Binary Linear Programming Research Articles

A note on the exact solution of the minimum squared load assignment problem

The problem of finding a fair assignment of tasks to agents that minimizes the total sum of squared workloads was introduced by Karsu and Azizoglu (2019) as the Minimum Squared Load Assignment Problem (MSLAP). To solve this problem, the authors developed a tailored branch-and-bound algorithm. While this algorithm was shown to produce better results than CPLEX on a mixed binary linear programming formulation of the MSLAP, about 71% of the 1200 benchmark instances yet remained unsolved. In this note, we test two state-of-the-art solvers on different mathematical programming formulations of the MSLAP. Our computational results show that the performance of the solvers is heavily dependent on the type of mathematical optimization model. The best results are obtained when the MSLAP is expressed as a quadratically-constrained program. Such a formulation allows one of the solvers to find and verify an optimal solution for every problem in the existing benchmark data sets within just a few seconds per problem, on average. Additional experiments on large-sized instances demonstrate that the solvers’ performances remain at a high level.

Placement of SDN controllers based on network setup cost and latency of control packets

Software-defined networking (SDN) was developed to simplify the management of computer networks. In the SDN architecture, the control layer is completely decoupled from the data layer. Moreover, network software configuration is also possible. To setup an SDN, you need a device called controller, which is not available in traditional networks. In the control layer, there are several controllers that control the data layer switches. The type, number and place of these controllers directly affect the cost and average latency of control packets. Since achieving the lowest setup cost and the minimum latency of the control packets (between switches and controllers, and among controllers) is of great importance at the same time, in this paper, a binary linear programming model is proposed to achieve the trade-off between them in wide area networks(WAN). The model determines the type, place and minimum number of required controllers by receiving the place of the switches, the amount of processing capacity of the controllers and the setup cost of each controller. Accordingly, it reduces the setup cost, average latency between switches and controllers as well as average latency among controllers in comparison with previous methods. The results of the study show that the model has the lowest setup cost and the minimum average latency of control packets (switch-to-controller and controller-to-controller) in controllers placement compared to the previous methods.

An optimization approach to financial and operational viabilities of spare aircraft

PurposeThe airlines cancel their flights frequently because of factors that they do not have any control over. Spare aircraft can potentially address some of the issues caused by cancelled flights. This paper aims to offer an exploratory study into the financial and operational viabilities of spare aircraft for airlines.Design/methodology/approachMathematical models are proposed to evaluate the financial and operational metrics under different scenarios. The models are applied to Delta, Spirit and Southwest Airlines with different business models. All data are extracted from US Bureau of Transport Statistics, Cirium Diio Mi and CAPA databases. The IBM Cplex solver was used to execute the binary linear program models.FindingsThe research revealed that factors such as airline network size, hub and spoke structure and average weekly flight cancellations are crucial in establishing the need for spare aircraft. For the number of weekly cancellations, there exist break-even values that reasonably justify spare aircraft.Practical implicationsModels can be customized and applied to other modes of transportations.Originality/valueThis study is the first to consider the use of spare aircraft in airlines from both financial and operational perspectives within the scope of the mathematical model. The analyses identify financial break-even points for a number of spare aircraft and their home base locations for three airlines. Operational utilization of spare aircraft is studied and contrasted with financial metrics.

