Linear Programming Research Articles

Measurement-Noise Filtering for Automatic Discovery of Flow Splitting Ratios in ISP Networks

Network telemetry and analytics is essential for providing highly dependable services in modern computer networks. In particular, network flow analytics for ISP networks allows operators to inspect and reason about traffic patterns in their networks in order to react to anomalies. High performance network analytics systems are designed with scalability in mind, and can consequently only observe partial information about the network traffic. Still, they need to provide a holistic view of the traffic, including the distribution of different traffic flows on each link. It is impractical to monitor such fine-grained telemetry, and in large, heterogeneous networks it is often too complex and error-prone, if not impossible, to access and maintain all technical specifications and router-specific configurations needed to determine e.g. the load balancing weights used when traffic is split onto multiple paths. The ratios by which flows are split on the possible paths must be derived indirectly from the measured flow demands and link utilizations. Motivated by a case study provided by a major European ISP, we suggest an efficient method to estimate the flow splitting ratios. Our approach, based on quadratic linear programming, is scalable and achieves robustness to the measurement noise found in a typical network analytics deployment by filtering out certain constraints in the linear program. Finally, we implement an automated tool for estimating the flow splitting ratios and document its applicability on real data from the ISP.

Strategic safeguarding: A game theoretic approach for analyzing attacker-defender behavior in DNN backdoors

Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks.

Energy efficient resource management in data centers using imitation-based optimization

Cloud computing is the paradigm for delivering streaming content, office applications, software functions, computing power, storage, and more as services over the Internet. It offers elasticity and scalability to the service consumer and profit to the provider. The success of such a paradigm has resulted in a constant increase in the providers’ infrastructure, most notably data centers. Data centers are energy-intensive installations that require power for the operation of the hardware and networking devices and their cooling. To serve cloud computing needs, the data center organizes work as virtual machines placed on physical servers. The policy chosen for the placement of virtual machines over servers is critical for managing the data center resources, and the variability of workloads needs to be considered. Inefficient placement leads to resource waste, excessive power consumption, and increased communication costs. In the present work, we address the virtual machine placement problem and propose an Imitation-Based Optimization (IBO) method inspired by human imitation for dynamic placement. To understand the implications of the proposed approach, we present a comparative analysis with state-of-the-art methods. The results show that, with the proposed IBO, the energy consumption decreases at an average of 7%, 10%, 11%, 28%, 17%, and 35% compared to Hybrid meta-heuristic, Extended particle swarm optimization, particle swarm optimization, Genetic Algorithm, Integer Linear Programming, and Hybrid Best-Fit, respectively. With growing workloads, the proposed approach can achieve monthly cost savings of €201.4 euro and CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CO}_2$$\\end{document} Savings of 460.92 lbs CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CO}_2$$\\end{document}/month.

Exact methods for the Selective Assessment Routing Problem

AbstractThe Selective Assessment Routing Problem (SARP) is a problem in humanitarian logistics addressing the site selection and routing decisions of rapid needs assessment teams which aim to evaluate the post-disaster conditions of different community groups, each carrying a distinct characteristic. The aim is to construct an assessment plan that maximizes the covering of different characteristics in a balanced way. We explore exact approaches based on mixed integer linear programming. Different mathematical formulations are presented, and theoretical results regarding their strengths are derived. The models are experimentally evaluated on a set of test instances including a real-world scenario.

Optimizing Supply Chain Design under Demand Uncertainty with Quantity Discount Policy

In typical business situations, sellers usually offer discount schemes to buyers to increase overall profitability. This study aims to design a supply chain network under uncertainty of demand by integrating an all-unit quantity discount policy. The objective is to maximize the profit of the entire supply chain. The proposed model is formulated as a mixed integer nonlinear programming model, which is subsequently linearized into a mixed integer linear programming model and hence able to obtain a global solution. Numerical examples in the manufacturing supply chain where customer demand follows normal distributions are used to assess the effect of quantity discount policies. Key findings demonstrate that the integration of quantity discount policies significantly reduces total supply chain costs and improves inventory management under demand uncertainty, and decision makers need to decide a balance level between service levels and profits.

Comparative Analysis of Conventional (Financial, Network) and Optimized Mixed Integer Linear Programming Scenarios for Telecom Network Investment Decision Making

The telecommunications industry in Indonesia faces numerous challenges in allocating resources for network development, including network complexity, technological changes, market competition, and customer expectations. To achieve optimal financial outcomes and customer satisfaction, investments must be well-managed, well-placed, and well-executed. This study analyses network investment portfolio selection outcomes at Telkomsel; Indonesia's largest cellular operator, comparing conventional scenarios (financial and network) with an optimized scenario using Mixed Integer Linear Programming (MILP). The research evaluates these scenarios based on total portfolio score, incremental revenue, and Internal Rate of Return (IRR). Financial indicators such as net present value (NPV), IRR, EBIT margin, incremental revenue, and network indicators such as capacity and customer satisfaction (download/upload throughput, latency, packet loss, jitter) assess investment feasibility. The MILP optimization scenario strongly correlates with incremental revenue, NPV, and IRR, indicating higher financial performance. Sites selected in the MILP optimization outperscenario formed others in total score (22% better than the financial scenario, 63% better than the network scenario), incremental revenue (3.5% better than the financial scenario, 90.2% better than the network scenario), and portfolio IRR (4% better than the financial scenario, 70% better than the network scenario).

