Integer Programming Optimization Research Articles

Reliability expansion method of urban distribution network based on mixed integer programming and multi-objective optimization

The power supply system in urban area has high complexity, and its expansion is difficult. Therefore, a reliability expansion method of urban distribution network based on mixed integer programming and multi-objective optimization is proposed in this paper. Considering the economic benefits and voltage difference of investment and operation, a general model for optimizing the overall installation of the power grid has been established. Enable particle swarm optimization algorithm to increase the energy storage capacity of the power grid and solve the optimal expansion rate through mixed integer linear programming. Finally, research has shown that this research method can achieve the best scaling effect.

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Leveraging Multi-Criteria Integer Programming Optimization for Effective Team Formation

Optimization Model for Electric Vehicle Routing Problem with Two Charging Options

The use of electric vehicles recently is an alternative way to lower pollutants and the emissions of carbon dioxide resulting from the usage of motor vehicle fuel oil. The limited battery capacity of this electric vehicle is a problem for its users. Vehicle routing problem (VRP) is a problem of integer programming and combinatorial optimization that is frequently used in planning and decision-making processes. One application of this issue is to find the best path for delivering items from a corporation to customers. VRP problems are frequently utilized in order to reduce internal expenditure. Model optimization in this paper uses two rehcarging options, recharging and swapping battery. The purpose of this paper is to present a VRP optimization model for electric vehicle routing problems to find the best route option that minimizes the total of the fees for fixed vehicles, transit, charging, battery changing, and waiting.

Economical revenue maximization in mobile edge caching and blockchain enabled space-air-ground integrated networks

In this paper, we study an edge caching and blockchain enabled space-air-ground integrated networking (SAGIN) network, where a low-earth-orbit (LEO) satellite serves as the content provider, and multiple edge caching enabled unmanned aerial vehicles (UAVs) will cache some contents to provide user equipments (UEs) with satisfactory content access services together with the satellite. Moreover, there’s a blockchain system that is deployed on UAVs, to provide the network with trust mechanism without requiring a centralized authority. From the standpoint of the operator, we intend to maximize the long-term averaged economical revenue by providing UEs with satisfactory and secure content access services. To achieve this purpose, we will jointly optimize the content placement of each UAV, content replacement when each UAV is full, the access control of each UE, and the blockchain deployment strategy about each UAV. the concept of queues in Lyapunov optimization is utilized to represent the backlog of edge equipment, ensuring the stability of virtual queues on UAVs and satellites, while satisfying the caching capacity constraints for content caching and blockchain deployment. Due to the tight coupling of optimization in each time slot and the variables within each time slot, our problem, which involves stochastic optimization and binary integer programming, is challenging to solve. To address this issue, we initially employ Lyapunov optimization theory to transform and decouple the problem into individual time-slot optimization problems. Subsequently, we utilize an effective heuristic algorithm called the fireworks algorithm to solve these individual optimization problems. However, the original fireworks algorithm cannot be directly applied to our problem due to its binary characteristics and inter-coupling constraints. Therefore, we have redesigned the explosion and mutation operations to adapt them to our specific problem. Simulation results demonstrate that our proposed algorithm outperforms other baseline algorithms.

Matheuristics: survey and synthesis

AbstractIn integer programming and combinatorial optimisation, people use the term matheuristics to refer to methods that are heuristic in nature but draw on concepts from the literature on exact methods. We survey the literature on this topic, with a particular emphasis on matheuristics that yield both primal and dual bounds (i.e., upper and lower bounds in the case of a minimisation problem). We also make some comments about possible future developments.

Robust Topological Construction of All-hexahedral Boundary Layer Meshes

We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it is optimal in the sense that the hexahedral valences of the boundary edges are as close as possible to their ideal values (local dihedral angle divided by 90°). Starting from a valid watertight surface mesh (all-quad in practice), we build a global optimization integer programming problem to minimize the mismatch between the hexahedral valences of the boundary edges and their ideal values. The formulation of the integer programming problem relies on the duality between boundary hexahedral configurations and triangulations of the disk, which we reframe in terms of integer constraints. The global problem is solved efficiently by performing combinatorial branch-and-bound searches on a series of sub-problems defined in the vicinity of complicated ridges/corners, where the local mesh topology is necessarily irregular because of the inherent constraints in hexahedral meshes. From the integer solution, we build the topology of the all-hexahedral layer, and the mesh geometry is computed by untangling/smoothing. Our approach is fully automated, topologically robust, and fast.

