Integer Programming Research Articles

An Algorithm for Clustering with Confidence-Based Must-Link and Cannot-Link Constraints

We study here the semisupervised k-clustering problem where information is available on whether pairs of objects are in the same or different clusters. This information is available either with certainty or with a limited level of confidence. We introduce the pair-wise confidence constraints clustering (PCCC) algorithm, which iteratively assigns objects to clusters while accounting for the information provided on the pairs of objects. Our algorithm uses integer programming for the assignment of objects, which allows us to include relationships as hard constraints that are guaranteed to be satisfied or as soft constraints that can be violated subject to a penalty. This flexibility distinguishes our algorithm from the state of the art, in which all pair-wise constraints are considered hard or all are considered soft. We developed an enhanced multistart approach and a model-size reduction technique for the integer program that contribute to the effectiveness and efficiency of the algorithm. Unlike existing algorithms, our algorithm scales to large-scale instances with up to 60,000 objects, 100 clusters, and millions of cannot-link constraints (which are the most challenging constraints to incorporate). We compare the PCCC algorithm with state-of-the-art approaches in an extensive computational study. Even though the PCCC algorithm is more general than the state-of-the-art approaches in its applicability, it outperforms the state-of-the-art approaches on instances with all hard or all soft constraints in terms of both run time and various metrics of solution quality. The code of the PCCC algorithm is publicly available on GitHub. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: The research of D. S. Hochbaum was supported by the AI Institute NSF Award [Grant 2112533]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0419 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0419 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Bi-objective Optimization in Role Mining

Role mining is a technique that is used to derive a role-based authorization policy from an existing policy. Given a set of users U , a set of permissions P and a user-permission authorization relation UPA ⊆ U × P , a role mining algorithm seeks to compute a set of roles R , a user-role authorization relation UA ⊆ U × R and a permission-role authorization relation PA ⊆ R × P , such that the composition of UA and PA is close (in some appropriate sense) to UPA . Role mining is therefore a core problem in the specification of role-based authorization policies. Role mining is known to be hard in general and exact solutions are often impossible to obtain, so there exists an extensive literature on variants of the role mining problem that seek to find approximate solutions and algorithms that use heuristics to find reasonable solutions efficiently. In this paper, we first introduce the Generalized Noise Role Mining problem (GNRM) – a generalization of the MinNoise Role Mining problem – which we believe has considerable practical relevance. In particular, GNRM can produce “security-aware” or “availability-aware” solutions. Extending work of Fomin et al., we show that GNRM is fixed parameter tractable, with parameter r + k , where r is the number of roles in the solution and k is the number of discrepancies between UPA and the relation defined by the composition of UA and PA . We further introduce a bi-objective optimization variant of GNRM, where we wish to minimize both r and k subject to upper bounds \(r \le \bar{r} \) and \(k\le \bar{k} \) , where \(\bar{r} \) and \(\bar{k} \) are constants. We show that the Pareto front of this bi-objective optimization problem (BO-GNRM) can be computed in fixed-parameter tractable time with parameter \(\bar{r} +\bar{k} \) . From a practical perspective, a solution to BO-GNRM gives security managers the opportunity to identify a mined policy offering the best trade-off between the number of policy discrepancies and the number of roles. We then report the results of our experimental work using the integer programming solver Gurobi to solve instances of BO-GNRM. Our key findings are that (a) we obtained strong support that Gurobi’s performance is fixed-parameter tractable, (b) our results suggest that our techniques may be useful for role mining in practice, based on our experiments in the context of three well-known real-world authorization policies. We observed that, in many cases, our solver is capable of obtaining optimal solutions when the values of either k or r are small.

