Integer Programming Framework Research Articles

Integer programming framework for pangenome-based genome inference.

https://github.com/at-cg/PHI.

An optimization framework to provide volunteers with task selection autonomy and group opportunities

Nonprofit Organizations (NPOs) rely on volunteers to support community needs but struggle with making strategic volunteer-to-task assignments to enable volunteer satisfaction, and completion of complex tasks. Creation of volunteer groups and their assignment to NPO tasks can help achieve these goals by providing volunteers with opportunity for networking, collaboration, and peer learning. However, strategically creating ideal assignments is challenging because (i) there are exponentially many ways a set of volunteers can be assigned in groups; and (ii) NPOs tend to have limited and uncertain data concerning volunteers' personal preferences, availabilities, and motivations to participate. To address these challenges, this research contributes by introducing an integer programming framework to offer volunteers a menu of tasks to choose from and then based on volunteers' willingness information, creates ideal homogenous volunteer group assignments. These groups are created such that the group collectively meet a task's skill requirements and groups of volunteers of similar skill and affinity levels are prioritized. We apply the developed methodology to a case study based on a partner NPO that works with remote volunteers from multiple countries to produce online educational content. The menu creation method can improve NPO and volunteer-based performance metrics, where the most improvement is observed when a NPO is faced with very picky volunteers. Presenting volunteers with larger menus of tasks also leads to an improvement in ideal group creations. Implementing the group creation methodology helps obtain a statistically significant increase in ideal group creations but results in a tradeoff of decreased benefits to volunteers and the NPO. Finally, implementing a minimum desired group size does not severely impact most KPIs and would be beneficial for an NPO to implement as it encourages the creation and assignment of volunteer groups to tasks.

A multi-objective planning and scheduling model for elective and emergency cases in the operating room under uncertainty

Hospitals are paramount hubs for delivering healthcare services, with their Operating Rooms (ORs) as a pivotal and financially substantial component. Efficient surgery ward planning is crucial in healthcare institutions, aiming to improve medical service quality while reducing costs. This research delves into the intricacies of integrated OR planning and scheduling, focusing on elective and emergency patients in an uncertain environment. To address these challenges, a mixed integer programming (MIP) framework is developed to minimize inactivity and patient wait times while optimizing high-priority resource allocation. Both upstream and downstream units of the ward, the Pre-operative Holding Unit (PHU), Post Anesthesia Care Unit (PACU), and Intensive Care Unit (ICU) are included. The inherently uncertain aspects of surgery, including surgical duration, Length of Stay (LOS), and the influx of emergency patients, demand an intelligent optimization approach. Consequently, a robust optimization strategy is harnessed to effectively grapple with this pervasive uncertainty. A deterministic model is introduced and improved using an enhanced epsilon constraint method. The culmination of this analytical journey yields a collection of Pareto-optimal solutions. Empirical results, supported by managerial insights, highlight the superiority of the proposed method over the traditional weighting approach.

A strength and sparsity preserving algorithm for generating weighted, directed networks with predetermined assortativity

Degree-preserving rewiring is a widely used technique for generating unweighted networks with given assortativity, but for weighted networks, it is unclear how an analog would preserve the strengths and other critical network features such as sparsity level. This study introduces a novel approach for rewiring weighted networks to achieve desired directed assortativity. The method utilizes a mixed integer programming framework to establish a target network with predetermined assortativity coefficients, followed by an efficient rewiring algorithm termed “strength and sparsity preserving rewiring” (SSPR). SSPR retains the node strength distributions and network sparsity after rewiring. It is also possible to accommodate additional properties like edge weight distribution, albeit with extra computational cost. The optimization scheme can be used to determine feasible assortativity ranges for an initial network. The effectiveness of the proposed SSPR algorithm is demonstrated through its application to two classes of popular network models.

Spread management priorities to limit emerald ash borer (Agrilus planipennis) impacts on United States street trees

AbstractThe invasive emerald ash borer (Agrilus planipennis) causes damage to street trees which is estimated to reach US$ 900 million over the next 30 years. Although millions of dollars are spent annually to control this species, spatiotemporal management plans are often based on rules of thumb that ignore future pest dispersal. Here, we reveal an optimal management strategy to protect urban trees in North America from A. planipennis. To achieve this, we embedded a pest dispersal model within a mixed integer programming framework. We discovered that optimized strategies consistently outperformed those based on rules of thumb, potentially resulting in the protection of an additional nearly 1 million street trees and savings of $ 629 million. Critically, the best management strategies always relied on quarantines and biological control (constituting 98–99% and 1–2% of the project budget, respectively), in contrast with current practices, where federal spending has been diverted to biological control. Our findings serve to inform future pest control efforts and can help protect many more trees from this invasive species.

