Binary Integer Linear Programming Research Articles

An Optimization Model for Scheduling Tour of Service Personnel in afterSale Service Process with Additional Side Conditions of Responsiveness and FCFS Service Policy

In this paper a binary integer linear programming model is proposed for scheduling tour of service personnel in aftersale service process. The model aims to minimize the service personnel’s overall travel time of visiting all customers with additional side conditions that customers should be served by first come first serve (FCFS) priority basis within specified service response time. These side conditions are important strategies in present era of time-based competition. The objective and side conditions are considered for both profitability and effectiveness. Indeed, for given service response time, optimal tour plan would minimize the quantity of service personnel. This decreases the hiring cost of service personnel and thus increases the profitability of after-sale service process. On the other hand, for given quantity of service personnel, optimal tour plan would reduce the service response time. Responsive after-sale service on FCFS priority basis will increase the customer satisfaction, which in turn leads to more repeat orders and hence improves the profitability. The proposed model can capture all realistic constraints of service management process, such as time windows, skill requirement, balanced workload distribution, etc. A numerical illustration is included to demonstrate the effectiveness of the proposed model in conducting economic analysis of an after-sale service process.

Optimized PMU Stationing for Wide Area Monitoring of Power Grid

Abstract At present time concerted efforts are being made for the implementation of smart grid technologies. PMUs play a significant role in the wide area monitoring system (WAMS). The major advantages of the WAMS include dynamic wide area measurements with faster rate and better accuracy. Observability of a complete power system with a minimum number of PMUs has always remained a challenge. This paper suggests a binary integer linear programming approach for finding out the optimal locations of PMUs in a system. Two indices viz. BOI (Bus Observability Index) and SORI (System Observability Redundancy Index) have been suggested to rank the various possible solutions of an OPP. IEEE 14, 24, 30 and New England 39 (NE 39) bus systems have been considered for simulation and the results show excellent computational efficiency of the algorithm.

OFDMA-based multicast with multiple base stations

We consider an orthogonal frequency division multiple access (OFDMA)-based multicast system where multiple base stations transmit a multicast session to a multicast group. The goal is to maximize the multicast rate (i.e. the minimum achievable user rate) subject to a total power constraint. We assume the use of an erasure code (e.g., a Reed--Solomon code) or rateless code (e.g., Luby transform code). This facilitates each user to accumulate rates from their best subchannels, so that the achievable multicast rate is not limited to the worst user. The resource allocation problem involves determining the transmitting base station at each OFDMA subchannel, the number of bits to be transmitted at each subchannel, and the set of nodes to decode the bits at each subchannel. We formulate the problem as a mixed binary integer linear programming and find the optimal solution as a benchmark. We also propose a greedy subchannel and bit allocation algorithm that is close to optimal.

A Novel BILP Model for Energy Optimization Under Data Precision Constraints in Wireless Sensor Networks

In this letter, we propose a binary integer linear programming (BILP) model of the problem of Energy Minimization under the constraint of Data Precision in the context of correlated data collection in wireless sensor networks, called EMDP. The exact solution of our BILP model determines, in each round of data collection, the role of each node in terms of sensing, data relaying, and processing. It gives the baseline for optimal network operations and helps characterizing the complexity of EMDP problem. Moreover, we propose a heuristic solution, namely, CORAD, which is an energy-aware correlation-based adaptive dynamic clustering algorithm for data collection.

MCentridFS: a tool for identifying module biomarkers for multi-phenotypes from high-throughput data.

Systematically identifying biomarkers, in particular, network biomarkers, from high-throughput data is an important and challenging task, and many methods for two-class comparison have been developed to exploit information of high-throughput data. However, as the high-throughput data with multi-phenotypes are available, there is a great need to develop effective multi-classification models. In this study, we proposed a novel approach, called MCentridFS (Multi-class Centroid Feature Selection), to systematically identify responsive modules or network biomarkers for classifying multi-phenotypes from high-throughput data. MCentridFS formulated the multi-classification model by network modules as a binary integer linear programming problem, which can be solved efficiently and effectively in an accurate manner. The approach is evaluated with respect to two diseases, i.e., multi-stages HCV-induced dysplasia and hepatocellular carcinoma and multi-tissues breast cancer, both of which demonstrated the high classification rate and the cross-validation rate of the approach. The computational results of the five-fold cross-validation of the two data show that MCentridFS outperforms the state-of-the-art multi-classification methods. We further verified the effectiveness of MCentridFS to characterize the multi-phenotype processes using module biomarkers by two independent datasets. In addition, functional enrichment analysis revealed that the identified network modules are strongly related to the corresponding biological processes and pathways. All these results suggest that it can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems by exploring both big biological data and network information. The Matlab code for MCentridFS is freely available from http://www.sysbio.ac.cn/cb/chenlab/images/MCentridFS.rar.