Reservation and allocation model considering the user cost and the utilization of parking space

In order to alleviate the problem of imbalance between parking supply and demand by improving the utilization rate of parking resources, and considering the game relationship between user benefits and system benefits in parking allocation, the optimization objective function of maximum parking space utilization and minimum user cost in parking reservation mode is established from the two aspects which are system optimization and user optimization respectively. Then, the optimal allocation parking integer programming model (OPA) considering users' preferences is established. An Augmented Lagrangian-Alternating Direction Method of Multipliers Algorithm is designed to solve the optimal solution of the model. Finally, in order to test the validity of the model, the proposed model and the classical distribution model are compared and analyzed under different supply and demand conditions. The results show that the performance of the proposed model in three performance metrics which are parking utilization, average user cost and request acceptance rate is significantly better than that of the classical allocation model. The research results of this paper can provide theoretical reference for the management of parking reservation platform.

Electric delivery vehicle routing problem optimization model with time-varying traffic congestion

In order to plan a reasonable scheme for the fleet travel and minimize the energy consumption of electric vehicles during traffic congestion periods, while relieving the mileage anxiety of delivery personnel, the pure electric delivery vehicle routing problem considering time-varying traffic congestion was studied. Firstly , a novel mixed integer programming model (TD-EVRP) is established to step for its extended model of EVRP, which especially characterizes the time-varying traffic congestion state and measures the energy consumption of electric delivery vehicles. This model also refines its constraints including customer time window, vehicle load, and vehicle charging requirements. Secondly, a traffic congestion avoidance strategy is introduced into the model, which allows vehicles to park and charge at customer points during peak traffic periods in order to actively avoid unnecessary energy consumption caused by traffic congestion. Finally, the improved ant colony algorithm is designed to acquire the optimal solution.

Modeling and optimization of two-stage emergency supply chain network under uncertain environment

In order to formulate an effective emergency supply chain network planning scheme, improve the efficiency of emergency organization rescue and realize the reasonable allocation of resources and materials, considering the uncertainty of supply and demand, a distribution mode combining multiple transportation modes is adopted, and the optimization objectives are to minimize network response time, cost and carbon emissions. A two-stage emergency supply chain mixed integer programming model is constructed. At the same time, an adjustable robust optimization model is constructed based on robust optimization theory to enhance the network's ability to cope with uncertain factors, and the constraints with uncertain parameters are transformed through linear duality theory. In order to improve the solution effect of the model, an optimize cuckoo search (OCS) algorithm is proposed, and a benchmark example is introduced to verify the superiority and applicability of the OCS algorithm in solving multi-objective functions. Finally, the emergency material distribution data during the COVID-19 epidemic in Wuhan is used to study the emergency supply chain network decision-making problem with uncertain parameters, and the effective suppression of the robust control coefficient on uncertain disturbances is proved through sensitivity analysis.

Urban Emergency Evacuation Path Optimization Based on Uncertain Environments to Enhance Response for Symmetric and Asymmetric Evacuation Problems

Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs fuzzy theory to construct a 0–1 integer programming model for emergency evacuation paths that minimizes the average expected travel time. Results: We enhanced the neighborhood search strategy of the traditional ACO_time by incorporating the 2-opt and 3-opt perturbation mechanisms from the SA algorithm. Additionally, we utilized improved ant-volume and ant-perimeter models, along with their combinations, in the pheromone-updating mechanism of the basic ACO. The heuristic principles of the A* algorithm were integrated, introducing the joint influence of path and time into the heuristic function of the ACO algorithm. Conclusions: The IACO3 algorithm was tested on the Sioux Falls network and the Berlin Heisenheimer Center network. The computation time of the improved IACO3 algorithm was reduced by up to 20% compared to the original IACO3 algorithm in relation to the SA algorithm, with only a 4–5% increase in computation time compared to the ACO_time algorithm, which translates to an increase of merely 4–5 s. This demonstrates the superior solution efficiency of the IACO3 algorithm.