Concurrent prediction of RNA secondary structures with pseudoknots and local 3D motifs in an integer programming framework.

The prediction of RNA structure canonical base pairs from a single sequence, especially pseudoknotted ones, remains challenging in a thermodynamic models that approximates the energy of the local 3D motifs joining canonical stems. It has become more and more apparent in recent years that the structural motifs in the loops, composed of noncanonical interactions, are essential for the final shape of the molecule enabling its multiple functions. Our capacity to predict accurate 3D structures is also limited when it comes to the organization of the large intricate network of interactions that form inside those loops. We previously developed the integer programming framework RNA Motifs over Integer Programming (RNAMoIP) to reconcile RNA secondary structure and local 3D motif information available in databases. We further develop our model to now simultaneously predict the canonical base pairs (with pseudoknots) from base pair probability matrices with or without alignment. We benchmarked our new method over the all nonredundant RNAs below 150 nucleotides. We show that the joined prediction of canonical base pairs structure and local conserved motifs (i) improves the ratio of well-predicted interactions in the secondary structure, (ii) predicts well canonical and Wobble pairs at the location where motifs are inserted, (iii) is greatly improved with evolutionary information, and (iv) noncanonical motifs at kink-turn locations. The source code of the framework is available at https://gitlab.info.uqam.ca/cbe/RNAMoIP and an interactive web server at https://rnamoip.cbe.uqam.ca/.

Global optimization of mixed-integer nonlinear programs with SCIP 8

AbstractFor over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version 8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

New Algorithms for Hierarchical Optimization in Kidney Exchange Programs

New Exact Approaches Tailored for Kidney Exchange Programs with Hierarchical Objectives Kidney exchange programs increase the rate of living donor kidney transplantation. Whereas effective integer programming models aimed at maximizing the total number of transplants have been proposed in the literature, these cannot always be extended to handle a hierarchy of objectives, which is often a requirement in practice. In “New Algorithms for Hierarchical Optimization in Kidney Exchange Programs,” Delorme, García, Gondzio, Kalcsics, Manlove, and Pettersson introduce a new integer programming framework to solve large-size instances of kidney exchange programs. The authors use an ad hoc preprocessing and a reduced-cost variable fixing algorithm to dramatically decrease the size of the models, and they devise a diving algorithm that exploits the hierarchical structure of the problem to significantly reduce the number of integer programs that need to be solved. They also show that it is possible to transition between models as different layers are traversed in the hierarchy, allowing each layer to be solved with the most effective model. Experiments on three different European kidney exchange programs show that running times can be reduced by up to three orders of magnitude.

Accelerated dual dynamic integer programming applied to short-term power generation scheduling

The short-term generation scheduling (STGS) problem defines which units must operate and how much power they must deliver to satisfy the system demand over a planning horizon of up to two weeks. The problem is typically formulated as a large-scale mixed-integer linear programming problem, where off-the-shelf commercial solvers generally struggle to efficiently solve realistic instances of the STGS, mainly due to the large-scale of these models. Thus, decomposition approaches that break the model into smaller instances that are more easily handled are attractive alternatives to directly employing these solvers. This paper proposes a dual dynamic integer programming (DDiP) framework for solving the STGS problem efficiently. As in the standard DDiP approach, we use a nested Benders decomposition over the time horizon but introduce multiperiod stages and overlap strategies to accelerate the method. Simulations performed on the IEEE-118 system show that the proposed approach is significantly faster than standard DDiP and can deliver near-optimal solutions.

SlicedRAN: Service-Aware Network Slicing Framework for 5G Radio Access Networks

5G mobile networks are envisioned to substantiate new vertical services with diverse performance requirements. Slicing in the radio access network (RAN) promises an efficient solution for these diversified needs of 5G networks, which foresees the separation of the base station functionality between the central unit (CU) and the distributed remote radio heads. In this article, we formulate a mixed integer programming (MIP) framework that maximizes the throughput by jointly selecting the optimal functional split and the routing path from a connected user equipment to the CU, while satisfying the agreed service level agreements (SLAs) of each service. Furthermore, we propose an effective heuristic, SlicedRAN, which creates isolated RAN slices premised on the service requirements connected through a fronthaul/backhaul (FH/BH) network and obtains near-optimal solutions in a short computing time compared to the MIP framework. Our results show that there is a tradeoff between the architecture of the FH/BH network and the minimum SLA of each slice, which provides a solution to efficiently design a virtualized network infrastructure. According to the results, the SlicedRAN outperforms existing state-of-the-art up to 112% gain in throughput. Results are shown close to the optimal results, with a loss below 5%.