Improving Quantum Computation by Optimized Qubit Routing

In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms formulated in the circuit model of computation onto specific quantum hardware. Our approach decomposes the routing problem into an allocation subproblem and a set of token swapping problems. This allows us to tackle the allocation part and the token swapping part separately. Extracting the allocation part from the qubit routing model of Nannicini et al. (Optimal qubit assignment and routing via integer programming, 2021, http://arxiv.org/abs/2106.06446), we formulate the allocation subproblem as a binary linear program. Herein, we employ a cost function that is a lower bound on the overall routing problem objective. We strengthen the linear relaxation by novel valid inequalities. For the token swapping part we develop an exact branch-and-bound algorithm. In this context, we improve upon known lower bounds on the token swapping problem. Furthermore, we enhance an existing approximation algorithm which runs much faster than the exact approach and typically is able to determine solutions close to the optimum. We present numerical results for the fully integrated allocation and token swapping problem. Obtained solutions may not be globally optimal due to the decomposition and the usage of an approximation algorithm. However, the solutions are obtained fast and are typically close to optimal. In addition, there is a significant reduction in the number of artificial gates and output circuit depth when compared to various state-of-the-art heuristics. Reducing these figures is crucial for minimizing noise when running quantum algorithms on near-term hardware. As a consequence, using the novel decomposition approach leads to compiled algorithms with improved quality. Indeed, when compiled with the novel routing procedure and executed on real hardware, our experimental results for quantum approximate optimization algorithms show an significant increase in solution quality in comparison to standard routing methods.

From Topology Optimization to 3-D Printing of an Electromagnetic Core

This paper presents a bridge between topology optimization and additive manufacturing. On the one hand, it presents an algorithm that considers the design variables as binary and then solves the problem by binary linear programming to optimize a ferromagnetic core. On the other hand, a 3D printing process is developed to manufacture the shapes obtained by topology optimization. Finally, these magnetic parts are characterized through electrical measurements.

Design model of an IEEE 802.11ad infrastructure for TSN-based industrial applications

This paper addresses two main aspects related to the application of the IEEE 802.11ad technology in an industrial environment, i.e., to guarantee a low latency and reliable data delivery while reducing the number of the deployed Access Points (APs). First, we discuss the parameter settings of the IEEE802.11ad MAC which guarantee a low delay by exploiting the synchronous service periods (SPs) mechanism. Then, we propose a binary linear programming model to enhance the reliability of the system under the Frame Replication and Elimination for Reliability (FRER). The model minimizes the number of deployed APs by taking into account the constraints on the available synchronous SPs. We also propose two heuristics, based on the described mathematical model, in order to efficiently solve the design problem, then compare the computational performance of the proposed approaches. The reported computational results highlight the complementary features of the compared methods and provide useful guidelines about the usage of the proposed approaches.

A novel grey multi-objective binary linear programming model for risk assessment in supply chain management

Robust and resilient agri-food supply chain management (AFSCM) is paramount to agribusinesses, given the many challenges and risks that this increased demand will bring in the coming decades. Interruptions caused by various risks to this crucial supply chain network, particularly in emerging economies, can put the lives of millions in danger, not to mention creating devastating impacts on the economy and the environment. Even so, there are only a limited number of quantitative risk management studies in the AFSCM literature. In this study, an integrated modified risk mitigation matrix (M-RMM) is developed to analyze the mitigation strategies for dealing with various risks in the context of the agri-food supply chain. The M-RMM is integrated with the grey multi-objective binary linear programming (GMOBLP) model to obtain the optimal risk mitigation strategies related to the three objective functions of risk, cost, and time minimization. The proposed model is a useful tool for formulating sustainable business policies and reducing food waste, and acquiring a context-specific (i.e., a developing economy), sector-specific (i.e., the agri-food processing sector), and multi-product (i.e., fresh and non-perishable) approach. The findings reveal that continuous training and development and vulnerability analysis of IT systems are the most effective risk mitigation strategies to lessen the impacts of lack of skilled personnel, sub-standard leadership, failure in IT systems, insufficient capacity to produce quality products, and poor customer relationships. The findings assist practitioners in managing risks in supply chains.