Cost-effective reliability level in 100% renewables-based standalone microgrids considering investment and expected energy not served costs

Loss of load probability (LOLP) and expected energy not served (EENS) are commonly used in electrical power systems to evaluate reliability. LOLP defined as the probability that available generation capacity will be inadequate to supply customer demand. EENS defined as the expected amount of energy not being served to consumers by the system during the period considered due to system capacity shortages or unexpected power outages. Loss of Load Frequency (LOLF) is referred to a number of loss of load (LOL) event happened in the operation life span of the SMG. Loss of Load Reduction (LOLR) is defined as the required reduction in LOLF to obtain a specific reliability level. While power systems are designed to minimize LOLP and EENS, this is constrained by the total cost: investment cost, operation and maintenance cost, and cost of customer interruption (CCI). This research considers Standalone Microgrid (SMG), also known as Autonomous Microgrid which only operates in off-grid mode and cannot be connected to wider electrical power system. When designing a 100 % renewable energy integrated SMGs, it is crucial to determine the cost-effective reliability level (CERL). The CERL occurs when the total cost is minimum. This research proposes an approach to calculate the CERL for a fully renewable SMG. An analytical formulation is proposed to represent the LOLR needed to obtain a specific reliability level as a function of the required size of reliability improvement alternatives. The CCI is evaluated using LOLF and EENS indices. Finally, the total cost of the SMG system is evaluated for each reliability level. Consequently, the total cost of the SMG system is expressed as a function of reliability levels, and the minimum value of total cost and the corresponding reliability level are evaluated. In this research, a Monte Carlo Simulation (MCS) approach is used to find hourly LOLF, considering 25 years (219,000 h) of SMG lifespan, regression analysis is used for an analytical formulation, and mixed integer linear programming (MILP) is used for the investment decision making based on a cost minimisation approach. The result demonstrates that the CERL of the SMG system evaluated in the case study is 98.71 %.

Location-aware job scheduling for IoT systems using cloud and fog

The rapid growth of Internet of Things (IoT) applications generates vast volumes of high-speed data streams from numerous devices. Cloud computing solutions often handle and manage this data; however, for certain applications, the latency introduced by transmitting data from edge devices to the cloud may be unacceptable. This issue is exacerbated by the bandwidth constraints of public networks, which become significant barriers in large-scale IoT implementations. Consequently, effective resource management, service management, data storage, and power management require more robust infrastructure and complex protocols. An "intelligent gateway" based on fog computing can enhance the efficient utilization of cloud and network resources. Resource planning and management in a fog-cloud environment significantly impact system performance, particularly latency. This problem is known to be NP-hard. This paper addresses the challenge of lifetime optimization for scheduling data-intensive tasks in fog and cloud-based IoT systems. Initially, we propose an Integer Linear Programming (ILP) optimization model to frame the problem. Subsequently, we introduce a heuristic method named Data-Locality Aware Job Scheduling in Fog-Cloud (DLSFC), which is derived from the proposed formulation. The effectiveness of DLSFC is evaluated across various system characteristics, with results demonstrating that DLSFC achieves solutions within 85 % of the ideal outcome provided by the LP solver.

THE BRANCH AND BOUND APPROACH TO A BOUNDED KNAPSACK PROBLEM (CASE STUDY: OPTIMIZING OF PENCAK SILAT MATCH SESSIONS)

A method commonly employed to solve integer programming problems is the Branch and Bound. In this article, maximizing the number of matches held on the first day of pencak silat tournaments is essential because it can impact the overall dynamics and results of the competition. The model used to maximize the number of match sessions in pencak silat competitions is a variant of the Bounded Knapsack Problem (BKP), belonging to the category of integer programming models. The result obtained using the Branch and Bound method ensures that the maximum number of match sessions can be conducted. The objective value obtained using the Branch and Bound method decreases as it descends, indicating a decreasing maximum value.

