Mixed-integer Programming Research Articles

Ultra-small world detection in networks: subgraphs with prescribed distance distributions

Abstract We introduce a class of distance-based clique relaxation models, which enforce certain distributions on vertex pairwise distances in the corresponding induced subgraphs. Both “local” and “global” versions of the proposed approach are studied. For the global case, the distribution of distances is considered for all vertex pairs in the subgraph. For the local (and, in a sense, more restrictive) case, the required property must be satisfied for any vertex with respect to its distances to the other vertices in the subgraph. We refer to the proposed clique relaxations as global and local $$\varvec{\gamma }$$ γ -ultra-small worlds, respectively, where parameter $$\varvec{\gamma }$$ γ controls the required distance distributions. Our modeling approach has several meaningful interpretations; in particular, it is closely related to the concept of an “effective” graph diameter. Furthermore, density- and degree-based quasi-cliques are two well-known special cases of the proposed concept. We exploit these relationships to develop mixed integer programs (MIPs) that can be used with an off-the-shelf solver for finding maximum global and local ultra-small worlds. Then, we outline a simple-to-implement algorithm that iteratively solves feasibility versions of our MIPs for each possible subgraph size within some lower and upper bounds; we derive one non-trivial upper bound using the linear programming relaxations. Our modeling approach also generalizes the k-club concept; hence, some links to this well-known distance-based clique relaxation are also explored. Finally, to illustrate the obtained results, we perform a computational study on graphs representing various types of real-world datasets and systems. Some interesting empirical observations and insights are provided.

Satellite Edge Computing for Mobile Multimedia Communications: A Multi-agent Federated Reinforcement Learning Approach

The rapid expansion of satellite mega-constellations has highlighted the potential of satellite edge computing as a promising solution for mobile multimedia communications. While reinforcement learning has been explored in satellite communication systems, significant challenges remain, including high latency and limited resources. This study addresses these challenges by focusing on the joint optimization of communication, computing, and caching resources in satellite edge computing to support mobile multimedia applications. A mixed-integer nonlinear programming (MINLP) problem is formulated with the objective of minimizing the total delay experienced by mobile users, subject to multidimensional resource capacity constraints, which is NP-hard and computationally intractable to solve in polynomial time. To address this complexity, we propose a multi-agent federated reinforcement learning (MAFRL) approach as an efficient solution. In this framework, each satellite operates as an autonomous learning agent equipped with an actor-critic network structure. The proposed MAFRL method demonstrates superior performance, achieving lower delays compared to all baseline approaches. It effectively optimizes delay-sensitive mobile multimedia communications by minimizing total delay and improving task offloading ratios. To the best of the authors’ knowledge, this study is the first to introduce a MAFRL-based approach for resource allocation in satellite edge computing, marking a significant contribution to the field.

Long-Term Energy Consumption Minimization Based on UAV Joint Content Fetching and Trajectory Design

Caching the contents of unmanned aerial vehicles (UAVs) could significantly improve the content fetching performance of request users (RUs). In this paper, we study UAV trajectory design, content fetching, power allocation, and content placement problems in multi-UAV-aided networks, where multiple UAVs can transmit contents to the assigned RUs. To minimize the energy consumption of the system, we develop a constrained optimization problem that simultaneously designs UAV trajectory, power allocation, content fetching, and content placement. Since the original minimization problem is a mixed-integer nonlinear programming (MINLP) problem that is difficult to solve, the optimization problem was first transformed into a semi-Markov decision process (SMDP). Next, we developed a new technique to solve the joint optimization problem: option-based hierarchical deep reinforcement learning (OHDRL). We define UAV trajectory planning and power allocation as the low-level action space and content placement and content fetching as the high-level option space. Stochastic optimization can be handled using this strategy, where the agent makes high-level option selections, and the action is carried out at a low level based on the chosen option’s policy. When comparing the proposed approach to the current technique, the numerical results show that it can produce more consistent learning performance and reduced energy consumption.