A heuristic for BILP problems: The Single Source Capacitated Facility Location Problem

In the Single Source Capacitated Facility Location Problem (SSCFLP) each customer has to be assigned to one facility that supplies its whole demand. The total demand of customers assigned to each facility cannot exceed its capacity. An opening cost is associated with each facility, and is paid if at least one customer is assigned to it. The objective is to minimize the total cost of opening the facilities and supply all the customers. In this paper we extend the Kernel Search heuristic framework to general Binary Integer Linear Programming (BILP) problems, and apply it to the SSCFLP. The heuristic is based on the solution to optimality of a sequence of subproblems, where each subproblem is restricted to a subset of the decision variables. The subsets of decision variables are constructed starting from the optimal values of the linear relaxation. Variants based on variable fixing are proposed to improve the efficiency of the Kernel Search framework. The algorithms are tested on benchmark instances and new very large-scale test problems. Computational results demonstrate the effectiveness of the approach. The Kernel Search algorithm outperforms the best heuristics for the SSCFLP available in the literature. It found the optimal solution for 165 out of the 170 instances with a proven optimum. The error achieved in the remaining instances is negligible. Moreover, it achieved, on 100 new very large-scale instances, an average gap equal to 0.64% computed with respect to a lower bound or the optimum, when available. The variants based on variable fixing improved the efficiency of the algorithm with minor deteriorations of the solution quality.

Radio Resource Management Scheme for Relieving Interference to MUEs in Relay-Based Cellular Networks

Relay nodes (RNs) have been recently introduced as a cost-effective solution to achieve ubiquitous high data rates in cellular networks. By providing a two-hop link between evolved nodeB (eNB) and user equipment (UE), RNs can improve the UE's signal-to-interference-plus-noise ratio (SINR) and throughput. A typical relay-based cellular network is comprised of macro UEs (MUEs) that are served directly by eNB and relay UEs (RUEs) that are served via RNs. The performance of the entire network is degraded if the interference between RNs and MUEs is not carefully managed. In this paper, we propose a radio resource management scheme that effectively exploits the advantages of RNs without causing severe interference to MUEs, which yields a better overall network and cell-edge user throughput. To improve channel quality of MUEs located nearby RNs, the proposed scheme determines a specific set of subchannels to be used by each RN. Second, the proposed scheme assigns subchannels to UEs and RNs considering channel quality, average UE data rate, and the number of required subchannels at RNs. For resource allocation, we formulate a binary integer linear programming (BILP) problem and propose a novel heuristic algorithm to reduce its computational complexity. Our simulation results show that the heuristic algorithm achieves similar performance with the BILP. In addition, we discuss a detailed procedure for control signal exchange and data transmission and analyze the lower bound of SINR gain of MUEs obtained from the proposed scheme. It has been shown that the proposed scheme improves the overall network throughput and the cell-edge user throughput compared with existing schemes.

Reliability‐based phasor measurement unit placement in power systems considering transmission line outages and channel limits

Since phasor measurement unit (PMU) was invented, there has been growing interest in developing methodologies for finding the minimum number of PMUs for complete system observability. The methods for the PMU placement must consider the fact that the network topology may change when the power system is affected by a contingency event. Therefore the PMU placement problem can be stated as finding the minimum number of PMUs for complete system observability considering the failure probability of transmission lines. In this study, the authors propose a new reliability- based model for the contingency constrained PMUs placement. Initially, a methodology, that considers the probability of failure of the power system components, is proposed. Next, an algorithm is presented for selecting the minimal number of PMUs and their locations to monitor the system under normal operation and the most credible contingencies. A probabilistic index is introduced to select a desired level of reliability for the wide-area monitoring system. Finally, the availability of PMU measuring channels is incorporated in the model, so more realistic and useful results can be obtained. The problem is formulated and solved as a binary integer linear programming model and tested on the IEEE 9-bus, IEEE 57-bus and RTS96 test systems.

