ILP Solver Research Articles

Enhanced conflict‐aware iterated integer linear programming for IEEE 802.1Qbv Time‐Sensitive Network scheduling

SummaryDeterministic communication plays a crucial role for real‐time distributed embedded systems by guaranteeing a low end‐to‐end delay and minimal jitter. Conflict‐aware iterated ILP‐based scheduling (IIS) is an incremental approach to enhance the scalability of single‐shot ILP computation to solve the computationally hard Qbv‐compliant offline scheduling problem for IEEE 802.1 Time‐Sensitive Networking (TSN). Taking into account the conflicting demands of the streams, IIS computes no‐wait schedules by dividing the set of streams into disjoint partitions, each of which is incrementally scheduled by an ILP solver. In this work, defining the no‐wait communication constraints for TSN scheduling, we propose a novel iterated scheduling approach, namely, O‐IIS, with a backtracking mechanism and partial solution support extending the conventional IIS procedure. O‐IIS relies on an ordering strategy to determine the order in which the constructed partitions will be processed by an ILP solver. We evaluate the performance of our approach in terms of schedulability success rate and schedule synthesis time using various network topologies and different partitioning schemes to construct the partitions. The evaluation results show that our approach provides significantly better scheduling performance compared to the existing work in the literature.

Family-Free Genome Comparison.

The comparison of large-scale genome structures across distinct species offers valuable insights into the species' phylogeny, genome organization, and gene associations. In this chapter, we review the family-free genome comparison tool FFGC that, relying on built-in interfaces with a sequence comparison tool (either BLAST+ or DIAMOND) and with an ILP solver (either CPLEX or Gurobi), provides several methods for analyses that do not require prior classification of genes across the studied genomes. Taking annotated genome sequences as input, FFGC is a complete workflow for genome comparison allowing not only the computation of measures of similarity and dissimilarity but also the inference of gene families, simultaneously based on sequence similarities and large-scale genomic features.

Dynamic Service Provisioning in the Edge-Cloud Continuum With Bounded Resources

We consider a hierarchical edge-cloud architecture in which services are provided to mobile users as chains of virtual network functions. Each service has specific computation requirements and target delay performance, which require placing the corresponding chain properly and allocating a suitable amount of computing resources. Furthermore, chain migration may be necessary to meet the services’ target delay. We model and formalize the problem of finding a feasible chain placement and resource allocation, while minimizing the migration, bandwidth, and computation costs. We tackle this problem by partitioning it into a (i) CPU allocation problem, and a (ii) placement problem. For the CPU allocation problem, we find an optimal solution. For the placement problem, we show that even finding a feasible solution is NP-hard, and envision an algorithm that is guaranteed to find a feasible solution while leveraging a bounded amount of resource augmentation. Our algorithms are incorporated into a solution framework that aims to minimize both the cost and the required resource augmentation. The results, obtained through trace-driven, large-scale simulations, show that our framework can provide a close-to-optimal solution while running several orders of magnitude faster than an ILP solver.

Now We’re Talking: Better Deliberation Groups through Submodular Optimization

Citizens’ assemblies are groups of randomly selected constituents who are tasked with providing recommendations on policy questions. Assembly members form their recommendations through a sequence of discussions in small groups (deliberation), in which group members exchange arguments and experiences. We seek to support this process through optimization, by studying how to assign participants to discussion groups over multiple sessions, in a way that maximizes interaction between participants and satisfies diversity constraints within each group. Since repeated meetings between a given pair of participants have diminishing marginal returns, we capture interaction through a submodular function, which is approximately optimized by a greedy algorithm making calls to an ILP solver. This framework supports different submodular objective functions, and we identify sensible options, but we also show it is not necessary to commit to a particular choice: Our main theoretical result is a (practically efficient) algorithm that simultaneously approximates every possible objective function of the form we are interested in. Experiments with data from real citizens' assemblies demonstrate that our approach substantially outperforms the heuristic algorithm currently used by practitioners.

