integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning (ML) applied...
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integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning (ML) applied to chemistry, we demonstrate the relevance of an ILP formulation to select molecular training sets for predictions of size-extensive properties. We show that our algorithm outperforms existing unsupervised training set selection approaches, especially when predicting properties of molecules larger than those present in the training set. We argue that the reason for the improved performance is due to the selection that is based on the notion of local similarity (i.e. per-atom) and a unique ILP approach that finds optimal solutions efficiently. Altogether, this work provides a practical algorithm to improve the performance of physics-inspired ML models and offers insights into the conceptual differences with existing training set selection approaches.
Coarse-Grained Reconfigurable Array (CGRA) architectures are potential high-performance and power-efficient platforms. However, mapping applications efficiently on CGRA, which includes scheduling and binding operation...
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Coarse-Grained Reconfigurable Array (CGRA) architectures are potential high-performance and power-efficient platforms. However, mapping applications efficiently on CGRA, which includes scheduling and binding operations on functional units and variables on registers, is a daunting problem. SiLago is a recently developed VLSI design framework comprising two large-scale reconfigurable fabrics: Dynamically Reconfigurable Resource Array (DRRA) and Distributed Memory Architecture (DiMArch). It uses the Vesyla compiler to map applications on these fabrics. The present version of Vesyla executes binding and scheduling sequentially, with binding first, followed by scheduling. In this paper, we proposed an integer linear programming (ILP)-based exact method to solve scheduling and binding simultaneously that delivers better solutions while mapping applications on these fabrics. The proposed ILP combines two objective functions, one for scheduling and one for binding, and both of these objective functions are coupled with weightage factors $\alpha $ and $\beta $ so that the user can have the flexibility to prioritize either scheduling or binding or both based on the requirements. We determined the binding and execution time of image processing tasks and various routines of the Basic linear Algebraic Subprogram (BLAS) using the proposed ILP for multiple combinations of weightage factors. Furthermore, a comparison analysis has been conducted to compare the latency and power dissipation of several benchmarks between the existing and proposed approaches. The experimental results demonstrate that the proposed method exhibits a substantial reduction in power consumption and latency compared to the existing method.
Purpose The site layout has a significant impact on the efficiency of construction operations. Planning an effective site layout partly involves identifying and positioning temporary facilities such as tower cranes an...
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Purpose The site layout has a significant impact on the efficiency of construction operations. Planning an effective site layout partly involves identifying and positioning temporary facilities such as tower cranes and areas on the jobsite for materials storage. This study proposes an approach to optimizing the type and location of the tower crane and material supply point on construction sites. Design/methodology/approach The problem is formulated into an integer linear programming (ILP) model considering the total cost of material transportation as the objective function and site conditions as constraints. The efficacy of the approach is demonstrated by finding the optimum site layout for a numerical example. The proposed model is validated and verified using two methods. Findings Results indicate that the proposed model successfully identifies the type and location of the tower crane and the location of material supply point, leading to approximately 20% cost reduction compared with when such features of a site layout are decided solely based on experience and educated guesses of the construction manager. Originality/value The primary contribution of this study is to present a modified linear mathematical model for site layout optimization that exhibits improved performance compared with previous models. The type and location of the tower crane and the material supply point as decision variables are extracted directly from solving the proposed model. The proposed model will help enhance time and cost efficiency on construction sites.
For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then v...
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For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then vertex v must have at least one neighbour u with . In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance.
In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its ow...
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In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its own specific set of constraints. In this work, we study the tutor allocation in the School of Mathematics at the University of Edinburgh, and solve it with an integer linear programming model. We tested the model on the 2019/2020 case, obtaining a significant improvement with respect to the manual assignment in use and we showed that such improvement could be maintained while optimizing other key metrics such as load balance among groups of tutors and total number of courses assigned. Further tests on randomly created instances show that the model can be used to address cases of broad interest. We also provide meaningful insights on how input parameters, such as the number of workshop locations and the length of the tutors' preference list, might affect the performance of the model and the average number of preferences satisfied.
Chiplet-based systems have become prominent in large Systems-on-Chips (SoCs) as a means to mitigate increasing design costs. However, the integration of multiple chiplets introduces new challenges in the interconnecti...
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This paper deals with the online fault diagnosis problem of discrete event systems under malicious external attacks. We consider a scenario where an attacker can intercept certain sensor measurements and alter them ar...
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This paper deals with the online fault diagnosis problem of discrete event systems under malicious external attacks. We consider a scenario where an attacker can intercept certain sensor measurements and alter them arbitrarily, potentially causing a diagnoser to malfunction. In the framework of labeled Petri nets, a novel integer linear programming problem is formulated by introducing binary variables to estimate the possible transition sequences of an observation that may have been tampered with by an attacker. The proposed approach makes two main contributions. The first one is that, by specifying two different objective functions to the integer linear programming problem, we can obtain the diagnosis results in the presence of attacks, which classic diagnosers may fail to achieve;the second is computational efficiency. In the absence of attacks, the proposed approach is experimentally verified to have lower computational overhead compared with the existing results that are based on integer linear programming and those using basis markings. Finally, the proposed approach is illustrated through a manufacturing system for assembling brake valves.
This paper presents a state-based method to address the verification of K-diagnosability and fault diagnosis of a finite-state vector discrete-event system (Vector DES) with partially observable state outputs due to l...
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This paper presents a state-based method to address the verification of K-diagnosability and fault diagnosis of a finite-state vector discrete-event system (Vector DES) with partially observable state outputs due to limited sensors. Vector DES models consist of an arithmetic additive structure in both the state space and state transition function. This work offers a necessary and sufficient condition for verifying the K-diagnosability of a finite-state Vector DES based on state sensor outputs, employing integer linear programming and the mathematical representation of a Vector DES. Predicates are employed to diagnose faults in a Vector DES online. Specifically, we use three different kinds of predicates to divide system state outputs into different subsets, and the fault occurrence in a system is detected by checking a subset of outputs. Online diagnosis is achieved via solving integer linear programming problems. The conclusions obtained in this work are explained by means of several examples.
In a recent paper published in this journal, Alonso-Pecina et al. collect several sets of benchmark instances for the label printing problem from the literature and they also propose their own instances. Due to the in...
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In a recent paper published in this journal, Alonso-Pecina et al. collect several sets of benchmark instances for the label printing problem from the literature and they also propose their own instances. Due to the intractability of the problem, no optimal solutions were declared for most of these instances. In this paper, we propose an integer linear programming model for the problem. We obtain optimal solutions or show that the solutions provided in the literature are already optimal for most of these instances based on the model. For some of the rest instances, we provide better solutions compared to the previous best solutions in the literature.
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit t...
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State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts that are encountered during the search for a solution. In this article, we extend these techniques to integer linear programming (ILP), where variables may take general integer values instead of purely binary ones, constraints are more expressive than just propositional clauses, and there may be an objective function to optimize. We explain how these methods can be implemented efficiently and discuss possible improvements. Our work is backed with a basic implementation showing that, even in this far less mature stage, our techniques are already a useful complement to the state of the art in ILP.
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