Event‐Triggered Secure Control of Positive Networked Control Systems Under Multi‐Channels Attacks

ABSTRACTThis paper focuses on the secure control of positive networked control systems under multi‐channel attacks characterized by a Bernoulli distribution. Specifically, the sensor‐to‐controller channel suffers from false data injection (FDI) attacks, whereas the controller‐to‐actuator channel suffers from denial of service (DoS) attacks. The objective is to design a static output feedback controller that guarantees the positivity and stochastic stability of the closed‐loop system in the presence of DoS and FDI attacks. To conserve communication resources, we employ an event‐triggered scheme to reduce the frequency of information transmission. Due to the positivity of the system, the proposed event‐triggering mechanism employs the 1‐norm form instead of the 2‐norm form, which allows that the controller parameter is determined via linear programming rather than LMI technique. Finally, two simulation examples are provided to verify the effectiveness of our methods.

A hybrid local search algorithm for the continuous energy-constrained scheduling problem

AbstractWe consider the continuous energy-constrained scheduling problem (CECSP). A set of jobs has to be processed on a continuous, shared resource. A schedule for a job consists of a start time, completion time, and a resource consumption profile. The goal is to find a schedule such that each job does not start before its release time, is completed before its deadline, satisfies its full resource requirement, and respects its lower and upper bounds on resource consumption during processing. The objective is to minimize the total weighted completion time. We present a hybrid local search approach, using simulated annealing and linear programming, and compare it to a mixed-integer linear programming (MILP) formulation. We show that the hybrid local search approach matches the MILP formulation in solution quality for small instances and is able to find a feasible solution for larger instances in reasonable time.

Comparative Study of R Programming and Lingo Software in Fully Fuzzy Linear Programming Problems

Authors: The paper begins with an introduction to the concept of fuzzy optimization, providing an in-depth explanation of its significance and applications. It then proceeds to define two distinct ranking functions that is Yager’s and vR – ranking functions within the context of fuzzy optimization along with the properties of vR- ranking function. Following this, a comprehensive overview of Lingo software and R programming is presented, delving into their respective features and capabilities. This paper further delves into a detailed comparison of Lingo and R programming, offering a thorough exploration of their strengths and limitations through the use of example problems. These examples illustrate the process of computing optimal solutions for fully fuzzy linear programming problems using both Lingo and R programming, providing a comprehensive and practical comparison of their effectiveness in this context.

Minimizing the earliness–tardiness for the customer order scheduling problem in a dedicated machine environment

AbstractThe customer order scheduling problem has garnered considerable attention in the recent scheduling literature. It is assumed that each of several customer orders consists of several jobs, and each customer order is completed only if each job of the order is completed. In this paper, we consider the customer order scheduling problem in a machine environment where each customer places exactly one job on each machine. The objective is to minimize the earliness–tardiness, where tardiness is defined as the time an order is finished past its due date, and earliness is the time a job is finished before its due date or the completion time of the corresponding order, whichever is later. Even though the earliness–tardiness criterion is an important objective for just-in-time production, this problem has not been studied in the context of the customer order scheduling problem. We provide a mixed-integer linear programming (MILP) formulation for this problem and derive multiple problem properties. Furthermore, we develop six different heuristics for this problem configuration. They follow the structure of the iterated greedy algorithm and additionally use a refinement function in which they differ. In a computational experiment, the algorithms were compared with each other and outperformed a solver solution of the MILP, which proves their ability to efficiently solve the problem configuration.

Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity

AbstractWe investigate a new family of distributionally robust optimization problem under marginal and copula ambiguity with applications to portfolio optimization problems. The proposed model considers the ambiguity set of portfolio returns in which the marginal distributions and their copula are close—in terms of the Wasserstein distance—to their nominal counterparts. We develop a cutting-surface method to solve the proposed problem, in which the distribution separation subproblem is nonconvex and includes bilinear terms. We propose three approaches to solve the bilinear formulation, namely (1) linear relaxation via McCormick inequalities, (2) exact mixed-integer linear program reformulation via disjunctive inequalities, and (3) inner approximation method via a novel iterative procedure that exploits the structural properties of the bilinear optimization problem. We further carry out a comprehensive set of computational experiments with distributionally robust portfolios featuring Conditional Value-at-Risk (CVaR) measures. These tests aim to compare the accuracy of the proposed algorithms, analyze the impact of the radius of the Wasserstein ambiguity ball on the portfolio, and assess portfolio performance. We use a rolling-horizon approach to conduct the out-of-sample tests, which show the superior performance of the portfolios under marginal and copula ambiguity over the equally weighted and ambiguity-free Mean-CVaR benchmark portfolios.