Matching Supply and Demand in Online Parking Reservation Platforms

Our work concerns online parking reservation platforms proposed in the last decade to cope with the parking challenge in cities worldwide. Enlisting parking resources from commercial operators (e.g., lots) and individuals (e.g., doorways) and letting drivers make online reservations through mobile apps, those platforms seek to ease transactions between the two sides and best match parking supply with parking demand. This way they maximize their value for drivers and parking space providers but also their revenue out of charged commissions. We distinguish between two types of commissions these platforms typically charge, fixed per transaction and proportional to its value, and formulate the respective optimization problems for the platform revenue maximization. We show that the two problems are NP-hard and design a novel algorithm that can treat both by combining greedy and dynamic programming principles. We study its optimality properties both analytically and experimentally, showing that the algorithm closely tracks optimal solutions for small and moderate problem sizes at run times that are several orders of size smaller than those needed by off-the-shelf ILP solvers. We then analyze real parking data we collected for the period 2018-2020 from the Bournemouth city in UK to realistically model the rich spatiotemporal dynamics of parking demand such as the location, start times and duration of parking events. These datasets drive the experimental evaluation of the proposed algorithm, which reports gains of up to 35% compared to the de facto parking resource reservation policy in such platforms. Notably, the highest gains are achieved when the platform operates under constrained supply conditions.

Stereo: Assignment and Scheduling in MPSoC Under Process Variation by Combining Stochastic and Decomposition Approaches

Aggressive scaling in integrated circuits creates new challenges such as an increase in power density, temperature, and especially process variation in designing Multiprocessor Systems-on-Chip (MPSoC). While most of the previous works attempt to mitigate the process variation effects at the system level, the eventual design still suffers from the variability of frequency and leakage power. In this paper, we propose a method called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stereo</i> that combines <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</u> tochas <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</u> ic and d <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</u> composition to solve task assignment and scheduling under p <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</u> oc <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</u> ss variati <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</u> n in MPSoCs. In our previous work, we formulated a Mixed Integer Linear Programming (MILP) problem for variation-aware task assignment and scheduling to optimize energy consumption while meeting the real-time constraints. To capture the stochastic behavior of process variation, we employed a chance-constrained programming technique to turn the problem into a corresponding stochastic optimization that can be solved by typical ILP solvers. However, it had a scalability problem. To address this issue, in this work, we leverage a Logic-based Benders Decomposition (LBD) approach to improve the running time for finding an optimal solution of assignments and schedulings under process variation phenomenon). We carried out extensive experiments using Embedded System Synthesis Benchmarks Suite (E3S). The experimental results of the Stereo method evince considerable improvements compared to the baseline method in terms of performance-yield and run-time. The Stereo-based MILP method ameliorates performance-yield up to 2× and run-time by 532×. Moreover, for manifold applications, the Stereo-based LBD method archives 3.47×-91.49× run-time improvement compared to the Stereo-based MILP approach and is capable of assigning and scheduling of more than 50 tasks on 9 processors.

Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-hop Inference

Abstract This paper presents Diff-Explainer, the first hybrid framework for explainable multi-hop inference that integrates explicit constraints with neural architectures through differentiable convex optimization. Specifically, Diff- Explainer allows for the fine-tuning of neural representations within a constrained optimization framework to answer and explain multi-hop questions in natural language. To demonstrate the efficacy of the hybrid framework, we combine existing ILP-based solvers for multi-hop Question Answering (QA) with Transformer-based representations. An extensive empirical evaluation on scientific and commonsense QA tasks demonstrates that the integration of explicit constraints in a end-to-end differentiable framework can significantly improve the performance of non- differentiable ILP solvers (8.91%–13.3%). Moreover, additional analysis reveals that Diff-Explainer is able to achieve strong performance when compared to standalone Transformers and previous multi-hop approaches while still providing structured explanations in support of its predictions.