Cooperative scheduling of airport ground electric service vehicles considering workload balance: A column generation approach

Under the trend of electrification in civil aviation, airports are promoting electric ground vehicles to reduce carbon emissions. This paper conducts on electric airport ground service vehicles in scheduling optimization problems. Moreover, driver psychology is also a growing concern as it can affect the efficiency and safety of ground services. Workload balance is one of the major factors affecting driver psychology. In the context of facing challenges for ground vehicle scheduling, fully using electric vehicles and guaranteeing the workload balance are major concerns in our study. This paper investigates the electric shuttle buses and towing tractors cooperative scheduling considering workload balance optimization problem (e-STCSWB). We introduce a mixed integer programming formulation for e-STCSWB that considers cooperative relationships, workload balance, energy consumption and time windows to minimize total energy consumption costs. The e-STCSWB is obtained small scale exact solutions using the CPLEX solver. Furthermore, a column generation approach is developed, which is enhanced through a problem-specific strategy. Extensive computational results using real-world instances from one of China’s largest airports show that it can obtain optimal or near-optimal solutions. The problem-specific strategy significantly improve the performance in terms of solution quality and solution time. Finally, we perform sensitivity analyses to demonstrate the impact under different numbers of vehicles and workload balance requirements parameter settings.

P-1917. Hospital-Acquired Infections and Their Impact on Length of Stay for Veterans with COVID-19: A Nationwide Cohort Study

Abstract Background The COVID-19 pandemic has intensified concerns about hospital-acquired infections (HAI) due to multidrug-resistant organisms (MDRO) in hospitalized patients. This study assesses the excess length of stay (LOS) attributed to MDRO HAI across all acute Veterans Affairs (VA) hospitals. Methods A retrospective cohort study was conducted within the VA healthcare system, including 115,000 hospital admissions from March 1, 2020, to August 31, 2022. We included 71,432 COVID-19 patients admitted within 14 days of a lab-confirmed diagnosis, excluding cases with community-acquired infections, non-MDRO HAIs, and readmissions. We utilized balanced risk-set matching (RSM) and mixed integer programming (MIP) to optimize covariate balance via Mahalanobis distance among key variables including demographic data, comorbidities, and both time-independent and -dependent treatments. Standardized mean differences (SMD) were used to ensure covariate balance, with an absolute value of less than 0.1 considered balanced. Results We matched 1,088 patients who experienced HAI with MDRO. Covariate balance was achieved, with only minor deviations (SMD slightly over 0.1). The mixed-effect Poisson regression model adjusted for temporal and facility-level factors revealed that HAIs associated with MDRO resulted in a 32% longer LOS compared to the non-HAI group (95% CI: 30% - 35%; mean LOS: 26.8 days vs. 20.5 days; median LOS: 22 days vs. 16 days). Conclusion This study highlights the significant impact of HAIs due to MDROs on the length of hospital stays among veterans with COVID-19. The findings underscore the need for enhanced infection control practices and targeted strategies to mitigate the burden of HAIs in this vulnerable population. Further research should explore the specific mechanisms by which HAIs extend hospitalization and the potential for intervention at various levels of healthcare delivery. Disclosures All Authors: No reported disclosures

Charging Scheduling of Electric Vehicles Considering Uncertain Arrival Times and Time-of-Use Price

To advance sustainable transportation solutions, this work investigates an electric vehicle charging scheduling problem under the uncertainty of vehicle arrival times. Given a set of appointed electric vehicles, the objective of the considered problem is to explore charging strategies that minimize the total charging cost for the charging station. To address this problem, this work first establishes a mixed-integer programming model. Then, an enhanced sample average approximation approach alongside two versions of distribution-free approaches are applied to solve the studied problem. Additionally, this study introduces a BP neural network-enhanced distribution-free approach to efficiently resolve the problem. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed approaches.

Dynamic Robot Routing and Destination Assignment Policies for Robotic Sorting Systems

Robotic sorting systems (RSSs) use mobile robots to sort items by destination. An RSS pairs high accuracy and flexible capacity sorting with the advantages of a flexible layout. This is why several express parcel and e-commerce retail companies, who face heavy demand fluctuations, have implemented these systems. To cope with fluctuating demand, temporal robot congestion, and high sorting speed requirements, workload balancing strategies such as dynamic robot routing and destination reassignment may be of benefit. We investigate the effect of a dynamic robot routing policy using a Markov decision process (MDP) model and dynamic destination assignment using a mixed integer programming (MIP) model. To obtain the MDP model parameters, we first model the system as a semiopen queuing network (SOQN) that accounts for robot movement dynamics and network congestion. Then, we construct the MIP model to find a destination reassignment scheme that minimizes the workload imbalance. With inputs from the SOQN and MIP models, the Markov decision process minimizes parcel waiting and postponement costs and helps to find a good heuristic robot routing policy to reduce congestion. We show that the heuristic dynamic routing policy is near optimal in small-scale systems and outperforms benchmark policies in large-scale realistic scenarios. Dynamic destination reassignment also has positive effects on the throughput capacity in highly loaded systems. Together, in our case company, they improve the throughput capacity by 35%. Simultaneously, the effect of dynamic routing exceeds that of dynamic destination reassignment, suggesting that managers should focus more on dynamic robot routing than dynamic destination reassignment to mitigate temporal congestion. Funding: This work was supported by The Fundamental Research Funds for the Central Universities [Grant WK2040000094] and the National Natural Science Foundation of China [Grants 71921001 and 72091215/72091210]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0458 .