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 %.

Analytical railway line capacity methods from graph-theoretical and polyhedral perspectives

ABSTRACT This paper rigorously addresses the consumed capacity underestimation caused by division-based methods in graph theory and polyhedral geometry. Graph-theoretically, such underestimation occurs because subgraphs in shorter sections approximate their combined graph. Our polyhedral study suggests that the capacity analysis is computationally ‘easy’ because its linear programme in the complete section has an orthogonal projection on the Euclidean plane containing five proper faces, one being the objective-defined one-dimensional optimal facet. Geometrically, we conclude that the polyhedra of the linear programmes in shorter and complete sections have parallel facets, with the former nested within the latter. Consequently, the optimal values of the former cannot exceed those of the latter. With these theoretical insights, we derive a train operation labelling algorithm that takes proven linear time. Beyond enabling faster capacity computation, the findings deepen our understanding of the connection between infrastructure capacity utilisation and timetable structure, ultimately leading to more efficient railway optimisation.

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.

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 %.

Bad data identification method considering the on-load tap changer model

With the connection and integration of renewable energy, the on-load tap-changer (OLTC) has become an important device for regulating voltage in distribution networks. However, due to non-smooth and non-linear characteristics of OLTC, traditional bad data identification and state estimation methods for transmission network are limited when applied to the distribution network. Therefore, the nonlinearity and droop control constraints of the OLTC model are considered in this paper. At the same time, the quadratic penalty function is introduced to realize the fast normalization of the tap position. It proposes a two-stage bad data identification method based on mixed-integer linear programming. In the first stage, suspicious measurements are identified using projection statistics and maximum normalized residual methods for preprocessing the measurement data. In the second stage, a linearization approach utilizing hyhrid data-physical driven is applied to handle nonlinear constraints, leading to the development of a bad data identification model based on mixed-integer linear programming. Finally, the proposed methodology is validated using a modified IEEE-33 node test feeder example, demonstrating the accuracy and efficiency of bad data identification.

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.

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.

Decision-Making Model to Support Agricultural Policies in Realizing Economic and Social Sustainability

Abstract Background Achieving economic and social sustainability is the goal of any policy when defining measures. We focus on the beef sector, where many challenges have arisen due to its structural characteristics, such as an unfavourable scale structure, high costs, low efficiency, and a low environmental footprint. This paper presents an example of the support provided by a mathematical programming model in the development of a Common Agricultural Policy Strategic Plan for the period 2023-2027. Methods/approach It is a model based on linear programming that allows such an ex-ante analysis by calculating production plans at the farm level and aggregating the results at the sector level. Objectives When defining the interventions, the question arose as to what the reform of the Common Agricultural Policy will bring and to what extent the sector should be supported in meeting these challenges. These were the concerns of agricultural policy that we sought to support by modelling different scenarios. Results The results show that the situation of the sector will worsen, especially for larger farms, but they also show the great importance of production-related payments to mitigate the negative trend. Conclusions The applied approach proves to be suitable for supporting the design of agricultural policy and achieving greater economic and social sustainability in the sector.

On mitigating reactive jamming with dynamic resource allocation in optical IRS and UAV-assisted FSO-based networks

Free space optics (FSO) offers a promising opportunity to enhance next-generation network’s capacity with its unlicensed spectrum and wide bandwidth. However, jamming attacks, coupled with inherent anomalies in the FSO-based channel, threaten the performance of these networks. This is especially problematic for security-sensitive applications that demand a resilient communication infrastructure. To address this issue, optical intelligent reflecting surfaces (IRS) and unmanned aerial vehicles (UAVs) can provide promising solutions. This work introduces an efficient approach for mirror element assignment in UAV-assisted FSO-based networks, aimed at mitigating reactive jamming attacks while satisfying users’ quality-of-service (QoS) requirements. To ensure network reliability, we formulate an optimization problem that enhances overall network performance by simultaneously allocating resources such as mirror elements with awareness of jamming attacks. The formulated optimization problem is a binary linear programming problem, which is generally NP-hard. To address this, we introduce a batch-based sequential fixing linear programming procedure called the Reactive Jamming-Aware Mirror Element Allocation (RJA-MEA) scheme. This scheme optimally assigns mirror elements to satisfy the users’ rate demands. In this paper, the performance of the RJA-MEA scheme is compared with reference schemes such as Reactive Jamming Unaware-Mirror Element Allocation (RJU-MEA), Reactive Jamming-Aware Equal Mirror Element Allocation (RJA-EMEA), and Reactive Jamming Unaware-Equal Mirror Element Allocation (RJU-EMEA) schemes. The simulation results reveal that the proposed RJA-MEA scheme surpasses existing reference schemes, thereby significantly improving the overall network sumrate performance.