Linear Programming Solution Research Articles

Stochastic Roadside Unit Location Optimization for Information Propagation in the Internet of Vehicles

This study investigates the problem of roadside unit (RSU) location optimization for information propagation under stochastic traffic conditions. The goal of RSU location optimization is to promote multihop information propagation in the Internet of Vehicles which is the promising application of the Internet of Things in transportation. Considering the information propagation time is significantly affected by traffic density and traffic density is endowed with randomness, the problem is formulated as a two-stage mixed-integer nonlinear stochastic programming. The model aims to minimize the sum of the cost associated with RSU investment and the expectation of the penalty cost associated with the network information propagation time exceeding an acceptable threshold. In the first stage of the programming, the number and location of RSUs are determined when network-wide traffic density is not realized. In the second stage, given the RSU location schemes determined in the first stage and the realization of traffic density, the information propagation shortest paths are determined for all origin-destination pairs to minimize network information propagation time. A genetic algorithm (GA) integrated with the solution of a mixed-integer linear programming (GA-MILP) is proposed to solve the model. Numerical results indicate that the advantage of the proposed model in the reduced information propagation time per cost over the deterministic model can be up to 15.54%. Compared with the conventional GA, the GA-MILP has 10.01% higher computation efficiency. This further leads to a 14.73% lower objective value achieved by the GA-MILP when the number of iterations is 50.

Choquet integral‐based measures of economic welfare and species diversity

Measures of diversity, spread and inequality can be important indicators in domains as diverse as ecology, economics and health. One of the key characteristics of such indices is the Pigou–Dalton (P-D) principle, also known as the principle of progressive transfers, whereby proportional redistribution from larger to smaller arguments should increase (or decrease, depending on the context) the overall measure of social or economic welfare, diversity and so on. Previous studies have identified the ordered weighted averaging operators as being appropriate for welfare measurement, subject to conditions on the weighting vectors. We propose the Choquet integral, defined with respect to a capacity or fuzzy measure, as a candidate for defining nonsymmetric measures of welfare. This allows for importance and interaction to be modelled between inputs while still satisfying the P-D principle. We extend the buoyancy concept to fuzzy measures and characterise the resulting classes of buoyant and antibuoyant fuzzy measures. We then turn to the problem of optimisation of the Choquet integral subject to linear constraints, which in the case of antibuoyant fuzzy measures permits an efficient linear programming solution.

Association rule hiding using integer linear programming

<span>Privacy preserving data mining has become the focus of attention of government statistical agencies and database security research community who are concerned with preventing privacy disclosure during data mining. Repositories of large datasets include sensitive rules that need to be concealed from unauthorized access. Hence, association rule hiding emerged as one of the powerful techniques for hiding sensitive knowledge that exists in data before it is published. In this paper, we present a constraint-based optimization approach for hiding a set of sensitive association rules, using a well-structured integer linear program formulation. The proposed approach reduces the database sanitization problem to an instance of the integer linear programming problem. The solution of the integer linear program determines the transactions that need to be sanitized in order to conceal the sensitive rules while minimizing the impact of sanitization on the non-sensitive rules. We also present a heuristic sanitization algorithm that performs hiding by reducing the support or the confidence of the sensitive rules. The results of the experimental evaluation of the proposed approach on real-life datasets indicate the promising performance of the approach in terms of side effects on the original database.</span>

Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming

To study the reasons of the low academic performance of students in Spain, authorities must consider emotional dimensions, such as well-being, which directly affect their learning achievement. Furthermore, it would be interesting to compare Spanish students with students from Finland, which stand out in international rankings. We analyze how to promote students’ well-being in Spain as a mechanism to enhance their academic achievement. Using data from PISA 2018, four indicators are used to measure well-being according to variables describing the students’ context. By means of econometric techniques, interval multiobjective linear programming problems are formulated for Spain and Finland and solved through a new methodological scheme proposed in this paper, assuring the generation of possibly and necessarily efficient solutions in interval multiobjective linear programming. The purpose is to determine which aspects would allow the best possible well-being to be reached. We found several differences between the students achieving optimal compromise levels in each country, and we analyzed how the improvement of one indicator might affect the remaining aspects of well-being. Spanish students can further enhance their well-being compared to Finnish students. Furthermore, the lowest improvement rate is associated with the bullying index, especially in Finland, highlighting the need to promote anti-bullying measures.