Planning municipal drainage infrastructure maintenance operations with finite available crews: pragmatic optimization approach

This paper proposes a streamlined approach to addressing the problem of allocating finite crew resources to concurrent jobs in the context of municipal drainage infrastructure maintenance. The problem was defined from the perspective of a project manager involved in planning such operations on a day-by-day basis. The problem statement was then transformed into a simplified Integer Linear Programming optimization model. Performance metrics were devised to evaluate the optimization model’s effectiveness. A heuristic algorithm representing the decision-making process by a seasoned planner in the partner company was also developed. Both methods were applied to a case study and contrasted based on the same performance metrics. The findings underscored substantial optimization benefits in rendering decision support in resource-constrained drainage construction operations planning. In conclusion, this research presents an alternative strategy for navigating the complexities inherent in finite crew resource allocation on multiple concurrent drainage projects; lends a cost-effective optimization solution to improving the utilization of finite available crews while satisfying service demands from multiple clients to the largest extent possible.

Optimization of the electric vehicle charging strategy problem for sustainable intercity travels with multiple refueling stops

Electric vehicle (EV) drivers considering long-distance trips still face range anxiety due to the limited range of EVs and the scarcity of charging stations. Thus, it becomes important to ensure the feasibility of the selected route and determine an optimal charging strategy. As a crucial aspect of decision support for EV drivers, this study proposes a mixed integer linear programming (MILP) approach for the EV charging strategy problem (EVCSP), incorporating a piecewise linear approximation technique to address the challenges posed by nonlinear charging times. The proposed optimization model, namely CSPM determines where, when, and how much to charge an EV for a specified route to minimize travel time and cost. The solution time of large-scale test problems and a case study on Türkiye reveal the robustness and reliability of the CSPM. Furthermore, two multi-objective optimization methods (the weighted sum and the lexicographic method) are applied to the case study, and the results are analyzed. The results indicate that the travel cost is more sensitive to the selected charging strategy, with a range of 46.09 % across the applied charging strategies, whereas travel time remains more resilient, with a maximum fluctuation of 19.77 %. A comparative analysis with a full charging strategy reveals that the CSPM reduces the travel time by 60.1 % and improves the cost efficiency by 105.72 %.

Robust Optimization Models for Planning Drone Swarm Missions

This article presents methods of planning unmanned aerial vehicle (UAV) missions in which individual platforms work together during the reconnaissance of objects located within a terrain. The planning problem concerns determining the flight routes of a swarm, where each UAV has the ability to recognize an object using a specific type of sensor. The experiments described in this article were carried out for drone formation; one drone works as a swarm information hub and exchanges information with the ground control station (GCS). Numerical models for mission planning are presented, which take into account the important constraints, simplifying the description of the mission without too much risk of losing the platforms. Several types of objective functions were used to optimize swarm flight paths. The mission models are presented in the form of mixed integer linear programming problems (MILPs). The experiments were carried out on a terrain model built on the basis of graph and network theory. The method of building a network on which the route plan of a drone swarm is determined is precisely presented. Particular attention was paid to the description of ways to minimize the size of the network on which the swarm mission is planned. The presented methods for building a terrain model allow for solving the optimization problem using integer programming tasks.

Multi-objective simulated annealing-based quantum circuit cutting for distributed quantum computation

In the current noisy intermediate-scale quantum (NISQ) era, the number of qubits and the depth of quantum circuits in a quantum computer are limited because of complex operation among increasing number of qubits, low-fidelity quantum gates under noise, and short coherence time of physical qubits. However, with distributed quantum computation (DQC) in which multiple small-scale quantum computers cooperate, large-scale quantum circuits can be implemented. In DQC, it is a key step to decompose large-scale quantum circuits into several small-scale subcircuits equivalently. In this paper, we propose a quantum circuit cutting scheme for the circuits consisting of only single-qubit gates and two-qubit gates. In the scheme, the number of non-local gates and the rounds of subcircuits operation are minimized by using the multi-objective simulated annealing (MOSA) algorithm to cluster the gates and to choose the cutting positions whilst using non-local gates. A reconstruction process is also proposed to calculate the probability distribution of output states of the original circuit. As an example, the 7-qubit circuit of Shor algorithm factoring 15 is used to verify the algorithm. Five cutting schemes are recommended, which can be selected according to practical requirements. Compared with the results of the mixing integer programming (MIP) algorithm, the number of execution rounds is efficiently reduced by slightly increasing the number of nonlocal gates.