Utility-oriented placement of actuator nodes with a collaborative serving scheme for facilitated business and working environments.

Places to be served by cyber-physical systems (CPS) are usually distributed unevenly over the area. Thus, different areas usually have different importance and values of serving. In other words, serving power can be excessive or insufficient in practice. Therefore, actuator nodes (ANs) in CPS should be focused on serving around points of interest (POIs) with considerations of “service utility.” In this paper, a utility-oriented AN placement framework with a collaborative serving scheme is proposed. Through spreading serving duties among correctly located ANs, deployment cost can be reduced, utility of ANs can be fully utilized, and the system longevity can be improved. The problem has been converted into a binary integer linear programming optimization problem. Service fading, 3D placements, multiscenario placements, and fault-tolerant placements have been modeled in the framework. An imitated example of a CPS deployment in a smart laboratory has been used for evaluations.

Open shop scheduling with stochastic release dates and processing times

In this paper, we study an open shop scheduling (OSS) problem subject to uncertain release dates and processing times. Open shop scheduling problems are one of shop problems in sequence and scheduling problems. The objective is to find the sequence of jobs and machines which minimises total completion times of jobs. We first formulate the problem as a stochastic programming model, and then we employ deterministic mixed binary integer linear programming to solve the linear programming solver. In this paper, we assumed the processing times and release times of jobs to be uncertain, but follow a specific probability function. It is clear that random variables are independent. We use GAMS software to solve it. The superiority and advantages of this study over previous studies are discussed.

Minimum violations and predictive meta‐rankings for college football

This article presents two meta‐ranking models that minimize or nearly minimize violations of past game results while predicting future game winners as well as or better than leading current systems—a combination never before offered for college football. Key to both is the development and integration of a highly predictive ensemble probability model generated from the analysis of 36 existing college football ranking systems. This ensemble model is used to determine a target ranking that is used in two versions of a hierarchical multiobjective mixed binary integer linear program (MOMBILP). When compared to 75 other systems out‐of‐sample, one MOMBILP was the leading predictive system while getting within 0.64% of the retrodictive optimum; the other MOMBILP minimized violations while achieving a prediction total that was 2.55% lower than the best mark. For bowls, prediction sums were not statistically significantly different from the leading value, while achieving optimum or near‐optimum violation counts. This performance points to these models as potential means of reconciling the contrasting perspectives of predictiveness versus the matching of past performance when it comes to ranking fairness in college football. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 17–33, 2014

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.

Minimum Near-Convex Shape Decomposition

Shape decomposition is a fundamental problem for part-based shape representation. We propose the minimum near-convex decomposition (MNCD) to decompose arbitrary shapes into minimum number of "near-convex" parts. The near-convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of nonintersecting cuts. Two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition. With the degree of near-convexity a user-specified parameter, our decomposition is robust to local distortions and shape deformation. The optimization can be efficiently solved via binary integer linear programming. Both theoretical analysis and experiment results show that our approach outperforms the state-of-the-art results without introducing redundant parts and thus leads to robust shape representation.

Lagrangian relaxation and pegging test for the clique partitioning problem

The clique partitioning problem is an NP-hard combinatorial optimization problem with applications to data analysis such as clustering. Though a binary integer linear programming formulation has been known for years, one needs to deal with a huge number of variables and constraints when solving a large instance. In this paper, we propose a size reduction algorithm which is based on the Lagrangian relaxation and the pegging test, and verify its validity through numerical experiments. We modify the conventional subgradient method in order to manage the high dimensionality of the Lagrangian multipliers, and also make an improvement on the ordinary pegging test by taking advantage of the structural property of the clique partitioning problem.

Dispersion for the point-feature cartographic label placement problem

The point-feature cartographic label placement problem (PFCLP) is a NP-Hard problem arising in design of maps and other graphic objects. For the sake of a better map legibility it is important to avoid overlaps in the process of labeling. This paper examines the PFCLP in the legibility context and proposes a dispersion approach for the problem. It is considered that when all points must to be labeled and overlaps are inevitable, the map can be more readable if overlapping labels are placed more distant from each other. The PFCLP is modeled as a dispersion problem on two mathematical formulations based on binary integer linear programming. Computational tests have provided good results on several generated instances.