AI-Enabled Supply Chain Optimization

As global supply chains become more intricate, the significance of supply chain risk management has significantly increased. This research delves into the utilization of artificial intelligence (AI) in managing supply chain risks, analyzing cutting-edge advancements, obstacles, and potential areas for further exploration. Through a comprehensive review of literature sources like Google Scholar, Web of Science, EI, and Scopus, this study investigates how AI methods such as machine learning, deep learning, neural networks, fuzzy logic, genetic algorithms, and evolutionary algorithms can help mitigate supply chain risks. These AI technologies have demonstrated remarkable efficacy in mitigating various risks, including forecasting, anomaly detection, image recognition, text mining, logistics optimization, and emergency response tactics. Apart from AI-driven approaches, optimization solvers and algorithms play a critical role in tackling complex supply chain dilemmas. Mathematical programming solvers, including linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP), are commonly used to model and optimize supply chain networks by considering factors like cost, capacity, and demand fluctuations. Fine-tuning solver parameters and strategies to enhance computational efficiency—known as solver tuning—has been crucial in enhancing solution quality and decreasing computation time for large-scale supply chain issues. Heuristic solvers like genetic algorithms, simulated annealing, and ant colony optimization are frequently employed to resolve conflicts in supply chains. These solvers offer practical solutions to problems where exact methods are computationally impractical, allowing for swift responses to disruptions such as production delays or spikes in demand. Pyramid classification, a hierarchical approach, further refines decision-making by categorizing risks and aligning response strategies based on priority and severity. Furthermore, the integration of AI technologies and solvers enables advanced conflict resolution techniques, including scenario-based modeling and multi-objective optimization. These approaches enable decision-makers to weigh trade-offs between conflicting objectives like minimizing costs versus maximizing service levels in real-time. The study underscores that AI technologies and optimization solvers significantly bolster risk management in supply chains. Nonetheless, challenges such as data privacy concerns, security vulnerabilities, technical intricacies, and implementation obstacles pose critical barriers to widespread adoption. The study offers practical suggestions for businesses and decision-makers while pinpointing key areas for future exploration, such as devising hybrid models that merge heuristic solvers with AI for adaptive and scalable risk management strategies.

Collaborative Sensing-Aware Task Offloading and Resource Allocation for Integrated Sensing-Communication- and Computation-Enabled Internet of Vehicles (IoV)

Integrated Sensing, Communication, and Computation (ISCC) has become a key technology driving the development of the Internet of Vehicles (IoV) by enabling real-time environmental sensing, low-latency communication, and collaborative computing. However, the increasing sensing data within the IoV leads to demands of fast data transmission in the context of limited communication resources. To address this issue, we propose a Collaborative Sensing-Aware Task Offloading (CSTO) mechanism for ISCC to reduce the sensing tasks transmission delay. We formulate a joint task offloading and communication resource allocation optimization problem to minimize the total processing delay of all vehicular sensing tasks. To solve this mixed-integer nonlinear programming (MINLP) problem, we design a two-stage iterative optimization algorithm that decomposes the original optimization problem into a task offloading subproblem and a resource allocation subproblem, which are solved iteratively. In the first stage, a Deep Reinforcement Learning algorithm is used to determine task offloading decisions based on the initial setting. In the second stage, a convex optimization algorithm is employed to allocate communication bandwidth according to the current task offloading decisions. We conduct simulation experiments by varying different crucial parameters, and the results demonstrate the superiority of our scheme over other benchmark schemes.

Research on the integration of MEMS and reliable transmission of deep space networks based on time-sensitive networking

With the continuous deepening of human space exploration, deep space networks far away from Earth have emerged. Unlike traditional ground networks, they have the characteristics of frequent link interruptions and time extensions. Traditional data transmission mechanisms cannot be well applied in deep space networks. We propose a data transmission technology that integrates time-sensitive networking and artificial intelligence to address the contradiction between deterministic delay and differentiated service quality assurance in deep space networks and construct a micro electromechanical system (MEMS). Considering the differences in service quality due to different business requirements, data transmission in deep space networks is transformed into a mixed integer programming problem that minimizes transmission delay and maximizes link utilization and solved using artificial intelligence imitation learning. Experimental results have shown that the proposed algorithm has fast convergence, strong applicability, and can achieve reliable and efficient data transmission while meeting the requirements of higher priority data transmission. It can also significantly improve throughput.