CAN LINEAR PROGRAMMING ASSIST METAHEURISTICS IN FOREST PRODUCTION PLANNING PROBLEM?

The planning of forest production requires the adoption of mathematical models to optimize the utilization of available resources. Hence, studies involving the improvement of decision-making processes must be performed. Herein, we evaluate an alternative method for improving the performance of metaheuristics when they are applied for identifying solutions to problems in forest production planning. The inclusion of a solution obtained by rounding the optimal solution of linear programming to a relaxed problem is investigated. Such a solution is included in the initial population of the clonal selection algorithm, genetic algorithm, simulated annealing, and variable neighborhood search metaheuristics when it is used to generate harvest and planting plans in an area measuring 4,210 ha comprising 120 management units with ages varying between 1 and 6 years. The same algorithms are executed without including the solutions mentioned in the initial population. Results show that the performance of the clonal selection algorithm, genetic algorithm, and variable neighborhood search algorithms improved significantly. Positive effects on the performance of the simulated annealing metaheuristic are not indicated. Hence, it is concluded that rounding off the solution to a relaxed problem is a good alternative for generating an initial solution for metaheuristics.

Request Reliability Augmentation With Service Function Chain Requirements in Mobile Edge Computing

Provisioning reliable network services for mobile users in edge computing environments is the top priority of network service providers, as unreliable services will result in tremendous losses of revenues and customers. In this paper, we study a novel service reliability augmentation problem in a mobile edge computing (MEC) network, where mobile users request network services with service function chain (SFC) and reliability expectation requirements. To enhance the service reliability of user requests, it is a common practice to make use of redundant virtualized network function (VNF) instance placement in case the primary VNF instance fails. We aim to augment the service reliability of each admitted request to its specified reliability expectation, subject to computing capacity on each cloudlet. To this end, we first formulate a novel service reliability augmentation problem for each request with an SFC and a reliability expectation requirement, by augmenting its reliability through redundant VNF instance deployment. We then show that the problem is NP-hard, and provide an admission framework of user requests by placing primary VNF instances of network functions in the SFC to different cloudlets. We then deal with the service reliability augmentation problem of an admitted request under the assumption that all secondary VNF instances of each primary VNF instance must be placed into the cloudlets no more than <inline-formula><tex-math notation="LaTeX">$l$</tex-math></inline-formula> hops from the cloudlet of its primary VNF instance for a fixed <inline-formula><tex-math notation="LaTeX">$l$</tex-math></inline-formula> with <inline-formula><tex-math notation="LaTeX">$1\leq l \leq n-1$</tex-math></inline-formula> , where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of cloudlets in the network, for which we formulate an integer linear program solution, and develop a randomized algorithm with a good approximation ratio and high probability, at the expense of moderate resource constraint violations. We also devise a deterministic heuristic for the problem without any resource violation. We third study the service reliability augmentation problem for a set of admitted requests by extending the proposed algorithm for the service reliability augmentation problem for a single request admission. We finally evaluate the performance of the proposed algorithms through experimental simulations. Experimental results demonstrate that the proposed algorithms are promising, and their empirical results are superior to their analytical counterparts.

Security-Constrained Optimal Sizing and Siting of BESS in Hybrid AC/DC Microgrid Considering Post-Contingency Corrective Rescheduling

Hybrid AC/DC microgrids allow the integration of diverse renewable energy resources. However, the security and the reliability of hybrid AC/DC microgrid systems are challenged by various contingencies. In this paper, we propose a BESS sizing and siting approach which uses a combined stochastic programming and robust optimization method to cope with uncertainties of loads, wind power generation, and BESS charging/discharging efficiency. The proposed iterative solution enhances voltage and frequency regulation performances in an islanded hybrid AC/DC microgrid which is subject to post-contingency corrective rescheduling. A successive linear power flow approximation method is adopted to simulate post-fault power flows and represent static frequency characteristics of loads and generators. The proposed iterative solution for the mixed-integer linear programming (MILP) formulation can achieve computational tractability for determining pre-fault and post-fault initial operation points. Case studies corroborate the effectiveness of the proposed model and the solution method.