Model Abstraction for Discrete-Event Systems Using a SAT Solver

Model abstraction for finite state automata is beneficial to reduce the complexity of discrete-event systems (DES), enhances the readability and facilitates the control synthesis and verification of DES. Supremal quasi-congruence computation is an effective way for reducing the state space of DES. Effective algorithms on the supremal quasi-congruence relation have been developed based on the graph theory. This paper proposes a new approach to translate the supremal quasi-congruence computation into a satisfiability (SAT) problem that determines whether there exists an assignment for Boolean variables in the state-to-coset allocation matrix. If the result is satisfied, then the supremal quasi-congruence relation exists and the minimum equivalence classes is obtained. Otherwise, it indicates that there is no such supremal quasi-congruence relation, and a new set of observable events needs to be modified or reselected for the original system model. The satisfiability problem on the computation of supremal quasi-congruence relation is solved by different methods, which are respectively implemented by mixed integer linear programming (MILP) in MATLAB, binary linear programming (BLP) in CPLEX, and a SAT-based solver (Z3Py). Compared with the MILP and BLP methods, the SAT method is more efficient and stable. The computation time of model abstraction for large-scale systems by Z3Py solver is significantly reduced.

The benefit of complete trip information in free-floating carsharing systems

Free-floating and instant-access carsharing systems are two features of the most flexible carsharing systems. In the former, users are allowed to freely park the car in any legal parking spot within the boundaries defined by the service operator. In the latter, users are not requested to make any reservation in advance before picking up the car. This paper aims at evaluating the importance of complete trip information in free-floating instant-access carsharing systems. To this aim, we consider a system, referred to as the look-ahead system, where users can reserve a car in advance and are also allowed to directly pick up a car without any reservation. In both cases, the user is requested to specify complete trip details, including the estimated usage duration and the location where the car will be returned. Taking advantage of a complete knowledge of the trip details, the service operator can assign a reservation request to a car that is in use at the time of reservation, provided it will become available at the time and location the user will need it. In its nature, the operational setting we consider is dynamic, as trip information is revealed to the service operator at the time the user requests a car. We also investigate the possibility of suggesting to the user that makes a reservation a pickup location different from the desired one, provided it is not too distant from the latter. We compare the performance of the look-ahead system with the case no information is anticipated, which resembles the service provided by the main carsharing operators currently active in Milan (Italy). Additionally, we use, as a benchmark, the static case where all the information about the users requests (pickup and return locations, as well as delivery time) is known before the start of the planning horizon. We consider a system with no car relocations performed by ad-hoc operators. This enables us to measure the pure benefit of anticipated information, i.e., the benefit coming only from knowing in advance where and when the vehicles will be returned, purged from potential vehicles availability related to relocation operations. The matching between user requests and cars is obtained, for the look-ahead system, iteratively at fixed time intervals through the solution of a Binary Linear Program (BLP) and, for the benchmark case, through the solution of a single BLP. No optimization model is needed for the case where no information is anticipated. A simulation study, based on real-world data from the city of Milan, shows that the look-ahead system can satisfy a number of requests much greater than the case without anticipated information and close to the benchmark case. Moreover, we perform a sensitivity analysis on different parameters, including the maximum distance a user is available to walk and the minimum amount of anticipation requested to users for booking requests, showing their impact on the performance of the systems.

A robust model for emergency supplies prepositioning and transportation considering road disruptions

Proper prepositioning of emergency supplies can dramatically improve the efficiency of emergency response work. However, the uncertainties of emergency demands and road conditions bring difficulties to the prepositioning of emergency supplies. This paper proposes a two-stage robust model to locate emergency supply points and preposition the corresponding storage amount of emergency supplies, in which we presented two budget sets to describe the uncertainties of demands and road conditions, respectively. The innovative use of variables in the model to limit road capacities addresses the representation of different road interruption scenarios. We proposed an algorithm based on Benders decomposition by transforming the second-stage model into a binary linear programming model. Computational experiments based on the Sioux Falls network demonstrate the validity of the model and algorithm. We conducted sensitivity analyses for some important parameters in the model, such as two uncertainty control parameters, unit transportation cost, budget for the construction of emergency supply points, etc. We find that the uncertainty of road disruptions has a greater impact on the model than the uncertainty of demands. In addition, when the control parameter of the road disruptions exceeds a certain threshold, its influence on the model remains essentially constant.

