Binary Integer Programming Research Articles

A Novel Framework for Road Side Unit Location Optimization for Origin-Destination Demand Estimation

This study deals with the problem of road side unit (RSU) location optimization for origin-destination (OD) demand estimation. With the point-to-point measurement provided by RSUs in connected vehicle environment, the errors of OD demand estimation come from two sources: 1) the lack of enough path flow information; and 2) the vehicle-to-RSU (V2R) communication delay. However, increasing the amount of path flow information collected by RSUs results in the increase of V2R communication delay encountered by each collected data packet. Moreover, it is difficult to find a global optimal solution by formulating the problem as a single objective program. To address the investigated problem, this study proposes a novel framework consisting of solving a bi-objective RSU location optimization problem and an OD demand estimation problem. This RSU location optimization problem is formulated as a bi-objective nonlinear binary integer program to balance the maximization of the amount of path flow information and the minimization of V2R communication delay. The OD demand estimation problem is formulated as a least square estimator to identify the RSU location scheme with the smallest OD demand estimation error, among the Pareto optimal solutions to the bi-objective program. An efficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method is developed to generate the Pareto optimal solutions. The numerical example demonstrates that the proposed framework achieves 6.95 lower root-mean-square error of OD demand estimation, compared with the baseline framework.

Fix-and-optimize metaheuristics for minmax regret binary integer programming problems under interval uncertainty

The Binary Integer Programming problem (BIP) is a mathematical optimization problem, with linear objective function and constraints, on which the domain of all variables is {0, 1}. In BIP, every variable is associated with a determined cost coefficient. The Minmax regret Binary Integer Programming problem under interval uncertainty (M-BIP) is a generalization of BIP in which the cost coefficient associated to the variables is not known in advance, but are assumed to be bounded by an interval. The objective of M-BIP is to find a solution that possesses the minimum maximum regret among all possible solutions for the problem. In this paper, we show that the decision version of M-BIP is Σp2-complete. Furthermore, we tackle M-BIP by both exact and heuristic algorithms. We extend three exact algorithms from the literature to M-BIP and propose two fix-and-optimize heuristic algorithms. Computational experiments, performed on the Minmax regret Weighted Set Covering problem under Interval Uncertainties (M-WSCP) as a test case, indicates that one of the exact algorithms outperforms the others. Furthermore, it shows that the proposed fix-and-optimize heuristics, that can be easily employed to solve any minmax regret optimization problem under interval uncertainty, are competitive with ad-hoc algorithms for the M-WSCP.

Point cloud-based optimization of roadside LiDAR placement at constructed highways

Current approaches for optimizing the placement of roadside LiDAR (RSL) at constructed highways work on handcrafted scenes which fail to precisely map real-world situations. This study proposes a computer-aided framework to address the issue. First, high-accuracy point cloud data are introduced to model the as-built highway infrastructures, based on which an unsupervised clustering approach is applied to segment the target monitoring area (TMA). Then, candidate RSL locations are generated in a semi-automated manner combining manual delineation and spline resampling. Next, new deterministic and a U-net-based LiDAR models are separately developed to virtually estimate candidate RSL's joint coverage. Finally, based on the proposed sensor models, a detection matrix is created to facilitate the application of binary integer programming that minimizes the number of RSL while ensuring complete coverage of TMA. The tests on point cloud data of the three different sites demonstrate the effectiveness of the proposed workflow.

An OCPP-Based Approach for Electric Vehicle Charging Management

This paper proposes a smart system for managing the operations of grid-connected charging stations for electric vehicles (EV) that use photovoltaic (PV) sources. This system consists of a mobile application for EV drivers to make charging reservations, an algorithm to optimize the charging schedule, and a remote execution module of charging operations based on the open charge point protocol (OCPP). The optimal charging schedule was obtained by solving a binary integer programming problem. The merits of our solution are illustrated by simulating different charging demand scenarios.

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.