User preference–based QoS-aware service function placement in IoT-Edge cloud

In the Internet of Things-Edge cloud, service provision presents a challenge to operators to satisfy user service-level agreements while meeting service-specific quality-of-service requirements. This is because of inherent limitations in the Internet of Things-Edge in terms of resource infrastructure as well as the complexity of user requirements in terms of resource management in a heterogeneous environment like edge. An efficient solution to this problem is service orchestration and placement of service functions to meet user-specific requirements. This work aims to satisfy user quality of service through optimizing the user response time and cost by factoring in the workload variation on the edge infrastructure. We formulate the service function placement at the edge problem. We employ user service request patterns in terms of user preference and service selection probability to model service placement. Our framework proposal relies on mixed-integer linear programming and heuristic solutions. The main objective is to realize a reduced user response time at minimal overall cost while satisfying the user service requirements. For this, several parameters, and factors such as capacity, latency, workload, and cost constraints, are considered. The proposed solutions are evaluated based on different metrics and the obtained results show the gap between the heuristic user preference placement algorithm and the optimal solution to be minimal.

System Economic Costs of Antibiotic Use Elimination in the US Beef Supply Chain.

There is consumer pressure on the US beef cattle industry to minimize antibiotic use (ABU) in order to aid in the global antimicrobial resistance mitigation efforts. Our objective was to estimate the economic costs of ABU constraints in a conceptual US integrated beef supply chain (IBSC) to aid the beef industry in mitigating the ever-increasing risk of antimicrobial resistance, by reducing their ABU. An IBSC network model was developed and differentiated into 37 different nodes of production. Each node could only raise a specific type of animals, differentiated based on the production technique and animal health status. The cost, as well as the weight gain coefficient, was estimated for each node, using an IBSC cost of production model. Linear programming solutions to this network model provided the least cost path of beef supply through the system, under various ABU constraints. The cost as well as weight gain coefficient of the 37 nodes, initial supply of 28.5 million calves weighing 0.65 million metric tons, and final demand of 16.14 million metric tons of slaughter-ready fed cattle were used as inputs/constraints to the three different linear programming scenarios, with different ABU constraints. Our first scenario, which placed no constraint on ABU, estimated that the minimum total economic cost to meet the final beef demand was $38.6 billion. The optimal solution was to use only the high health status calves for beef production. Because low health calves occur in the beef system, our second scenario required all the calves irrespective of their health status to be used, which increased the system cost to $41.5 billion. Thus, the value of only producing high health status calves is $2.9 billion. Our third scenario, which restricted feedlots from using antibiotics even for low health calves, incurred a total cost of $41.9 billion for antibiotic-free beef production. We concluded that the additional cost of $367 million for implementing antibiotic-free beef production is relatively low, ~0.90% of the minimum cost incurred for the conventional beef supply chain (model 2 cost of $41.5 billion). However, a much higher cost savings is obtained by producing only high health status calves.

DEA Cross-Efficiency Aggregation with Deviation Degree Based on Standardized Euclidean Distance

Data envelopment analysis (DEA) has been extended to cross-efficiency to provide better discrimination and ranking of decision-making units (DMUs). Current researches about cross-efficiency mainly focus on the non-uniqueness of optimal solution of linear programming and information aggregation. As a common distance metric, standardized Euclidean distance is introduced to define the discrimination power between two vectors and the deviation degree for measuring the difference between the individual preference and group ideal preference. Based on above definitions, an alternative method is presented to compare multiple optimal solutions, and further, a universal weighted cross-efficiency model considering both dynamic adjustment of weights and preference formulation is constructed for evaluation and ranking. Two numerical examples are given to illustrate the effectiveness of the comparison method for multiple optimal solutions and weights determination method of DMUs, respectively. At last, a practical application aimed at evaluating environmental treatment efficiency in western area of China is given. Comparative analysis shows that our model could be more moderate, flexible, and general than some available models and methods, which can extend the theoretical research of cross-efficiency evaluation.