A systemic model predictive control based on adaptive power pinch analysis for load shifting and shedding in an isolated hybrid energy storage system

This paper presents a novel systemic algorithm based on conservative power pinch analysis principles using a computationally efficient insight-based binary linear programming optimization technique in a model predictive framework for integrated load shifting and shedding in an isolated hybrid energy storage system. In a receding 24-hour predictive horizon, the energy demand and supply are integrated via an adaptive power grand composite curve tool to form a diagonal matrix of predicted hourly minimum and maximum energy constraints. The intgrated energy constraints must be satisfied recursively by the binary optimisation to ensure the energy storage’s state of charge only operates within 30% and 90%. Hence, the control command to shift or shed load is contingent on the energy storage state of the charge violating the operating constraints. The controllable load demand is shifted and/or shed to prevent any violations while ensuring energy supply to the most critical load without sacrificing the consumers' comfort. The proposed approach enhances efficient energy use from renewable energy supply as well as limits the use of the Hydrogen resources by a fuel cell to satisfy controllable load demands which can be shifted to periods in the day with excess renewable energy supply.

Robust binary linear programming under implementation uncertainty

This article studies binary linear programming problems in the presence of uncertainties that may prevent implementing the computed solution. This type of uncertainty, called implementation uncertainty, is modelled affecting the decision variables rather than model parameters. The binary nature of the decision variables invalidates using existing robust models for implementation uncertainty. The robust solutions obtained are optimal for a worst-case min–max objective. Structural properties allow the reformulation of the problem as a binary linear program. Constraint relaxation and cardinality-constrained parameters control the degree of solution conservatism. An optimization problem permits the selection of solutions from the obtained set of robust solutions. Results from a case study in the context of the knapsack problem suggest the methodology yields solutions that perform well in terms of objective value and feasibility. Furthermore, the selection approach can identify robust solutions with desirable implementation characteristics.

Innovative Optimization Model for Planning Upgrade and Maintenance Interventions for Buildings

Building operation and maintenance costs are reported to be the longest and most costly phase of a building’s life cycle, where it exceeds costs of design and construction. Although buildings are regularly maintained, water- and energy-saving investments are not often analyzed. This paper presents the development of a novel model for optimizing the selection of upgrade and maintenance interventions for existing buildings to minimize their equivalent annual operation and maintenance cost (EAOMC) while complying with specified annual budgets and building operational performance. The optimization model is developed in three main phases that focus on (1) identifying model decision variables and formulating objective function and constraints; (2) implementing the model computations using binary linear programming; and (3) analyzing the performance of the optimization model using a case study. The primary contributions this research adds to the body of knowledge are (1) a new computationally efficient model for identifying optimal selection of building upgrade and maintenance interventions to minimize EAOMC; (2) modeling reactive, preventive, and predictive maintenance strategies based on component types; (3) integrating a simulation-based upgrade and maintenance approach to evaluate energy and water consumption of buildings; and (4) integrating maintenance and upgrade interventions to maximize economic benefits from building operation by reducing operational and maintenance costs. The results of the case study illustrated the new capabilities of the model in identifying optimal upgrade and maintenance interventions for various operational budgets with up to 32% reduction in EAOMC.