A method to find the optimum routes and stations for bus rapid transit in urban areas

Public transportation (PT) is an essential system for cities to achieve sustainability. However, determination of proper locations for PT stations and finding suitable routes are critical decisions. The aim of the present study is to propose a novel method to determine bus rapid transit (BRT) stations and routes in cities, using a fuzzy inference system (FIS) and binary integer programming (BIP). In the proposed method, first, a set of potential locations for BRT stations is selected based on engineering judgement. Then, by considering several variables and with the help of FIS, a weight is calculated for each location. Subsequently, the optimum corridors for BRT are identified with BIP. The objective function of the BIP model is to maximise the sum of the stations’ weights (involving the most suitable locations for BRT stations), while ensuring that the maximum number of passengers can travel each route. Constraints related to technical, social and economic considerations are also taken into account. To control the model efficiency, the outputs are compared with the stations and corridor suggested by experts. Based on the results, the most important features of the developed model are its simplicity, its ability to consider various factors, a short running time and its high level of accuracy.

Bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance with a dynamic speed-scaling technique

Nowadays, industries contribute to a substantial consumption of energy. This consumption leads to significant greenhouse gas emissions, energy dependence and ever-increasing costs for manufacturers. Controlling consumption and improving energy efficiency in industry are therefore major challenges in terms of environmental issues. In this context, this article examines an energy-efficient bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance activities problem to minimize both makespan and total energy consumption. The parallel machines are speed-scaling. To solve the problem, we propose a bi-objective mixed integer linear programming (MILP) model. Since the problem involves assigning jobs to machines and selecting an appropriate processing speed level for each job, we characterize each individual by two vectors: a job-machine assignment vector and a speed vector. To the best of our knowledge, no papers considering both production scheduling and Preventive Maintenance periods with minimizing the bi-objective makespan and the total of energy consumption. The gap between theory and practice prevents the satisfying performance of the schedules in industry. The purpose of this paper is to establish a joint model for integrating the production and PM scheduling to optimize the bi-objective of the total of energy consumption (TEC) and makespan (Cmax) simultaneously; and to make the theory applied in practice more efficaciously. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of Branch and Bound integrated on the CPLEX solver plus analyses using MATLAB software. A study of the results proved the performance of the model developed.

Discrete Optimization Model in Constructing Optimal Decision Tree

Decision trees have been well studied and widely used in knowledge discovery and decision support systems. One of the applications of binary integer programming to form decision trees or decision making is the knapsack problem. The knapsack problem is an integer programming problem that involves only one constraint. The knapsack problem is generally illustrated with a bag and an item. The problem to be solved is to maximize the price of goods with a certain capacity that can be loaded by a bag with a certain capacity too. In solving the knapsack problem, it can generally be done directly. In this paper we are interested to show how the implicit enumeration method solves the knapsack problem to form an optimal decision tree

Decision Model for Unplanned ICU Transfer in a Hospital with Association Rule Learning

The initial decision after treatment in the hospital emergency room is very important because apart from being an indicator of the quality of care for emergency room practitioners, it is also needed to achieve health goals, namely improving the quality of critical care and preventing death. The initial decision was also for an unplanned ICU transfer. Unplanned ICU transfer is the transfer of patients who originally came from the ER (Emergency Room), then to the Inpatient Room (having been treated for 24-48 hours), then to the ICU. Many studies have been carried out to predict the initial decision of unplanned ICU transfer using univariate analysis, logistic regression analysis, and association rules. The association rule algorithm generates rules between patient diagnosis features that form a decision model for unplanned ICU transfers, so it is essential to get an association rule algorithm that is more efficient in generating rules. In this study, we compare two association rule algorithms to get a more efficient algorithm; then, the rules are used to form a decision model for unplanned ICU transfers. The study results obtained that the Apriori algorithm requires a completion time of 3 ms and the FP-Growth algorithm requires a completion time of 31 ms. Hence, the FP-Growth algorithm is 28 ms more efficient than the Apriori algorithm, while the resulting rule generation is the same number of 67 rules. Only 11 rules meet the minsupp and minconf threshold and include the set of Class Association Rules (CAR), which are used to form a decision model for unplanned ICU transfers with binary integer programming