Energy-Efficient Joint User Association, Backhaul Bandwidth Allocation, and Power Allocation in Cell-Free mmWave UAV Networks

In this article, we propose a cell-free network architecture for an unmanned aerial vehicle (UAV) base station (BS), i.e., UBS, incorporating high-altitude platform stations (HAPSs) as central processing units (CPUs). The goal is to guarantee the quality of service (QoS) of user equipment (UE), reduce energy consumption, extend communication time, and facilitate rescue operations. The millimeter-wave (mmWave) frequency band is deployed in access and backhaul links to satisfy UE QoS requirements and high backhaul demands. The proposed framework jointly optimizes user association, backhaul bandwidth allocation, and power allocation to maximize energy efficiency while meeting QoS requirements. The optimization problem, modeled as non-convex mixed-integer nonlinear fractional programming, is solved through a three-stage iterative algorithm. This includes (1) optimizing power allocation based on Dinkelbach transformation and a successive convex approximation (SCA) method, (2) clustering UBSs using the Lagrangian method, and (3) deriving a closed-form bandwidth allocation factor. The proposed algorithm significantly outperforms many traditional algorithms in performance while maintaining low computational complexity.

A Markov decision optimization of medical service resources for two-class patient queues in emergency departments via particle swarm optimization algorithm

In the modern healthcare system, the rational allocation of emergency department (ED) resources is crucial for enhancing emergency response efficiency, ensuring patient safety, and improving the quality of medical services. This paper focuses on the issue of ED resource allocation and designs a priority sorting system for ED patients. The system classifies patients into two queues: urgent and routine. Considering different service rates, a multi-server preemptive priority queueing model and a multi-server non-preemptive priority queueing model are constructed. Additionally, the number of beds, K, is introduced as the capacity of the urgent queue. By comprehensively considering the costs associated with patient waiting time, the cost of rejecting the most critical patients, and the total costs of beds and servers, a mixed-integer programming model was constructed with the objective of minimizing the total cost. The particle swarm optimization algorithm was applied to determine the optimal number of servers, service rate, and number of beds. Compared with the model proposed by Alipour-Vaezi et al., our model significantly improves patient waiting times and queue lengths using the same data set: the waiting time decreased by 74.44%, by 5.79%, and by 1.13%; the queue length decreased by 78% and by 3.33%. Our model effectively reduces patient waiting times and queue lengths while controlling costs, identifies the optimal number of beds, and achieves optimized resource allocation. Finally, we conducted a sensitivity analysis and provided some valuable management insights.

Mixed integer programming model based on branch delimitation-relaxation variables application in sustainable supply chain enterprise management

Mixed integer programming model based on branch delimitation-relaxation variables application in sustainable supply chain enterprise management

Solution Algorithms for the Capacitated Location Tree Problem with Interconnections

This paper addresses the Capacitated Location Tree Problem with Interconnections, a new combinatorial optimization problem with applications in network design. In this problem, the required facilities picked from a set of potential facilities must be opened to serve customers using a tree-shaped network. Costs and capacities are associated with the opening of facilities and the establishment of network links. Customers have a given demand that must be satisfied while respecting the facilities and link capacities. The problem aims to minimize the total cost of designing a distribution network while considering facility opening costs, demand satisfaction, capacity constraints, and the creation of interconnections to enhance network resilience. A valid mixed-integer programming was proposed and an exact solution method based on the formulation was used to solve small- and medium-sized instances. To solve larger instances two metaheuristic approaches were used. A specific decoder procedure for the metaheuristic solution approaches was also proposed and used to help find solutions, especially for large instances. Computational experiments and results using the three solution approaches are also presented. Finally, a case study on the design of electrical transportation systems was presented and solved.

Optimization of Material Flow and Product Allocation in Inter-Unit Operations: A Case Study of a Refrigerator Manufacturing Facility

Background: Logistics operations are integral to manufacturing systems, particularly in the transportation processes that occur not only between facilities and stakeholders but also between warehouses and workstations within a facility. The design of functional areas and allocating goods to appropriate zones within the warehouse management system (WMS) are critical activities that substantially influence the efficiency of manufacturing logistics operations. Methods: This study develops a mixed-integer programming (MIP) model to optimize material flow and product routing in manufacturing. The model identifies efficient pathways, assigns products to routes, and determines the required material-handling equipment. It is implemented in Python (3.11.5) using the Pyomo (6.7.3) package and the CBC solver (2.10.11), with sensitivity analysis performed on constraints and decision variables to evaluate robustness. Results: The findings indicate that Material Flow 3 and Material-Handling Equipment 1 represent the optimal configurations for managing the majority of goods within the manufacturing system. Conclusions: The proposed mathematical model supports the decision-making process by enabling adjustments to the proportions of functional areas within the manufacturing logistics system, ensuring operational efficiency and flexibility in response to changing demands. Furthermore, the study offers managerial insights and suggests directions for future research.