Coalition Structure Generation in Edge Computing Environment With Multitasking Concurrency

Edge computing (EC) is a distributed computing paradigm that brings computation and data storage closer to the data sources. With the rapid development of EC, offloading scientific computing and data processing tasks from end devices to edge nodes (ENs) can satisfy these tasks’ requirements. However, a single EN with limited computing capacity is usually insufficient to handle these tasks. Hence, using a coalition structure (CS) of many ENs to handle multiple concurrent tasks in an EC environment becomes a feasible scheme. Still, many existing methods cannot be used directly in this scenario because of enormous CS solution space, low search speed, long-running time, poor optimal solution quality, etc. In response, we propose an arbitrary discrete political optimizer (ADPO) algorithm with a discrete recent-past position updating strategy to explore the potential CS space. Unlike other heuristic algorithms, ADPO further improves the better solutions by interacting with each other in the parliamentary affairs phase. After that, we formulate an integer programming (IP) optimization model to alleviate the low search speed or long time consuming. Finally, extensive experiments demonstrate that ADPO is superior to the existing heuristic algorithm. In addition, the IP model excels in exiting algorithms at the running time (milliseconds level) and resource occupied ratio.

Modeling the development of a carbon capture and transportation infrastructure for Swedish industry

This work presents and applies a mixed integer programming (MIP) optimization model that minimizes the net present costs for CO2 capture and storage (CCS) systems for cases with defined emissions costs and/or capture targets. The model covers capture from existing large point sources of CO2 emissions in Sweden, liquefaction, intermediate storage and transportation using trucks to hubs on the coast, followed by ship transport to a storage location (excluding storage cost). The results show that the capture and transportation infrastructure, in terms of both the sites chosen for capture and the associated transportation setup, differs depending on whether the system is incentivized to capture biogenic or fossil CO2, or both. Waste-fired combined heat and power (CHP) plants are only chosen for capture at scale when biogenic capture targets and fossil emissions costs are combined, since the emissions from these sites comprise a combination of biogenic and fossil CO2. The value for the system in mitigating the costs from fossil CO2 emissions exceeds the increased cost of BECCS at waste-fired CHPs compared to larger pulp mills given the fossil emissions cost development assumed in this work. Although the cost for capture and liquefaction dominates the total cost of the CCS system, it is not the only factor determining the choice of sites for capture. Proximity to transport hubs with short offshore transportation distances to the final storage location is also an important factor. For the transportation infrastructure, it is shown that the cost for ships is the main cost driver.

MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

The present paper aims at validating a Model Predictive Control (MPC), based on the Mixed Logical Dynamical (MLD) model, for Hybrid Dynamic Systems (HDSs) that explicitly involve continuous dynamics and discrete events. The proposed benchmark system is a three-tank process, which is a typical case study of HDSs. The MLD-MPC controller is applied to the level control of the considered tank system. The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints. This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed. Once the MLD model of the system is well-posed, then the MPC law synthesis can be developed based on the Mixed Integer Programming (MIP) optimization problem. For solving this MIP problem, a Branch and Bound (B&B) algorithm is proposed to determine the optimal control inputs. Then, a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach. Performances results show that the MLD-MPC approach outperforms the standard MPC one that doesn’t consider the hybrid aspect of the system. The paper also shows a behavioral test of the MLD-MPC controller against disturbances deemed as liquid leaks from the system. The results are very satisfactory and show that the tracking error is minimal less than 0.1% in nominal conditions and less than 0.6% in the presence of disturbances. Such results confirm the success of the MLD-MPC approach for the control of the HDSs.