A Binary Integer Programming Approach to find a Sudoku Matrix

In the basic Sudoku game, players must fill the entries of a n × n matrix, except some given entries, under the conditions that each row, each column, and each m × m sub matrix contains integers 1 through n exactly once. In this research paper, in addition to the basic game, conditions and solution process for three advanced versions, such as Sudoku X, Four Square Sudoku and Four Pyramid Sudoku were also studied. In this study, the above-mentioned conditions are converted into appropriate mathematical forms as constraints of the Integer Linear Programming Problem using Pascal Programming Language, such a way that the objective function and the constraints suit as an input mathematical model for the LINGO mathematical optimization software. Here, an unlimited version of the LINGO software has been used with the built-in Branch and Bound algorithm as the number of constraints is very high. Finally, solutions to the given Sudoku problems obtained from the solutions acquired through LINGO software.

Priority‐based resource allocation in wireless powered UAV‐assisted networks

Unmanned aerial vehicles (UAVs) can be deployed to combine terrestrial and aerial networks to provide flexible connectivity to a large number of devices in three-dimensional (3D) space. Powering wireless devices through energy harvesting and wireless power transfer have been investigated to provide uninterrupted operations. Resource allocation is critical to improving the overall performance of the network. This paper focusses on a downlink network in which UAVs serve as base stations to provide connectivity to ground users. A priority-based charging of UAVs from the ground charging stations needs to be efficiently designed for the sustainable operation of the overall network. A binary linear integer programming (BLIP) problem is formulated to minimise the charging cost and maximise the number of UAVs that can be charged by charging stations. First, the BLIP is transformed into a quadratic programming problem to solve it in polynomial time. A sequential quadratic programming algorithm is developed to solve the optimisation problem. Simulation results demonstrate the effectiveness of the proposed work compared to existing solutions.

Optimal matchday schedule for Turkish professional soccer league using nonlinear binary integer programming

Sports scheduling problems are interesting optimization problems that require the decision of who play with whom, where and when to play. In this work, we study the sports scheduling problem faced by the Turkish Football Federation. Given the schedule of games for each round of the season, the problem is to determine the match days with the goal of having a fair schedule for each team. The criteria we employ to establish this fairness are achieving an equal distribution of match days between the teams throughout the season and the ideal assignment of games to different days in each round of the tournament. The problem is formulated as a nonlinear binary integer program and is solved optimally for each week. Our results indicate that significant improvements over the existing schedule can be achieved if the optimal solution is implemented.

Integer programming for selecting set of informative markers in paternity inference

BackgroundParentage information is fundamental to various life sciences. Recent advances in sequencing technologies have made it possible to accurately infer parentage even in non-model species. The optimization of sets of genome-wide markers is valuable for cost-effective applications but requires extremely large amounts of computation, which presses for the development of new efficient algorithms.ResultsHere, for a closed half-sib population, we generalized the process of marker loci selection as a binary integer programming problem. The proposed systematic formulation considered marker localization and the family structure of the potential parental population, resulting in an accurate assignment with a small set of markers. We also proposed an efficient heuristic approach, which effectively improved the number of markers, localization, and tolerance to missing data of the set. Applying this method to the actual genotypes of apple (Malus × domestica) germplasm, we identified a set of 34 SNP markers that distinguished 300 potential parents crossed to a particular cultivar with a greater than 99% accuracy.ConclusionsWe present a novel approach for selecting informative markers based on binary integer programming. Since the data generated by high-throughput sequencing technology far exceeds the requirement for parentage assignment, a combination of the systematic marker selection with targeted SNP genotyping, such as KASP, allows flexibly enlarging the analysis up to a scale that has been unrealistic in various species. The method developed in this study can be directly applied to unsolved large-scale problems in breeding, reproduction, and ecological research, and is expected to lead to novel knowledge in various biological fields. The implementation is available at https://github.com/SoNishiyama/IP-SIMPAT.