Neighborhood Approach for Solving One Class of Mixed Integer Non-Linear Programming

Integer programming is not new subject in optimization. However, given its practical applicability, we face computational difficulties in solving the large-scale problems. In this paper we solve a class of mixed-integer nonlinear programming problem by adopting a strategy of releasing non-basic variables from their bounds found in the optimal continuous solution in such a way to force the appropriate non-integer basic variables to move to their neighborhood integer points.

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.

Robust Optimization for Electric Vehicle Routing Problem Considering Time Windows Under Energy Consumption Uncertainty

Compared to fossil fuel-based internal combustion vehicles, electric vehicles with lower local pollution and noise are becoming more and more popular in urban logistic distribution. When electric vehicles are involved, high-quality delivery depends on energy consumption. This research proposes an electric vehicle routing problem considering time windows under energy consumption uncertainty. A mixed-integer programming model is established. The robust optimization method is adopted to deal with the uncertainty. Based on the modification of adaptive large neighborhood search algorithm, a metaheuristic procedure, called novel hybrid adaptive large neighborhood search, is designed to solve the problem, and some new operators are proposed. The numerical experiments show that the proposed metaheuristic can obtain high-performance solutions with high efficiency for large-scale instances. Furthermore, the robust solution based on the proposed model can achieve a satisfactory tradeoff between performance and risk.

Production scheduling with multi-robot task allocation in a real industry 4.0 setting

The demand for efficient Industry 4.0 systems has driven the need to optimize production systems, where effective scheduling is crucial. In smart manufacturing, robots handle material transfers, making precise scheduling essential for seamless operations. However, research often oversimplifies the Robotic Flexible Job Shop problem by focusing only on transportation time, ignoring resource allocation and robot diversity. This study addresses these gaps, tackling a Multi-Robot Flexible Job Shop (MRFJS) scheduling problem with limited buffers. It involves non-identical parallel machines and robots with varying capabilities overseeing material handling under blocking conditions. The case study is based on a real Industry 4.0 scenario, where the layout restricts each robotic arm’s access, requiring strategic buffer placement for part transfers. A Mixed-Integer Programming (MILP) model aims to minimize makespan, followed by a new Genetic Algorithm (GA) using Roy and Sussman’s Alternative Graph. Computational tests on various scales and real data from a manufacturing plant demonstrate the GA’s efficacy in solving complex scheduling problems in real-world production settings. Based on the data, the Proposed Genetic Algorithm (PGA), with an average Relative Deviation (ARD) of 0.25%, performed approximately 34% better compared to the Basic Genetic Algorithm (BGA), with an average ARD of 0.38%. This percentage indicates that the PGA significantly outperforms in solving complex scheduling problems.

Multi-Objective Coordinated Control of Smart Inverters and Legacy Devices

This work proposes multi-objective two-stage distribution optimal power flow (D-OPF) to coordinate the use of smart inverters (SIs) and existing voltage control legacy devices. The first stage of multi-objective D-OPF aims to solve a mixed-integer nonlinear programming (MINLP) formulation that minimizes both voltage variation and active power loss, with SI modes, SI settings, voltage regulator (VR) taps, and capacitor bank (CB) status as control variables. The Pareto Optimal Solutions obtained from the first-stage MINLP are used to determine the optimal active–reactive power dispatch from the SIs by solving a nonlinear programming formulation in the second stage of the proposed D-OPF. This model guarantees that the setpoints for active–reactive power align with the droop characteristics of the SIs, ensuring practicability and the autonomous dispatch of active–reactive power by the SIs according to IEEE 1547-2018. The effectiveness of the proposed method is tested on the IEEE 123 distribution network by contrasting the two proposed D-OPF models, with one prioritizing SIs for voltage control and power loss minimization and the other not prioritizing SIs. The simulation results demonstrate that prioritizing SIs with optimal mode and droop settings can improve voltage control and power loss minimization. The proposed model (with SI prioritization) also reduces the usage of traditional grid control devices and optimizes the dispatch of active–reactive power. The POS also shows that the SI modes, droops, and legacy device settings can be effectively obtained based on the desired objective priority.