Estimating and Exploiting the Impact of Photo Layout: A Structural Approach

Host-generated property images as a visual channel reveal substantial information about properties. Selecting proper images to display can lead to higher demand and increased rental revenue. In this paper, we define, estimate, and optimize the impacts of Airbnb photos on customers’ renting decisions. We apply ResNet-50, a convolutional neural network model, to build two separate, supervised learning models to evaluate the image quality and room types posted by Airbnb hosts. Then, we characterize the overall impacts of photo layout by the room type featured in the photo, photo quality, and order of display on the listings’ web pages. To address two estimation challenges in the Airbnb setting, namely, censored demand and changing consideration sets, we propose a novel pairwise comparison model that utilizes customers’ booking sequence data to consistently estimate the impact of photo layout on customers’ renting decisions. Our estimation results suggest that the cover image has a significantly larger impact than noncover photos and a high-quality bedroom cover image leads to the largest increase in demand. Furthermore, we build a nonlinear integer programming optimization problem and develop an algorithm to determine the optimal photo layout. Our counterfactual analysis suggests that a listing’s unilateral adoption of optimal photo layout leads to 11.0% more bookings on average. Moreover, depending on the neighborhood and market size, when listings simultaneously switch to the optimal photo layout, they get booked for two to five additional days in a year on average, which boosts revenue by $500 to $1,100. This paper was accepted by Swaminathan, Jayashankar, operations management. Funding: This research was partially sponsored by the MIT Data Science Lab and also benefited from generous support provided by Zalando. Supplemental Material: The online companion and data are available at https://doi.org/10.1287/mnsc.2022.4616 .

Flexible analytic model to inform multi-stakeholder pediatric vaccine scheduling decisions

BackgroundPediatric immunization is important for preventing potentially life-threatening diseases in children. Over time, the number of recommended pediatric vaccines has increased and is likely to increase further as new vaccines are developed. Given the different number of doses for available vaccines and various constraints (e.g., the appropriate age for each dose of a vaccine or the time between doses), it is challenging to develop a recommended vaccination schedule or a catch-up schedule when a child falls behind on one or more vaccinations. MethodsWe developed an integer programming optimization model, enabled by Python programming and embedded into an Excel-based decision tool, to recommend childhood vaccination schedules or personalized catch-up schedules. The model recommends a vaccination schedule that balances the goal of being as close as possible to the clinically-indicated dosing schedules and the goal of minimizing clinic visits, and gives users the ability to trade off between these two goals. We illustrated the broad applicability of our proposed model with commonly-faced vaccine scheduling challenges in the United States. ResultsThe illustrative computational case study confirms our model’s ability to create personalized schedules based on each child’s age and vaccination history, and to adjust appropriately when a new vaccine becomes available. ConclusionsThe model presented in this paper fills the need for an easy-to-use tool to recommend vaccination schedules for de novo and catch-up purposes. It provides straightforward recommendations that can be easily used by physicians, is flexible to handle the requirements varying by region, and can be updated as new vaccines are approved for use.

A mixed-integer programming model for identifying intuitive ambulance dispatching policies

Markov decision process models and algorithms can be used to identify optimal policies for dispatching ambulances to spatially distributed customers, where the optimal policies indicate the ambulance to dispatch to each customer type in each state. Since the optimal solutions are dependent on Markov state variables, they may not always correspond to a simple set of rules when implementing the policies in practice. Restricted policies that conform to a priority list for each type of customer may be desirable for use in practice, since such policies are transparent, explainable, and easy to implement. A priority list policy is an ordered list of ambulances that indicates the preferred order to dispatch the ambulances to a customer type subject to ambulance availability. This paper proposes a constrained Markov decision process model for identifying optimal priority list policies that is formulated as a mixed integer programming model, does not extend the Markov state space, and can be solved using standard algorithms. A series of computational examples illustrate the benefit of intuitive policies. The optimal mixed integer programming solutions to the computational examples have objective function values that are close to those of the unrestricted model and are superior to those of heuristics.