Integrated train routing and timetabling problem in a multi-station high-speed railway hub

ABSTRACT With multiple stations being built in the high-speed railway hub, how to schedule trains among stations is of great significance. This paper studies the integrated train routing and timetabling problem in a multi-station high-speed railway hub. Based on a specific bi-level network, a binary integer programming model using cumulative flow variables is proposed to minimize the total cost of trains and passengers. An extended Alternating Direction Method of Multipliers (ADMM) algorithm is developed to decompose the model into train and passenger subproblems. The performance of the algorithm is investigated on small-scale and large-scale networks. Compared with the commonly used Lagrangian Relaxation (LR) algorithm, the results indicate that the extended ADMM obtain better solutions with less iterations, where the lower bound decreases by 3.79% and iterations are reduced by 83.54%. Another comparative experiment shows the total cost of the optimization scheme is 16.22% lower than that of the current fixed scheme.

Structured Controller Design for Interconnected Systems via Nonlinear Programming

Dear Editor, This letter deals with the structural controller design problem of interconnected systems with unknown feedback topology. Firstly, under a cardinality constraint on the directed communication links among sub-controllers, a distributed controller's feedback gain and feedback topology are incorporated in a unified co-design framework. Secondly, the cardinality constraint introduced in the distributed control is represented by a binary integer programming. To deal with the complementary constraint, a nonlinear programming (NLP) is proposed to relax the binary integer programming. Finally, incorporating the NLP into the standard distributed event-triggered control method, an algorithm is developed for interconnected systems to simultaneously design the feedback topology and controller gain.

The location routing problem for cooling shelters during heat waves

Given the increasing frequency, duration, and intensity of heat waves around the globe, more research is needed on the allocation and operations of cooling shelters for efficient heat mitigation. To address this need, this study considers a cooling shelter operating system that uses shuttle buses to transport heat-vulnerable people and presents a binary integer programming model for the multi-depot location routing problem (LRP) that decides optimal locations of cooling shelters and routes of shuttle buses simultaneously with the objective of minimizing the total operating cost for full accommodation of the heat-vulnerable population. Since the LRP is NP-hard, we further present the simulated annealing to efficiently derive a near-optimal solution. We then validate the proposed methodology with an application to the 14 administrative regions of Ulsan Metropolitan City in the Republic of Korea to assign heat-vulnerable residents and provide them with ride services to the associated cooling shelters. The overall results demonstrate the proposed methodology's competitive performance compared with the traditional two-phased solution approach that separately solves the location problem and routing problem. In particular, our results show that the proposed methodology can save up to 49,000 USD in addressing the cooling shelter location routing problem compared to the two-phased solution approach. Subsequently, a sensitivity analysis is conducted regarding three factors that are likely to impact the effectiveness and efficiency of cooling shelter operations: shuttle bus capacity, traveling cost, and maximum walking distance. Our research provides recommendations for policymakers to carry out the best heat mitigation strategy for their unique circumstances and reduce heat-related illness and death.

An Efficient Binary Integer Programming Model for Residency Time-Constrained Cluster Tools With Chamber Cleaning Requirements

Cluster tools play a significant role in the entire process of wafer fabrication. As the width of circuits in semiconductor chips shrinks down to less than 10nm, strict operational constraints are imposed on the operations of cluster tools in order to ensure the quality of processed wafers. Particularly, wafer residency time constraints and chamber cleaning requirements are commonly seen in etching, chemical vapor deposition, coating processes, etc. They make the scheduling problem of cluster tools more challenging. This work aims to provide a solution for dual-arm cluster tools with wafer residency time constraints and chamber cleaning requirements. To do so, it proposes a novel virtual wafer-based scheduling method. By this method, under a steady state, a PM processes either a real or virtual wafer at a time. When a PM processes a virtual one, its chamber can perform a cleaning operation. In this way, we can meet not only the strict residency time constraints for real wafers, but also innovatively meet chamber cleaning requirements. Based on such a novel scheduling method, an efficient binary integer programming model is established to optimize the throughput of cluster tools. Finally, experiments are performed to show the efficiency and effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To ensure wafer quality in semiconductor manufacturing, engineers have to impose wafer residency time constraints and chamber cleaning requirements on the operations of cluster tools. In order to tackle their scheduling problem with these constraints, this work proposes a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for time-constrained cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a PM processes a virtual wafer, a chamber cleaning operation can be performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. To do so, this work establishes an efficient binary integer programming model to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has a high practical value to numerous semiconductor manufacturers.