Optimization of multi-path approach flight sequencing based on rolling horizon control

Arrival flight sequencing optimization is an effective method to improve the landing efficiency of incoming flights and reduce flight delays. Based on this, with the goal of maximizing landing efficiency, combined with multi-runway and multi-route selection, and considering the actual waypoint restrictions, a mixed integer programming model for multi-path and multi-runway integrated arrival flight sequencing optimization is proposed. In order to solve the real-time problem of large-scale flight sequencing calculation, a multi-waypoint rolling horizon control algorithm is proposed. The terminal area of Guangzhou Baiyun International Airport is used as an example for verification, and the actual arrival flight data is used to carry out calculation experiments. In terms of wake turbulence safety interval, the RECAT-CN operation standard is used. The calculation results show that when the number of small-scale flights (23 flights) is small, the maximum landing time of the proposed model is 55 s earlier than the first-come-first-served method and 271 s earlier than the non-optimized one; when the number of large-scale flights (104 flights) is large, the solver alone cannot find a feasible solution within 3600 s, and the proposed algorithm finds a solution within 128.65 s. The proposed model and algorithm are effective and can be applied to actual flight scheduling optimization.

Approximate and Exact Optimization Algorithms for the Beltway and Turnpike Problems with Duplicated, Missing, Partially Labeled, and Uncertain Measurements.

The Turnpike problem aims to reconstruct a set of one-dimensional points from their unordered pairwise distances. Turnpike arises in biological applications such as molecular structure determination, genomic sequencing, tandem mass spectrometry, and molecular error-correcting codes. Under noisy observation of the distances, the Turnpike problem is NP-hard and can take exponential time and space to solve when using traditional algorithms. To address this, we reframe the noisy Turnpike problem through the lens of optimization, seeking to simultaneously find the unknown point set and a permutation that maximizes similarity to the input distances. Our core contribution is a suite of algorithms that robustly solve this new objective. This includes a bilevel optimization framework that can efficiently solve Turnpike instances with up to 100,000 points. We show that this framework can be extended to scenarios with domain-specific constraints that include duplicated, missing, and partially labeled distances. Using these, we also extend our algorithms to work for points distributed on a circle (the Beltway problem). For small-scale applications that require global optimality, we formulate an integer linear program (ILP) that (i) accepts an objective from a generic family of convex functions and (ii) uses an extended formulation to reduce the number of binary variables. On synthetic and real partial digest data, our bilevel algorithms achieved state-of-the-art scalability across challenging scenarios with performance that matches or exceeds competing baselines. On small-scale instances, our ILP efficiently recovered ground-truth assignments and produced reconstructions that match or exceed our alternating algorithms. Our implementations are available at https://github.com/Kingsford-Group/turnpikesolvermm.

Robust day-ahead scheduling of cooperative energy communities considering multiple aggregators

Future cities must play a vital role in reducing energy consumption and decarbonizing the electricity sector, thus evolving from passive structures towards more efficient smart cities. This transition can be facilitated by energy communities. This emerging paradigm consists of collectivizing a set of residential installations equipped with onsite renewable generators and storage assets (i.e., prosumers), which can eventually share resources to pursue collective welfare. This paper focuses on cooperative communities, where prosumers share resources without seeking selfish monetary counterparts. Despite their apparent advantages, energy management and scheduling of energy communities suppose a challenge for conventional tools due to the high level of uncertainty (especially due to intermittent renewable generation and random demand), and privacy concerns among prosumers. This paper addresses these issues. Specifically, a novel management structure based on multiple aggregators is proposed. This paradigm preserves users' confidential features while allowing them to extract the full potential of their assets. To efficiently manage the variety of assets available under uncertainty, an adaptive robust day-ahead scheduling model is developed, which casts as a solvable and portable Mixed Integer Linear Programming framework, which eases its implementation in real-world cases. The new proposal concerns uncertain generation and demand using a polyhedral representation of the uncertainty set. A case study is conducted to validate the developed model, showing promising results. Moreover, different results are obtained and analysed. Finally, it is worth remarking on how the level of robustness impacts the collective bill, incrementing it by 75 % when risk-averse conditions are assumed. In addition, the role of storage assets under pessimistic conditions is remarked, pointing out that these assets rule the scheduling plan of the community instead of renewable generators.