Using ℓ1-Relaxation and Integer Programming to Obtain Dual Bounds for Sparse PCA

Dual Bounds of Sparse Principal Component Analysis Sparse principal component analysis (PCA) is a widely used dimensionality reduction tool in machine learning and statistics. Compared with PCA, sparse PCA enhances the interpretability by incorporating a sparsity constraint. However, unlike PCA, conventional heuristics for sparse PCA cannot guarantee the qualities of obtained primal feasible solutions via associated dual bounds in a tractable fashion without underlying statistical assumptions. In “Using L1-Relaxation and Integer Programming to Obtain Dual Bounds for Sparse PCA,” Santanu S. Dey, Rahul Mazumder, and Guanyi Wang present a convex integer programming (IP) framework of sparse PCA to derive dual bounds. They show the worst-case results on the quality of the dual bounds provided by the convex IP. Moreover, the authors empirically illustrate that the proposed convex IP framework outperforms existing sparse PCA methods of finding dual bounds.

Empowering the configuration-IP: new PTAS results for scheduling with setup times

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/varepsilon )cdot mathrm {poly}(|I|). Previously, only constant factor approximations of 5/3 and 4/3 + varepsilon , respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.

Polyhedral properties of the induced cluster subgraphs

A cluster graph is a graph whose every connected component is a complete graph. Given a simple undirected graph G, a subset of vertices inducing a cluster graph is called an independent union of cliques (IUC), and the IUC polytope associated with G is defined as the convex hull of the incidence vectors of all IUCs in the graph. The Maximum IUC problem, which is to find a maximum-cardinality IUC in a graph, finds applications in network-based data analysis. In this paper, we derive several families of facet-defining valid inequalities for the IUC polytope. We also give a complete description of this polytope for some special classes of graphs. We establish computational complexity of the separation problem for most of the considered families of valid inequalities and explore the effectiveness of employing the corresponding cutting planes in an integer (linear) programming framework for the Maximum IUC problem through computational experiments.

Dual dynamic programming for multi-scale mixed-integer MPC

We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal discretizations as well as mixed-integer states and controls (e.g., scheduling logic and discrete actuators). The approach uses a nested cutting-plane scheme that performs forward and backward sweeps along the time horizon to adaptively approximate cost-to-go functions. The DDIP scheme proposed can handle general MPC formulations with mixed-integer controls and states and can perform forward-backward sweeps over block time partitions. We demonstrate the performance of the proposed scheme by solving mixed-integer MPC problems that arise in the scheduling of central heating, ventilation, and air-conditioning (HVAC) plants. We show that the proposed scheme is scalable and dramatically outperforms state-of-the-art mixed-integer solvers.

Temporal Ordered Clustering in Dynamic Networks: Unsupervised and Semi-Supervised Learning Algorithms

In temporal ordered clustering , given a single snapshot of a dynamic network in which nodes arrive at distinct time instants, we aim at partitioning its nodes into $K$ ordered clusters $\mathcal {C}_1 \prec \cdots \prec \mathcal {C}_K$ such that for $i , nodes in cluster $\mathcal {C}_i$ arrived before nodes in cluster $\mathcal {C}_j$ , with $K$ being a data-driven parameter and not known upfront. Such a problem is of considerable significance in many applications ranging from tracking the expansion of fake news to mapping the spread of information. We first formulate our problem for a general dynamic graph, and propose an integer programming framework that finds the optimal clustering, represented as a strict partial order set, achieving the best precision (i.e., fraction of successfully ordered node pairs) for a fixed density (i.e., fraction of comparable node pairs). We then develop a sequential importance procedure and design unsupervised and semi-supervised algorithms to find temporal ordered clusters that efficiently approximate the optimal solution. To illustrate the techniques, we apply our methods to the vertex copying (duplication-divergence) model which exhibits some edge-case challenges in inferring the clusters as compared to other network models. Finally, we validate the performance of the proposed algorithms on synthetic and real-world networks.