Improved solution of the Budget constrained Fuel Treatment Scheduling problem and extensions

This paper considers the budget constrained fuel treatment scheduling (BFTS) problem where, in the context of wildfire mitigation, the goal is to inhibit the potential of fire spread in a landscape by proper fuel treatment activities. Given a time horizon represented by consecutive unit periods, the landscape is divided into cells and represented as a grid graph where each cell has a fuel age that increases over time and becomes old if no treatment is applied in the meantime: this induces a potential high fire risk whenever two contiguous cells are old. Cells fuel ages can be reset to zero under appropriate fuel treatments but there is a limited budget for treatment in each period. The problem calls for finding a suitable selection of cells to be treated so as to minimize the presence of old contiguous cells over the whole time horizon. We prove that problem BFTS is strongly NP-complete on paths and thus on grid graphs and show that no polynomial time approximation algorithm exists unless P=NP. We provide an enhanced integer linear programming formulation of the problem with respect to the relevant literature that shows up to be efficiently solved by an ILP solver on reasonably large size instances. Finally, we consider a harder periodic variant of the problem with the aim of finding a cyclic treatment plan with cycles of length T and propose a matheuristic approach capable of efficiently tackling those instances where an ILP solver applied to the ILP formulation runs into difficulties.

A Population-Based Iterated Greedy Algorithm for Maximizing Sensor Network Lifetime.

Finding dominating sets in graphs is very important in the context of numerous real-world applications, especially in the area of wireless sensor networks. This is because network lifetime in wireless sensor networks can be prolonged by assigning sensors to disjoint dominating node sets. The nodes of these sets are then used by a sleep–wake cycling mechanism in a sequential way; that is, at any moment in time, only the nodes from exactly one of these sets are switched on while the others are switched off. This paper presents a population-based iterated greedy algorithm for solving a weighted version of the maximum disjoint dominating sets problem for energy conservation purposes in wireless sensor networks. Our approach is compared to the ILP solver, CPLEX, which is an existing local search technique, and to our earlier greedy algorithm. This is performed through its application to 640 random graphs from the literature and to 300 newly generated random geometric graphs. The results show that our algorithm significantly outperforms the competitors.

Systematic search space design for energy-efficient static scheduling of moldable tasks

Static scheduling of independent, moldable tasks on parallel machines with frequency scaling comprises decisions on core allocation, assignment, frequency scaling and ordering, to meet a deadline and minimize energy consumption. Constraining some of these decisions reduces the solution space, i.e. may increase energy consumption, but may also open the path to new, near-optimal approaches. We investigate how constraints of different steps influence energy consumption, starting with an unrestricted scheduler for moldable tasks. The constraints are partly derived from existing schedulers, but also generalized in a systematic way. We present integer linear programs for all scheduling variants. We compare energy consumption of schedules for a benchmark suite of synthetic task sets of different sizes and for task sets derived from real applications. In addition, we check how close the results are to the optimum results when the ILP solver meets a timeout. Our results indicate that constraints on task execution order, which avoid explicit representation of task order in ILPs, are mostly responsible for near-optimal energy consumption among large task sets. Furthermore, we find that for all steps except allocation, non-optimal fast heuristics can be used without sacrificing too much energy for the resulting schedule. Finally, we can show that an ILP for a new scheduler, for which also a heuristic version exists, is comparable in quality to more complicated schedulers.

Reliable controller placement in software‐defined networks using reliability covering graph and irregular cellular learning automata

SummarySoftware‐defined networking is a new paradigm in network management that has received much attention in recent years. One of the important challenges in designing software‐defined networks (SDNs) is the reliable controller placement problem (RCPP) that is the problem of finding the number and locations of controllers to satisfy the reliability requirements. The high complexity of exact reliability measurement led researchers to use estimation techniques that results in overestimating the number of controllers and incorrect placement. In this paper, we introduce a new concept named reliability covering graph (RCG) that enables us to use the exact reliability measurement (ERM) methods in solving the RCPP with desired level of complexity. To construct the RCG, for each candidate node, a subgraph with the adjustable radiusris extracted from the network graph. In the next step, the RCG is developed by calculating the exact reliability between the central node and any other nodes in the resulting subgraphs. In the last step, the RCG is converted to a machine learning tool named irregular cellular learning automata (ICLA) that determines the number and locations of controllers as well as the switches they cover. To study the efficiency of the proposed method, its performance is compared with the optimal results obtained from the ILP solver. The simulation results of 800 case studies on 100 standard topologies show that the average difference in results is 0.00125. Thanks to our innovative structure RCG, the number of controllers required is significantly reduced compared to previous methods.