Special Issue: Integer Programming and Combinatorial Optimization (IPCO) 2021

Special Issue: Integer Programming and Combinatorial Optimization (IPCO) 2021

Sizing of a Scattered Housing Microgrid in a Remote Rural Area

Power solutions for remote rural regions are mainly based on generator sets or individualized generation systems per household. These solutions have low reliability and high financial and environmental costs, especially those involving fossil fuels. However, current solutions incorporate hybrid systems with renewable energy sources to reduce pollutant gas emissions and costs and increase the reliability and robustness of power generation. These hybrid systems can be considered micro-grid (MG) and could contribute to energizing remote noninterconnected areas. However, implementing MGs in these regions must challenge energizing dispersed households. Thus, both the sizing of the generation and distribution systems must be considered to guarantee the correct operation of the MG and a low cost. This paper explores coordinated sizing between the power sources and the distribution system to address the challenges of energizing remote areas with dispersed loads through MG. It presents a literature review on energization strategies for remote regions and proposes coordinated MG sizing. Finally, it applies coordinated sizing to a case study in Colombia. The sizing is approached as a mixed-integer nonlinear integer programming optimization problem and is solved by a particle swarm optimization (PSO) algorithm.

A Mixed Integer Programming Optimization of Blood Plasma Supply Chain in the Uncertainty Conditions during COVID-19: A Real Case in Iran

Blood and its products, like plasma, are among the most sensitive products for the sake of transportation and storage. Special storage conditions, short shelf life, and lack of particular demand for blood products are among the most significant challenges to managing it. In this respect, it is necessary to implement the problem of supply chain network design in uncertain conditions to find a proper solution for the management of blood products. In this study, a multilevel supply chain is designed to supply plasma in the COVID-19 pandemic. First, the blood is sent to blood donation centers and then to the laboratory. Moreover, after that, it is sent to hospitals. To optimize the transfer rate at each level of the supply chain, a mathematical model is proposed to reduce total costs. Also, the fuzzy programming approach is used to deal with uncertainty in the parameters of the mathematical model. The results of model optimization show that this mathematical model has the required efficiency in finding optimal solutions for the distribution of blood products. According to the obtained results, value objective function in certain and uncertain values is determined. According to the results, the objective certain value is lower than the uncertain value. Uncertain value calculated is of three dimensions. According to this, the categorized objective value increased when the dimension is equal to 0.5. Finally, it shows that when demand increases, more blood and plasma need to be collected to meet the demand, which increases operating and health testing costs and ultimately increases total system costs.

$O(\log^2{k}/\log\log{k})$-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial Time Algorithm

In the directed Steiner tree (DST) problem, we are given an $n$-vertex directed edge-weighted graph, a root $r$, and a collection of $k$ terminal nodes. Our goal is to find a minimum-cost subgraph that contains a directed path from $r$ to every terminal. We present an $O(\log^2 k/\log\log{k})$-approximation algorithm for DST that runs in quasi-polynomial time, i.e., in time $n^{{poly}\log (k)}$. By assuming the projection game conjecture and ${NP}\not\subseteq{\bigcap}_{0<\epsilon<1}{ZPTIME}(2^{n^\epsilon})$ and adjusting the parameters in the hardness result of [Halperin and Krauthgamer, Polylogarithmic inapproximability, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing, 2003, pp. 585--594], we show the matching lower bound of $\Omega(\log^2{k}/\log\log{k})$ for the class of quasi-polynomial time algorithms, meaning that our approximation ratio is asymptotically the best possible. Our algorithm is proceeded by reducing DST to an intermediate problem, namely, the group Steiner tree on trees with dependency constraint problem, which we approximate using the framework developed by [Rothvoß, Directed Steiner Tree and the Lasserre Hierarchy, preprint, arxiv:1111.5473, 2011] and [Friggstad et al., Linear programming hierarchies suffice for directed Steiner tree, in Proceedings of the 17th Annual Conference on Integer Programming and Combinatorial Optimization, 2014, pp. 285--296].

