer linear programming (MILP) model and the determination of appropriate big- M values. Finally, numerical experiments based on historical passenger data from a realistic urban railway network in China were implemented to verify the effectiveness of our approach. The results demonstrate that our intercity railway and Metrorail coordination strategies could, in practice, significantly improve passenger transfer efficiency by over 35% compared with the train schedule without coordination.

Integrated truck drone delivery services with an optimal charging stations

Battery-powered drones, or unmanned aerial vehicles (UAVs), present significant market potential for faster, economical, and eco-friendly urban delivery solutions. Many firms are investing in drone logistics ventures to capitalize on their capabilities. However, the limited range of drone deliveries, dictated by battery capacity, poses a significant challenge. Hybrid delivery systems combining trucks and drones have gained attention to overcome this challenge. Traditional models assume trucks park at customer sites while drones handle additional deliveries, yet this approach may hinder drone efficiency due to constraints in parking availability. Alternative approaches like battery swapping and mobile charging stations on trucks have been explored but exhibit limitations such as blind spots and substantial battery reserves. We propose establishing dedicated drone charging stations and optimizing drone routing for efficient deliveries to address these issues We present a MINLP (Mixed Integer Non-Linear Programming) model aimed at identifying the most cost-effective solution that optimizes both transportation efficiency and charging infrastructure investment. Quantitative experiments demonstrate the efficacy of this approach, alongside sensitivity analysis aiding economic decision-making across various operational scenarios. Notably, our experiments show a 15% reduction in total costs when extending the operational lifespan of charging stations from 2 to 4 years.

Efficiently handling constraints in mixed-integer nonlinear programming problems using gradient-based repair differential evolution

Efficiently handling constraints in mixed-integer nonlinear programming problems using gradient-based repair differential evolution

Economic predictive control-based sizing and energy management for grid-connected hybrid renewable energy systems

Hybrid renewable energy systems (HRES) comprise a group of different energy sources and storage units that feed a specific load, efficiently. This research paper aims to develop a new methodology that provides the optimal size of the proposed HRES and runs it efficiently. Bi-level mixed-integer nonlinear programming (BMINLP) optimization approach is used to combine the sizing task and the energy management strategy (EMS) established utilizing the economic model predictive control (EMPC) method. The sizing task (upper layer) is formulated as mixed integer nonlinear programming (MINLP) optimization that has been implemented by the solver: multi-objective genetic algorithm (MOGA). EMS task (lower layer) is represented as a constraint embedded within the upper layer and executed as mixed integer linear programming (MILP) per each applied solution of the sizing task. The principal findings indicate that the total cost of the system is about 114,224 $. In detail, the annual fixed operation and maintenance, investment, and operating costs are 15,090 $, 28,351 $, and 70,783 $, correspondingly. Furthermore, around 90 % of the overall produced power is imported from the grid, while the load power represents about 95 % of the total demanded power.

Supply chain network design based on Big Data Analytics: heuristic-simulation method in a pharmaceutical case study

Digital technology is a pivotal aspect of the ongoing digital transformation upon which supply chain networks (SCNs) heavily rely. Through the utilization of Big Data Analytics (BDA), organizations can gain insights into sales, production and formulate decision support systems. The pharmaceutical supply chain emerges as a crucial player in producing and distributing medications vital for treating COVID-19 patients. In this study, we have innovatively designed a multi-echelon Pharmaceutical Supply Chain Network (PSCN) using BDA during the COVID-19 pandemic. We have developed a novel Mixed-Integer Non-Linear Programming model addressing allocation, production planning, and inventory control decisions, known as the LAPI problem. A transformation method is employed to convert the non-linear model into a linear one to enhance computational efficiency. The primary objective of our mathematical model is to minimize the total cost and CO2 emissions of the transportation system and established centres while maximizing the shelf life of medicines. Our experiments reveal that medium- and large-scale problems, characterized by the three main attributes of BDA – variety, velocity and volume (3 V‟s), pose challenges for optimal solutions. We present a case study of Iran to validate the mathematical model for large-scale problems. Employing a simulation approach, we estimate the demand for required pharmaceuticals, underscoring our proposed model’s real-world applicability and effectiveness. This research contributes to the growing necessity of eco-friendly and efficient supply chain strategies, especially in the critical domain of pharmaceuticals during pandemic situations.