Throughput Optimization and Delay Guarantee VNF Placement for Mapping SFC Requests in NFV-Enabled Networks

Nowadays, network softwareization is an emerging techno-economic transformation trend that significantly impacts how enterprises deploy their network services. As an essential technology in this trend, Network Function Virtualization (NFV) enables scalable and inexpensive network services by flexibly instantiating Virtualized Network Functions (VNFs) on commercial-off-the-shelf devices. In this paper, we focus on the VNF placement problem in NFV-enabled networks, aiming to maximize the number of accepted Service Function Chain Requests (SFCRs) while guaranteeing their delay requirements. To improve resource utilization efficiency, we take account of Fundamental Resource Overheads (FROs) and the shareability of VNF instances. We mathematically formulate the VNF placement problem and propose the Throughput Optimization and Delay Guarantee (TO-DG) heuristic solution, consisting of an affinity-based SFCR mapping algorithm and a VNF request adjustment algorithm. The evaluation results show that the performance of TO-DG is near to results derived by ILP solver for small scale problems. Moreover, TO-DG obtains higher network throughput than contrasting schemes in different scenarios and significantly improves network resource utilization.

Computing a Consensus Phylogeny via Leaf Removal.

Given a set [Formula: see text]. of phylogenetic trees with the same leaf-label set X, we wish to remove some leaves from the trees so that there is a tree T with leaf-label set X displaying all the resulting trees. Note that the labels of leaves removed from one input tree may be different from those of leaves removed from another input tree. One objective is to minimize the total number of leaves removed from the trees, whereas the other is to minimize the maximum number of leaves removed from an input tree. Chauve et al. refer to the problem with the first (respectively, second) objective as AST-LR (respectively, AST-LR-d), and they show that both problems are NP-hard, where NP is the class of problems solvable in non-deterministic polynomial time. They further present algorithms for the parameterized versions of both problems. In this article, we point out that their algorithm for the parameterized version of AST-LR is flawed and present a new algorithm. Since neither Chauve et al.'s algorithm for AST-LR-d nor our new algorithm for AST-LR looks practical, we further design integer-linear programming (ILP for short) models for AST-LR and AST-LR-d, and we discuss speedup issues when using popular ILP solvers (say, GUROBI or CPLEX) to solve the models. Our experimental results show that our ILP approach is quite efficient.

A Task-Based Greedy Scheduling Algorithm for Minimizing Energy of MapReduce Jobs

MapReduce and its open source implementation, Hadoop, have gained widespread adoption for parallel processing of big data jobs. Since the number of such big data jobs is also rapidly rising, reducing their energy consumption is increasingly more important to reduce environmental impact as well as operational costs. Prior work by Mashayekhy et al. (IEEE Trans. Parallel Distributed Syst. 26, 2720–2733, 2016), has tackled the problem of energy-aware scheduling of a single MapReduce job but we provide a far more efficient heuristic in this paper. We first model the problem as an Integer Linear Program to find the optimal solution using ILP solvers. Then we present a task-based greedy scheduling algorithm, TGSAVE, to select a slot for each task to minimize the total energy consumption of the MapReduce job for big data applications in heterogeneous environments without significant performance loss while satisfying the service level agreement (SLA). We perform several experiments on a Hadoop cluster to measure characteristics of tasks for nine different applications to evaluate our proposed algorithm. The results show that the total energy consumption of MapReduce jobs obtained by TGSAVE is up to 35% less than that achieved by EMRSA proposed in Mashayekhy et al. (IEEE Trans. Parallel Distributed Syst. 26, 2720–2733, 2016), its closest rival, for same workloads. Besides, TGSAVE is capable of finding a solution in same order of time for up to 74% tighter deadlines than the tightest deadline that EMRSA can find a feasible one. On average, TGSAVE solution is approximately 1.4% far from the optimal solution, and it can meet deadlines as tight as 12%, on average, above the energy-oblivious minimum makespan in the benchmarks we examined.