Measures of global sensitivity in linear programming: applications in banking sector

The paper examines the sensitivity for the solution of linear programming problems using Bayesian techniques, when samples for the coefficients of the objective function are uncertain. When data is available, we estimate the solution of the linear program and provide statistical measures of uncertainty through the posterior distributions of the solution in the light of the data. When data is not available, these techniques examine the sensitivity of the solution to random variation in the coefficients of the linear problem. The new techniques are based on two posteriors emerging from the inequalities of Karush–Kuhn–Tucker conditions. The first posterior is asymptotic and does not require data. The second posterior is finite-sample-based and is used whenever data is available or if random samples can be drawn from the joint distribution of coefficients. A by-product of our framework is a robust solution. We illustrate the new techniques in two empirical applications to the case of uncertain Data Envelopment Analysis efficiency, involving two large samples, of US commercial banks and a sample of European commercial banks regulated by the Single Supervisory Mechanism. We analyse whether some pre-determined criteria, associated with size and new supervisory framework, can adequately affect the solution of linear program. The results provide evidence of substantial improvements in statistical structure with respect to sensitivities and robustification. Our methodology can serve as a consistency check of the statistical inference for the solution of linear programming problems in efficiency under uncertainty in data.

Optimal control and learning for cyber‐physical systems

Optimal control and learning for <scp>cyber‐physical</scp> systems

A New Algorithm for Privacy-Preserving Horizontally Partitioned Linear Programs

In a linear programming for horizontally partitioned data, the equality constraint matrix is divided into groups of rows. Each group of the matrix rows and the corresponding right-hand side vector are owned by different entities, and these entities are reluctant to disclose their own groups of rows or right-hand side vectors. To calculate the optimal solution for the linear programming in this case, Mangasarian used a random matrix of full rank with probability 1, but an event with probability 1 is not a certain event, so a random matrix of full rank with probability 1 does not certainly happen. In this way, the solution of the original linear programming is not equal to the solution of the secure linear programming. We used an invertible random matrix for this shortcoming. The invertible random matrix converted the original linear programming problem to a secure linear program problem. This secure linear programming will not reveal any of the privately held data.

Avoiding redundant columns by adding classical Benders cuts to column generation subproblems

When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are not generated. We introduce a sufficient condition for strong redundancy that can be checked by solving a compact LP. Using a dual solution of this compact LP we generate classical Benders cuts for the subproblem so that the generation of strongly redundant columns can be avoided. The potential of these cuts to improve the dual bound of the column generation master problem is evaluated computationally using an implementation in the branch-price-and-cut solver GCG. While their efficacy is limited on classical problems, the benefit of applying the cuts is demonstrated on structured models to which a temporal decomposition can be applied.

Minimizing activity exposures in project scheduling under uncertainty

We propose a model to solve a project scheduling problem where resource assignments and activity schedules need to be determined to achieve a set of due-date requirements as well as possible. The concept of activity duration tolerance levels is introduced to describe the longest activity durations over which the due-dates are guaranteed to be achieved. Based on this, we propose a due-date achievement model using a proposed performance measure termed as the activities exposure level, which accounts for the total amount of durations exceeding tolerance levels for a given scheduling solution. We describe various properties and characteristics of the proposed scheduling optimization model and its practical implications. We show that the associated stochastic scheduling problem with resource constraints can be equivalently computed as the solution of a modest-sized mixed-integer linear program using the sample average approximation approach. Computational results show that our proposed models perform well when compared to different standard approaches across various performance measures.

Persistency of linear programming relaxations for the stable set problem

The Nemhauser–Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to some variables, there exists an optimal integer solution in which these variables retain the same values. While the standard LP is defined by only non-negativity and edge constraints, a variety of other LP formulations have been studied and one may wonder whether any of them has this property as well. We show that any other formulation that satisfies mild conditions cannot have the persistency property on all graphs, unless it is always equal to the stable set polytope.