CARSP: A Smart Parking System Based on Doubly Periodic Rolling Horizon Allocation Approach

Blind search for available parking space is accountable for most traffic congestion, accident, and pollution in cities, which severely impact people’s life. Parking management based on an online smart parking system is practical to alleviate parking problems in which parking allocation is the core. However, existing researches are weak at satisfying allocation effect and speed simultaneously when solving large-scale dynamic parking allocation problem. To address this problem, we firstly construct an online “Collection-Allocation-Response” smart parking system (CARSP) to offer parking services to users and rent parking spaces from owners so as to obtain revenue for system managers. We then propose a novel Doubly Periodic Rolling Horizon allocation approach (DPRH) that circularly conduct allocation within a short period and reallocation within a long period. We formulate a narrow allocation model (without reallocation) and broad allocation model (with reallocation), both of which are binary integer programming models with the objective of maximizing system integrated benefit. We design seven performance metrics to evaluate the overall allocation effect and speed of CARSP based on DPRH. According to the three-day district-level instance in Beijing, CARSP based on DPRH performs excellently in balancing allocation effect and speed. This study is meaningful for constructing and optimizing an online smart parking system.

On the integrality gap of binary integer programs with Gaussian data

For a binary integer program (IP) \(\max c^{\mathsf {T}}x, Ax \le b, x \in \{0,1\}^n\), where \(A \in {\mathbb {R}}^{m \times n}\) and \(c \in {\mathbb {R}}^n\) have independent Gaussian entries and the right-hand side \(b \in {\mathbb {R}}^m\) satisfies that its negative coordinates have \(\ell _2\) norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by \({\text {poly}}(m)(\log n)^2 / n\) with probability at least \(1-2/n^7-2^{-{\text {poly}}(m)}\). Our results give a Gaussian analogue of the classical integrality gap result of Dyer and Frieze (Math OR, 1989) in the case of random packing IPs. In constrast to the packing case, our integrality gap depends only polynomially on m instead of exponentially. Building upon recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), we show that the integrality gap implies that branch-and-bound requires \(n^{{\text {poly}}(m)}\) time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed. We derive this result via a novel meta-theorem, which relates the size of branch-and-bound trees and the integrality gap for random logconcave IPs.

Transmit or Backscatter: Communication Mode Selection for Narrowband IoT Systems

Backscatter communication is an energy-efficient communication technique for the Internet of things (IoT) devices. It enables data transmission by reflecting the incident radio signals. In this paper, we propose a communication mode selection scheme for IoT devices that can communicate using either active transmission or backscattering. In the active transmission mode, the IoT devices can transmit data over narrowband subcarriers using power-domain non-orthogonal multiple access (NOMA). In the backscattering mode, which operates over shorter distance than active transmission, nearby user equipment (UE) devices are used as relays. The UEs receive the backscattered signals from the IoT devices and forward them to the base station. We formulate a connection density maximization problem to select the communication mode used by each IoT device. We determine the IoT device pairing for active transmission mode with NOMA and UE-IoT device association for backscattering mode. The formulated problem is a binary integer programming problem. Although it can be solved optimally, the optimal algorithm incurs exponential computational complexity. Hence, we propose a low-complexity suboptimal algorithm to solve this problem. Results show that our proposed algorithm can enhance the connection density of narrowband IoT systems by up to 64&#x0025; when compared with using single communication mode.