Mapping of synchronous dataflow graphs on MPSoCs based on parallelism enhancement

Multi-processor systems-on-chips are widely adopted in implementing modern streaming applications to satisfy the ever increasing computation requirements. To take advantage of this kind of platform, it is necessary to map tasks of the application properly to different processors, so as to fully exploit the inherent task-level parallelism and satisfy the stringent timing requirements. We propose the Parallelism Graph to capture the task-level parallelism of the application and transform the mapping problem to a graph partitioning problem. The graph partitioning problem is formulated as an Integer Linear Programming problem, which is solved optimally using the ILP solver. To reduce the complexity, a two-step local search algorithm, i.e., the greedy partition and refinement algorithm, is proposed. Since one-shot heuristics cannot guarantee the solution quality, evolutionary algorithms are widely used to search the solution space such that better results can be found. We also integrate the idea of parallelism enhancement into the genetic algorithm and propose a hybrid genetic algorithm to improve the performance. Sets of synthesized Synchronous Data Flow Graphs and some practical applications are used to evaluate the performance of the proposed algorithms. Experiment results demonstrate that the proposed algorithms outperform available algorithms.

A unified approach for location-allocation analysis

In this article, we develop an efficient unified solver for location-allocation analysis based on the VAOMP model without using ILP solvers. Our aim is to develop a fast heuristic algorithm based o...

Computing maximal and minimal trap spaces of Boolean networks

Asymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal trans- duction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called trap spaces, can be exploited to investigate attractor properties as well as for model reduction techniques. In this paper, we propose a novel optimization-based method for com- puting all minimal and maximal trap spaces and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a study of a MAPK pathway model. To test the efficiency and scalability of the method, we compare the performance of the ILP solver gurobi with the ASP solver potassco in a benchmark of random networks.

Assessment of assignment policies of users in medico-social service sector

This paper is focused on the assignment of users to medico-social institutions. The main goal is to study if alternative assignment policies can improve global response to users’ demands and assess the performances of each alternative compared to the current practice. We formulated a mathematical model of the user assignment to medico-social structures and professionals, under constraints of resource capacity, professional's skills and user requirement covering (formulated in an individual support project). The alternative assignment policies allow respectively to partially cover the need of users, and to authorize the involvement of several structures and several professionals in the response to the request. This model is solved thanks to a mixed ILP solver, following a lexicographic approach with regard do the partial covering policy. We used real size data gathered in a cluster of institution for disabled children and teenagers. We present and compare computational results over several scenarios, highlighting the improvement provided by alternative assignment policies.

SNV-PPILP: refined SNV calling for tumor data using perfect phylogenies and ILP.

Recent studies sequenced tumor samples from the same progenitor at different development stages and showed that by taking into account the phylogeny of this development, single-nucleotide variant (SNV) calling can be improved. Accurate SNV calls can better reveal early-stage tumors, identify mechanisms of cancer progression or help in drug targeting. We present SNV-PPILP, a fast and easy to use tool for refining GATK's Unified Genotyper SNV calls, for multiple samples assumed to form a phylogeny. We tested SNV-PPILP on simulated data, with a varying number of samples, SNVs, read coverage and violations of the perfect phylogeny assumption. We always match or improve the accuracy of GATK, with a significant improvement on low read coverage. SNV-PPILP, available at cs.helsinki.fi/gsa/snv-ppilp/, is written in Python and requires the free ILP solver lp_solve. Supplementary data are available at Bioinformatics online.

Design space exploration for high-level synthesis of multi-threaded applications

We present an ESL methodology creating a direct path from high-level multi-threaded OpenMP applications to automatically synthesized, heterogeneous hardware/software systems implemented onto FPGA devices. The work addresses a number of challenges, including the definition of a novel system-oriented Model of Computation (MoC), capturing the essential aspects of the structure of a parallel software application related to the optimization and translation process, a key element to enable automated design space exploration. The paper also presents an analytical optimization model based on Integer Linear Programming, as well as innovative techniques for early hardware cost prediction used to speed up the design space exploration process. The methodology is supported by a set of ad hoc tools, including a custom OpenMP compiler and a hardware cost estimator, interacting with an existing ILP solver and a hardware high-level synthesis engine. The resulting prototypical environment demonstrates an innovative design flow that can extend the spectrum of ESL design to high-level multi-threaded applications, successfully meeting the current trends in complex embedded systems design. The work also presents a case-study to show the effectiveness of the proposed methodology with a real-world application.