Underground mine scheduling under uncertainty

Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value; constraints enforce geotechnical precedence between activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic schedules address these start dates at a coarse level, whereas tactical schedules must account for the day-to-day variability of underground mine operations, such as unanticipated equipment breakdowns and ground conditions, both of which might slow production. At the time of this writing, the underground mine scheduling literature is dominated by a deterministic treatment of the problem, usually modeled as a Resource Constrained Project Scheduling Problem (RCPSP), which precludes mine operators from reacting to unforeseen circumstances. Therefore, we propose a stochastic integer programming framework that: (i) characterizes uncertainty in duration and economic value for each underground mining activity; (ii) formulates a new stochastic variant of the RCPSP; (iii) suggests an optimization-based heuristic; and, (iv) produces implementable, tactical schedules in a practical amount of time and provides corresponding managerial insights.

Graph computing based security constrained unit commitment in hydro-thermal power systems incorporating pumped hydro storage

This paper proposes a graph computing based mixed integer programming (MIP) framework for solving the security constrained unit commitment (SCUC) problem in hydro-thermal power systems incorporating pumped hydro storage (PHS). The proposed graph computing-based MIP framework considers the economic operations of thermal units, cascade hydropower stations and PHS stations, as well as their technical impacts towards the network security. First, the hydro-thermal power system data and unit information are stored in a graph structure with nodes and edges, which enables nodal and hierarchical parallel computing for the unit commitment (UC) solution calculation and network security analysis. A MIP model is then formulated to solve the SCUC problem with the mathematical models of thermal units, cascade hydropower stations and PHS stations. In addition, two optimization approaches including convex hull reformulation (CHR) and special ordered set (SOS) methods are introduced for speeding up the MIP calculation procedure. To ensure the system stability under the derived UC solution, a parallelized graph power flow (PGPF) algorithm is proposed for the hydro-thermal power system network security analysis. Finally, case studies of the IEEE 118-bus system and a practical 2749-bus hydro-thermal power system are introduced to demonstrate the feasibility and validity of the proposed graph computing-based MIP framework.

Dynamic Disruption Management in Airline Networks Under Airport Operating Uncertainty

Air traffic disruptions result in flight delays, cancellations, passenger misconnections, and ultimately high costs to aviation stakeholders. This paper proposes a jointly reactive and proactive approach to airline disruption management, which optimizes recovery decisions in response to realized disruptions and in anticipation of future disruptions. The approach forecasts future disruptions partially and probabilistically by estimating systemic delays at hub airports (and the uncertainty thereof) and ignoring other contingent disruptions. It formulates a dynamic stochastic integer programming framework to minimize network-wide expected disruption recovery costs. Specifically, our Stochastic Reactive and Proactive Disruption Management (SRPDM) model combines a stochastic queuing model of airport congestion, a flight planning tool from Boeing/Jeppesen and an integer programming model of airline disruption recovery. We develop a solution procedure based on look-ahead approximation and sample average approximation, which enables the model’s implementation in short computational times. Experimental results show that leveraging even partial and probabilistic estimates of future disruptions can reduce expected recovery costs by 1%–2%, as compared with a myopic baseline approach based on realized disruptions alone. These benefits are mainly driven by the deliberate introduction of departure holds to reduce expected fuel costs, flight cancellations, and aircraft swaps.

Analysis of compressive sensing and energy harvesting for wireless multimedia sensor networks

One of the main concerns of Wireless Multimedia Sensor Networks (WMSNs) is the huge data size causing the higher energy consumption in transmission. The high energy consumption is a critical problem for lifetime of network includes sensor nodes with limited battery. The data size reduction and Energy Harvesting (EH) methods are the promising solutions to improve the network lifetime. The main objective of this paper is to evaluate the impact of the different data size reduction methods, such as image compression and Compressive s Sensing (CS), and EH methods, such as vibration, thermal and indoor solar, on WMSNs lifetime in industrial environments. In addition, a novel Mixed Integer Programming (MIP) framework is proposed to maximize the network lifetime when EH, CS, and Error Control (EC) approaches are utilized together. Comparative performance results show that utilizing Binary Compressive Sensing (BCS) and Indoor Solar Harvester (ISH) extends industrial network lifetime significantly.

A note on optimization modelling of piecewise linear delay costing in the airline industry

We present a mathematical model in an integer programming (I.P.) framework for non-linear delay costing in the airline industry. We prove the correctness of the model mathematically. Time is discretized into intervals of, for example, 15 minutes. We assume that the cost increases with increase in the number of intervals of delay in a piecewise linear manner. Computational results with data obtained from Sydney airport (Australia) show that the integer programming non-linear cost model runs much slower than the linear cost model; hence fast heuristics need to be developed to implement non-linear costing, which is more accurate than linear costing. We present a greedy heuristic that produces a solution only slightly worse than the ones produced by the I.P. models, but in much shorter time.