Data-based polyhedron model for optimization of engineering structures involving uncertainties

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

Lifetime Optimization of Dense Wireless Sensor Networks Using Continuous Ring-Sector Model

Wireless sensor networks (WSNs) are becoming increasingly utilized in applications that require remote collection of data on environmental conditions. In particular dense WSNs are emerging as an important sensing platforms for the Internet of Things (IoT). WSNs are able to generate huge volumes of raw data, which require network structuring and efficient collaboration between nodes to ensure efficient transmission. In order to reduce the amount of data carried in the network, data aggregation is used in WSNs to define a policy of data fusion and compression. In this paper, we investigate a model for data aggregation in a dense {WSN} with a single sink. The model divides a circular coverage region centered at the sink into patches which are intersections of sectors of concentric rings, and data in each patch is aggregated at a single node before transmission. Nodes only communicate with other nodes in the same sector. Based on these assumptions, we formulate a linear programming problem to maximize system lifetime by minimizing the maximum proportionate energy consumption over all nodes. Under a wide variety of conditions, the optimal solution employs two transmissions mechanisms: direct transmission, in which nodes send information directly to the sink; and stepwise transmission, in which nodes transmit information to adjacent nodes. An exact formula is given for the proportionate energy consumption rate of the network. Asymptotic forms of this exact solution are also derived, and are verified to agree with the linear programming solution. We investigate three strategies for improving system lifetime: nonuniform energy and information density; iterated compression; and modifications of rings. We conclude that iterated compression has the biggest effect in increasing system lifetime.

A Team Allocation Decision for Aircraft Fleet Maintenance

This paper is about a computer application for planning maintenance of aircraft fleet in what regards allocation of skilled technicians. The formalization for this planning is a mathematical programming problem written as a minimizing one. The decision variables are the allocation of the skilled technicians. The data are the number of available technicians, the working hours needed to accomplish maintenance, the costs due to the daily operation of facilities, and due to the fleet downtime. Although, the formalization is of a non-linear integer-programming problem, a transformation of variables from positive integer ones to Boolean ones is conceivable and allows a reformulation as a pure integer linear programming problem. Also, a relaxation of the integer variables to continuous ones allows for a relaxed formulation as a convex non-linear programming problem. A case study of two fleets illustrates both formulations: solved by the pyomo library calling the GLPK for the pure linear integer programming problem and calling solvers in Scipy library for the relaxed formulation. An inference presented about the results of the case study addresses the issue of using nonlinear programming to emulate the solution of linear integer programming.

Dynamic Hierarchical Caching Resource Allocation for 5G-ICN Slice

Network slicing and Multiple-Access Edge Computing (MEC) are key technologies in fifth-generation (5G) networks. The flexible programmability of network slicing and the decentralization of MEC facilitate the deployment of Information-Centric Networking (ICN). The caching feature of ICN can provide users with low-latency data services. Although many existing works have addressed the cache deployment problem or the cache optimization problem, most of them do not consider the issue of caching resource allocation in the dynamic and hierarchical environment. Dynamic deployment of cache nodes can improve the operator’s revenue as much as possible while accurately allocating the caching resources can reduce the user-requested latency. Therefore, in this study, a problem of the operator’s expected revenue maximization is presented in an environment combining dynamic deployment of the MECs and the caching-enabled node ICN-Gateway (ICN-GW). To solve this problem, we propose an optimal stopping theory (OST)-based dynamic hierarchical caching resources allocation (ODH-CRA) algorithm. The algorithm consists of three parts. Firstly, an Integer Linear Programming (ILP) solution is proposed to determine the optimal deployment of the MECs. This method determines the optimal location and number of the MECs by considering deployment costs and service requirement costs synthetically. Secondly, a redeployment technique based on the OST is proposed to determine the best redeployment time of the MECs according to the values of latency violations and the service latency requirements. Finally, an improved elite genetic algorithm (IEGA) is proposed to find the optimal solution of the hierarchical caching resource allocation. This method searches the optimal scheme by maximizing the operator’s revenue joint caching costs and energy consumption. Ultimately, we perform a series of simulation experiments to compare the proposed method’s performance to dynamic and hierarchical methods. Our solution can effectively reduce the latency for users’ requesting, improve the revenue of ICN Communication Service Provider (ICSP), and provide an effective caching resource allocation scheme for the next generation of Internet of Things (IoT) networks.