Mixed-Cell-Height Placement With Complex Minimum-Implant-Area Constraints

Mixed-cell-height standard cells are prevailingly used in advanced technologies to achieve better design tradeoffs among timing, power, and routability. As feature size decreases, the placement of cells with multiple threshold voltages may violate the complex minimum-implant-area (MIA) layer rule arising from the limitations of patterning technologies. Existing works consider the mixed-cell-height placement problem only during legalization or handle the MIA constraints during detailed placement. In this article, we address the mixed-cell-height placement problem with MIA constraints in two major stages: 1) post-global placement (Post-GP) and 2) MIA-aware legalization. In the Post-GP stage, we first present a continuous and differentiable cost function to address the Vdd/Vss alignment constraints and add weighted pseudonets to MIA-violation cells dynamically. Then, we propose a proximal optimization method based on the given global placement result to simultaneously consider Vdd/Vss alignment constraints, MIA constraints, cell distribution, cell displacement, and total wirelength. In the MIA-aware legalization stage, we develop a graph-based method to cluster cells of specific threshold voltages and apply a strip-packing-based binary linear programming to reshape cells. Then, we propose a matching-based technique to resolve intrarow MIA violations and reduce filler insertion. Furthermore, we formulate inter-row MIA-aware legalization as a quadratic programming problem, which is efficiently solved by a modulus-based matrix splitting iteration method. Finally, MIA-aware cell allocation and refinement are performed to further improve the result. Experimental results show that without any extra area overhead, our algorithm still can achieve 5.4% shorter final total wirelength than the state-of-the-art work.

Parallel assembly lines worker assignment and balancing problem: A mathematical model and an artificial bee colony algorithm

In today’s competitive world, assembly lines are one of the most important industrial manufacturing systems, which can accommodate the massive increase in customer demands and product range, for the production industry. One possible way to increase the capacity and efficiency of assembly lines is to design a parallel assembly line system, consisting of two or more assembly lines placed next to each other. In the literature, the assembly lines are usually balanced according to tasks with fixed processing times without considering worker–task compatibility. In real-life applications, however, since the processing time of each task may vary according to the capability of each worker, the assignment of tasks to stations in the assembly line depends on the skills of the worker assigned to the related station. Considering the worker and task assignments together for each assembly line will provide a more realistic perspective. This paper, to the best of our knowledge, is the first study that considers the minimization of joint cycle time for the worker assignment and assembly line balancing problem in parallel assembly lines (PALWABP-II). Accordingly, a binary linear mathematical programming (BLP) model is developed and an artificial bee colony (ABC)-based solution approach is proposed for medium and large-sized problems. A new set of test problems is presented to the literature for a computational experiment. In addition, a summary of the literature is presented. An example problem is solved using the BLP model. In order to evaluate the effectiveness of the proposed model and approach, they are compared with the classical particle swarm optimization (PSO) algorithm and ten different priority rules. The computational results on test problems prove the effectiveness of the proposed ABC algorithm for the PALWABP-II.

Selecting Bus Stops for Accessibility Improvements for Riders with Physical Disabilities

Bus stops are key links in the journeys of riders with disabilities. Inaccessible bus stops prevent people with physical disabilities from using fixed-route bus services, thus limiting their mobility. Due to limited budgets, transit agencies must select bus stops for which their improvements, as part of the effort to comply with the Americas with Disabilities Act (ADA), can maximize the overall benefits to riders with physical disabilities. In this paper, an analytic hierarchy process (AHP) was applied to combine the factors affecting the benefits to riders with physical disabilities, and a binary linear programming model was used to identify bus stops for ADA improvements based on budgetary and construction cost constraints. As an application example, the optimization model was applied to the 5,034 bus stops in Broward County, Florida. Compared to the usual approaches, the optimization model provides a more objective platform on which to identify bus stops for ADA improvements.

Evaluating the Security and Economic Effects of Moving Target Defense Techniques on the Cloud

Moving Target Defense (MTD) is a proactive security mechanism that changes the attack surface with the aim of confusing attackers. Cloud computing leverages MTD techniques to enhance the cloud security posture against cyber threats. While many MTD techniques have been applied to cloud computing, there has so far been no joint evaluation of the effectiveness of MTD techniques with respect to security and economic metrics. In this paper, we first introduce mathematical definitions for the combination of three MTD techniques: Shuffle, Diversity, and Redundancy. Then, we utilize four security metrics – namely, system risk, attack cost, return on attack, and reliability – to assess the effectiveness of the combined MTD techniques applied to large-scale cloud models. Second, we focus on a specific context based on a cloud model for e-health applications to evaluate the effectiveness of the MTD techniques using security and economic metrics. We introduce (1) a strategy to effectively deploy the Shuffle MTD technique using a virtual machine placement technique, and (2) two strategies to deploy the Diversity MTD technique through operating system diversification. As deploying the Diversity technique incurs costs, we formulate the optimal diversity assignment problem (O-DAP), and solve it as a binary linear programming model to obtain the assignment that maximizes the expected net benefit.