Evacuation planning for persons with mobility needs: A combined optimization and traffic microsimulation modelling approach

This study presents a framework of optimization and traffic microsimulation modelling that account for a mass evacuation of persons with mobility needs. The study optimizes emergency vehicle and destination allocation and implements an emergency evacuation route within the traffic microsimulation model. The emergency vehicle and destination allocation follow an integer programming optimization approach within a mathematical programming language modelling system. This study tests two evacuation scenarios that consider emergency vehicle operations with and without a dedicated route for the evacuation of five hundred and twelve persons, requiring mobility assistance from six hospitals and nursing homes. Additionally, the evacuation modelling framework considers collision risks in assessing evacuation process, particularly, how it affects evacuation of this group of vulnerable population. Optimization results indicate that this group can be evacuated by ninety emergency vehicles, and it takes 19.5 h for an optimal allocation of emergency vehicles. Traffic simulation results suggest that it takes 21 h to evacuate all persons with mobility needs using ninety emergency vehicles. The study found that travel time along the evacuation route is reduced by 32.31% compared to a sceanrio without a dedicated route. Results also indicate that implementing a dedicated evacuation route yields a reduction of 6 min and 25.2 min in average and the maximum trip time for emergency vehicles, respectively. On the other hand, 68% of emergency vehicles make 0.5–3.5 fewer tour to a case without the collision, leading to an incomplete evacuation (72.2%). This research will provide emergency professionals with insights into the challenges associated with the evacuation of persons with mobility needs and help develop proactive evacuation plans to accommodate the special requirements of the vulnerable population.

A bi-objective optimization of energy consumption and investment cost for public building envelope design based on the ε-constraint method

As a basic part of building energy-saving designs, the design of the building envelope provides an opportunity to achieve sustainable development goals. However, it is not comprehensive to blindly pursue the lowest energy consumption when optimizing design schemes. In this case, it is of great research significance to build a fast and efficient optimal model to balance different objectives. A bi-objective integer programming optimization model is proposed to minimize energy consumption and investment costs based on the analysis of the architectural and social environments in which public buildings are located. The key parameters of the building envelope are thus identified on this basis, and a variety of optimal design schemes that consider investment cost and energy consumption are designed. The model is then implemented in AMPL equipped with the CPLEX solver and solved by the improved epsilon-constraint method. Finally, a real-world case study in Qingdao is taken to validate the developed model, and the resultant Pareto frontier is evaluated to prove the trade-off between objectives. The results show that the proposed model effectively reduces building energy consumption and investment costs in the design stage. The comparison with other algorithms proves that the proposed method has good search and optimization capabilities. This study can provide a quantitative reference standard for public building designers in the design phase, coordinating economic and energy-efficiency optimization.

Cruise ship itinerary design considering port attractiveness for passengers

Cruise tourism has been a fast-growing industry and one of the key factors of success in this industry is the ability to create highly seductive itineraries, capable of attracting tourists while maximizing the total profit for the cruise shipping company. Itineraries must be carefully selected, combining a maximization of the total attraction value of the itinerary, given by the destinations and attractions included, with the minimization of the total cost of the itinerary. The objective of this paper is to develop a mixed integer programming optimization model to find optimum cruise ship itineraries. The model presented in this paper calculates cost and revenue of the itinerary separately, using a cost structure based on the cruise ship's size and the duration of the itinerary, and a revenue structure based on the month of the year and the selected ports attractiveness. An application is made to evaluate possible new optimal cruise itineraries along the Atlantic coast of the Iberian Peninsula and Morocco. The results confirm that an increased profit is possible during the Summer season and show clear opportunities for new cruise itineraries in this region, calling ports which are not currently involved in cruising activities, but which present advantages for cruise itinerary design as transit ports or suitable gateways for major attractions.

A mat-heuristic based solution approach for an extended nurse rostering problem with skills and units

The Nurse Rostering Problem (NRP) is a combinatorial optimization problem that deals with assignment of nurses to shifts based on a set of constraints. The real-life NRP applications are difficult to solve because of the fact that the problem is NP-hard. In this paper, we focus on two main aspects of the problem, model and solution methodology. Firstly, we propose a novel model that also considers unit assignments. Majority of the studies in the literature accounts for nurse, day, and shift assignments. Due to skill and experience levels, not every nurse can be assigned to every unit. Therefore, accounting for unit assignments helps the model to be more accurate in terms of real-life scenarios. Lastly, we propose a new mathematical based heuristic that combines Integer Programming (IP) and Discrete Particle Swarm Optimization (PSO). IP is used to generate initial schedules and PSO further improves the schedule. Any infeasibility is corrected by IP along the process. IP and PSO coordinate until final stopping criterion. Computational experiments on test data show that the proposed algorithm generates near optimal solutions.