Energy-water-carbon system management in response to climate change in China under uncertainties (2026–2050)

Climate change has seriously affected the resource utilization of the energy-water-carbon system, while the system carbon emissions continuously act on climate change. Given the interaction between the two, there is an urgent need to facilitate the rational allocation of system resources to realize the positive feedback between climate change and energy-water-carbon system development. In this study, an interval stochastic fuzzy integer programming (ISFIP) model is developed to support resource planning and management of the energy-water-carbon system in response to climate change in China. The developed model has advantages in characterizing the complexity and uncertainty of the energy-water-carbon system and providing optimal system decision-making options under multiple climate change scenarios. The results show that the SSP126-NZE scenario power system would reduce carbon emissions by 16.23 %, air pollutant emissions by 19.31 %, water consumption by 30.96 %, and increase economic benefits by 10.97 %, respectively, compared to the SSP585-STEPS baseline scenario.

Deep reinforcement learning driven trajectory-based meta-heuristic for distributed heterogeneous flexible job shop scheduling problem

As the production environment evolves, distributed manufacturing exhibits heterogeneous characteristics, including diverse machines, workers, and production processes. This paper examines a distributed heterogeneous flexible job shop scheduling problem (DHFJSP) with varying processing times. A mixed integer linear programming (MILP) model of the DHFJSP is formulated with the objective of minimizing the makespan. To solve the DHFJSP, we propose a deep Q network-aided automatic design of a variable neighborhood search algorithm (DQN-VNS). By analyzing schedules, sixty-one types of scheduling features are extracted. These features, along with six shaking strategies, are used as states and actions. A DHFJSP environment simulator is developed to train the deep Q network. The well-trained DQN then generates the shaking procedure for VNS. Additionally, a greedy initialization method is proposed to enhance the quality of the initial solution. Seven efficient critical path-based neighborhood structures with three-vector encoding scheme are introduced to improve local search. Numerical experiments on various scales of instances validate the effectiveness of the MILP model and the DQN-VNS algorithm. The results show that the DQN-VNS algorithm achieves an average relative percentage deviation (ARPD) of 3.2%, which represents an approximately 88.45% reduction compared to the best-performing algorithm among the six compared, with an ARPD of 27.7%. This significant reduction in ARPD highlights the superior stability and performance of the proposed DQN-VNS algorithm.

Augmented ɛ‐constraint‐based matheuristic methodology for Bi‐objective production scheduling problems

AbstractMatheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ‐constraint‐based matheuristic methodology (ɛ‐MH) is proposed to apply the idea of ɛ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

An Improved Variable Neighborhood Search for the Reconfigurable Assembly Line Reconfiguring Problem

Throughout the past several decades, the manufacturing industry has been confronted with rapidly evolving market demands. The Reconfigurable Assembly Line (RAL) changes the quantity and variety of products produced through reconfiguration at different stages. The reconfiguration stages of RAL include the reallocation of operations and resources. However, existing research has neglected the resources. In the paper, a mixed integer linear program for the Reconfigurable Assembly Line Reconfiguring Problem is first formulated. Subsequently, an efficient data structure is developed to model the process precedence constraint and alternative resources. And an improved Variable Neighborhood Search which includes new problem-specific neighborhood structures and local search for resource selection is proposed to solve the problem. Computational results demonstrate the contribution of the proposed data structure and the improved procedure. Furthermore, the experiments verify the superiority and stability of the proposed method compared with other heuristic algorithms.