A Novel Approach for the Optimal PMU Placement using Binary Integer Programming Technique

Phasor measurement units (PMUs) are considered as a promising tool for future monitoring, protection and control of power systems. In this paper, a novel approach is proposed in order to determine the optimal number and locations of PMUs to make the power system observable. The PMU placement problem is formulated as a binary integer linear programming, in which the binary decision variables (0, 1) determine where to install a PMU, preserving the system set observability, such as full or partial. The proposed approach integrates the impacts of both existing conventionalpower injection/flow measurements (if any) and the possible failure of single or multiple PMU / communication line into the decision strategy of the optimal PMU allocation. The network topology and hence network connectivity matrix remains unaltered for the inclusion of conventional measurements. Program is developed usingMatlabsoftware and is tested on sample seven-bus system and IEEE 14 bus system.

A demand-based weighted train delay approach for rescheduling railway networks in real time

Rail systems are highly complex and their control in real time requires mathematical–computational tools. The main aim of these tools is to perform swift optimal rescheduling in response to disruptions or delays caused by events not foreseen in the original plans, so that there is no knock-on effect on other services due to these primary delays. This paper proposes a novel weighted train delay based on demand approach based on the alternative graph concept for rescheduling passenger train services. This problem is formulated as a binary integer linear programming problem which tries to maximize consumer satisfaction by minimizing total passenger delay at destinations. A heuristic method, the so-called Avoid Most Delayed Alternative Arc (AMDAA) algorithm, is proposed to solve the model. AMDAA is an adaptation of Avoid Maximum Current Cmax (AMCC) developed by Mascis and Pacciarelli (2002) to the new model. A numerical comparison is carried out with AMDAA, a Branch-and-Cut method, AMCC and the heuristic First Come First Served (FCFS). Numerical research carried out with data from the Renfe Cercanias Madrid rail network (Spain) shows the high computational performance in real applications of the algorithms and the suitability of this weighted train delay based on demand model versus the classical makespan minimization approach.

Minimizing makespan in a group shop with fuzzy release dates and processing times

This paper deals with a fuzzy group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the flow shop, the job shop, and the open shop scheduling problems. Job release dates and processing times are considered to be triangular fuzzy numbers. The objective is to find a job schedule that minimizes the maximum completion time or makespan. First, the problem is formulated in a form of fuzzy programming and then prepared in a form of deterministic mixed binary integer linear programming by applying the chance-constrained programming. To solve the problem, an efficient genetic algorithm hybridized with an improvement procedure is developed. Both Lamarckian and Baldwinian versions are then implemented and evaluated through computational experiments.

Protein complex prediction based on maximum matching with domain–domain interaction

With the development of high-throughput methods for identifying protein–protein interactions, large scale interaction networks are available. Computational methods to analyze the networks to detect functional modules as protein complexes are becoming more important. However, most of the existing methods only make use of the protein–protein interaction networks without considering the structural limitations of proteins to bind together. In this paper, we design a new protein complex prediction method by extending the idea of using domain–domain interaction information. Here we formulate the problem into a maximum matching problem (which can be solved in polynomial time) instead of the binary integer linear programming approach (which can be NP-hard in the worst case). We also add a step to predict domain–domain interactions which first searches the database Pfam using the hidden Markov model and then predicts the domain–domain interactions based on the database DOMINE and InterDom which contain confirmed DDIs. By adding the domain–domain interaction prediction step, we have more edges in the DDI graph and the recall value is increased significantly (at least doubled) comparing with the method of Ozawa et al. (2010) [1] while the average precision value is slightly better. We also combine our method with three other existing methods, such as COACH, MCL and MCODE. Experiments show that the precision of the combined method is improved. This article is part of a Special Issue entitled: Computational Methods for Protein Interaction and Structural Prediction.

TEAM ASPAR Uses Binary Optimization to Obtain Optimal Gearbox Ratios in Motorcycle Racing

In this paper, we present a binary integer linear program for obtaining the optimal combination of gears to install on a competitive racing motorcycle. Our objective is to meet the requirements of both the rider and track at a set of points on the racing circuit. This requires determining the best transmission (gearbox) for each circuit and rider. We discuss a solution for a rider in the World Motorcycling Racing Championship.