The carbon footprint of Italian schools meals: An optimal choice of dishes in vegan, vegetarian, and omnivorous menus.

This study aims to assess the carbon footprint associated with vegan, vegetarian, and omnivorous menus for primary school lunches in Italy. For this purpose, healthy and acceptable menus with minimal greenhouse gas emissions have been designed by a binary linear programming model. The results show that the adoption of a specific diet may help in reducing the carbon footprint of menus, but it is the optimal selection of dishes that ultimately makes the difference. Interestingly enough, the optimal choice of dishes and the restriction of meat consumption in omnivorous menus can lead up to a 40% emission reduction compared to the current school lunch menu of the municipality of Rome. Moreover, the optimal choice of dishes in vegan menus provides the menu with the lowest carbon footprint among all kinds of diets.

Simple and fast algorithm for binary integer and online linear programming

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and is free of matrix inversion. It can be viewed as both an approximate algorithm for solving binary integer LPs and a fast algorithm for solving online LP problems. The algorithm is inspired by an equivalent form of the dual problem of the relaxed LP and it essentially performs (one-pass) projected stochastic subgradient descent in the dual space. We analyze the algorithm in two different models, stochastic input and random permutation, with minimal technical assumptions on the input data. The algorithm achieves \(O\left( m \sqrt{n}\right) \) expected regret under the stochastic input model and \(O\left( (m+\log n)\sqrt{n}\right) \) expected regret under the random permutation model, and it achieves \(O(m \sqrt{n})\) expected constraint violation under both models, where n is the number of decision variables and m is the number of constraints. The algorithm enjoys the same performance guarantee when generalized to a multi-dimensional LP setting which covers a wider range of applications. In addition, we employ the notion of the permutational Rademacher complexity and derive regret bounds for two earlier online LP algorithms for comparison. Both algorithms improve the regret bound by a factor of \(\sqrt{m}\) by paying more computational cost. Furthermore, we demonstrate how to convert the possibly infeasible solution to a feasible one through a randomized procedure. Numerical experiments illustrate the general applicability and effectiveness of the algorithms.

Robust competitive facility location model with uncertain demand types.

In competitive settings, firms locate their facilities according to customers’ behavior to maximize their market share. A common behavior is consuming from different motivations: one is for convenient demand, and the other is for quality demand. In this behavioral pattern, consumers patronize facilities within convenience for some demands, and patronize high quality facilities beyond convenience range for other demands. This behavior has never been included in competitive facility location problems. Given several other companies’ facilities in the market offering similar products or services, we study how a new entrant company can locate facilities based on this customer behavior to maximize its market share. A two-level robust model for the new entrant company is proposed to locate its facilities by taking into account the uncertainty of the types of customers’ demands. For medium size problems, we propose an equivalent mixed binary linear programming to obtain exact solutions. For large size problems, an exact algorithm (GCKP-A) for solving the inner-level model is given first by exploring the optimal solution. Then a heuristic algorithm is proposed by imbedding (GCKP-A) and 2-opt strategy into the framework of the improved ranking-based algorithm. The performance of the proposed heuristic algorithm is checked for different size problems. The sensitivity analysis of a quasi-real example shows that: (1) in most cases, the uncertainty between two types of demands does not affect the location scheme; (2) the convenience range, the quality range and the quality threshold play an important role in the market share of the new entrant company.