Binary Integer Linear Programming Research Articles

Optimal placement of wide area monitoring system components in active distribution networks

Abstract The optimal placement of micro-Phasor Measurement Units (µPMUs) reduce the cost of wide area monitoring system (WAMS) in active distribution networks (ADNs); therefore, it is becoming a popular research topic. However, µPMUs alone cannot minimize the WAMS cost. An appropriate location of Phasor Data Concentrator (PDC) and a fiber optic communication link (CL) that transfers data from µPMUs to PDCs also need to be optimized. Hence this paper proposes a hybrid algorithm that determines the optimal cost-effective solution of the placement problem of µPMUs, PDC, and CL. The proposed algorithm uses the graph theory and binary integer linear programming (BILP) with the constraints of distribution generation (DG) presence, regular network reconfiguration, and maximizing system redundancy. The proposed algorithm is tested on IEEE 69 bus, IEEE 123 bus, and 345 bus active distribution system. The results obtained show the reduction in cost mainly through the CL and optimal placement of µPMUs in decentralized WAMS.

Range coverage location model: An optimization model for the charging station location problem in a transportation network to cover intercity travels

Equipping highways with charging stations (CSs) is a fundamental step for travelling with electric vehicles (EVs) between cities and countries conveniently. This article focuses on locating CSs to fully connect roads that may require multiple charging events by considering the minimum driving range for all possible paths in a transportation network. For this purpose, we present a new binary integer linear programming model named the Range Coverage Location Model (RCLM) to find the minimum required CSs and their locations that the driving range can cover without defining the paths in the network. By adding the result of RCLM as a constraint to the model, the optimum locations that maximize the EV flows are determined with the RCLM-Max model. Two versions of the RCLM are introduced. The link-based RCLM is designed for problems in which there are CSs in each of the origin/destination (OD) nodes (intersections), while the network-based RCLM aims to connect links without stopping by the OD nodes, making the model stricter but convenient for EV travels. The proposed models are validated through extensive computational experiments with real data from a highway network in Turkey. The experiments show that RCLM and RCLM-Max can solve very large-scale problems in a very short CPU time. The findings suggest that the link-based RCLM can be applied when the budget is at the forefront, and the network-based model is preferred if the aim is to connect the main roads without stopping by the OD nodes.

Analysis and assessment of weighted combinatorial criterion for test suite reduction

AbstractSoftware plays an important role in modern society. New software features have to be completed and tested rapidly due to business and user needs and goals. To ensure the quality of modified software components, new test cases must be generated and included in the current test pool. Furthermore, test pool size often grows too large to test all cases. A considerably large test pool typically consumes an exorbitant quantity of time, leading to inefficient regression testing. Test suite reduction is often used to solve this problem by removing redundant test cases. Thus, time and resource constraints make it necessary to minimize the test suite. That is, test pool size should be efficiently reduced, while the remaining test cases should be adequate to provide the same coverage as the pool. The main purpose of this paper is to propose four weighted combinatorial algorithms and a three‐objective binary integer linear programming (ILP) model to improve fault detection effectiveness. We first consider both the control flow and data flow as our testing criteria and combine them by using a weighted means with four existing test suite reduction algorithms. A genetic algorithm is used to find the best combination of weighting factors to assign to the two testing criteria. Experiments based on real subject programs are presented. Experimental results demonstrate that 77.5% of our proposed weighted combinatorial algorithms have an even or better performance in suite size reduction, 83.75% of our approaches perform even or better in fault detection effectiveness, and 82.5% of our approaches have even or better effectiveness in fault‐to‐test ratio. For the three‐objective binary ILP model, test suite size is significantly reduced without any accompanying loss in fault detection ability.

Energy Optimization and Power Stack Shed Reduction of Oil Depots by using Renewable Energy Resources

Most of the industries including the oil sector are looking forward towards the renewable energy resources with proper energy management system (EMS) as it is the need of time. For this purpose, solar and wind energy are the renewable energy resources, which are obtained from natural resources and produce clean and environment -friendly electrical energy and can be used for oil depots. The proper utilization of solar and wind energy from natural resource may result in economical and cost-effective EMS. In the proposed research work, an effective energy management demonstration is delivered to ensure the ceaseless flexibility of power. Furthermore, reduction of production per unit cost to the oil sector industry by utilizing multiple objectives streamlining. In the proposed oil depot, connected loads are divided into Shiftable and Non-Shiftable loads and then apply Branch and Bound Algorithm (BnB) with binary integer linear programming (BILP). By using the BnB technique, selected shiftable loads are shifted to the low cost energy resource automatically and resultantly, we get the low price unit cost and continuous power supply. Simulation results for the above-mentioned research work are performed on MATLAB. The proposed technique helps to reduce the power stack shedding issue as well.

Some binary products and integer linear programming for [formula omitted]-metric dimension of graphs

A sharp upper bound and a closed formula for the k-metric dimension of the hierarchical product of graphs is proved. Also, sharp lower bounds for the k-metric dimension of the splice and link products of graphs are presented. An integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. These results are applied to bound or to compute the k-metric dimension of some classes of graphs that are of interest in mathematical chemistry.

Tactical runway scheduling for demand and delay management

PurposeAirports are limited in terms of capacity. Particularly, runways can only accommodate a certain number of movements (arrivals and departures) while ensuring safety and determined operational requirements. In such a constrained operating environment, any reduction in system capacity results in major delays with significant costs for airlines and passengers. Therefore, the efficient operation of airports is a critical cornerstone for demand and delay management of the whole air transportation system. Runway scheduling deals with the sequencing of arriving and departing aircraft at airports such that a predefined objective is optimized subject to several operational constraints, like the dependency of separation on the leading and trailing aircraft type or the runway occupancy time. This study aims to develop a model that acts as a tactical runway scheduling methodology for reducing delays while managing runway usage.Design/methodology/approachBy considering real airport performance data with scheduled and actual movements, as well as arrival/departure delays, this study presents a robust model together with an optimization algorithm, which incorporates the knowledge of uncertainty into the tactical operational step. The approach transforms the planning problem into an assignment problem with side constraints. The coupled landing/take-off problem is solved to optimality by exploiting a time-indexed (0, 1) formulation for the problem. The Binary Integer Linear Programming approach allows to include multi-criteria and multi-constraints levels and, even with some major simplifications, provides fewer sequence changes and target time updates, when compared to the usual approach in which the plan is simply updated in case of infeasibility. Thus, the use of robust optimization leads to a protection against tactical uncertainties, reduces delays and achieves more stable operations.FindingsThis model has been validated with real data from a large international European airport in different traffic scenarios. Results are compared to the actual sequencing of flights and show that the algorithm can significantly contribute to the reduction of delay, while adhering as much as possible to the operative procedures and constraints, and to the objectives of the airport stakeholders. Computational experiments performed on the case study illustrate the benefits of this arrival/departure integrated approach: the proposed algorithm significantly reduces weighted aircraft delay and computes efficient runway schedule solutions within a few seconds and with little computational effort. It can be adopted as a decision-making tool in the tactical stage. Furthermore, this study presents operational insights regarding demand and delay management based on the results of this work.Originality/valueScheduling arrivals and departures at runways is a complex problem that needs to address diverse and often competing considerations among involved flights. In the context of the Airport Collaborative Decision Making programme, airport operators and air navigation service providers require arrival and departure management tools that improve aircraft flows at airports. Airport runway optimization, as the main element that combines airside and groundside operations, is an ongoing challenge for air traffic management.

Optimizing forest road planning in a sustainable forest management area in the Brazilian Amazon

The construction of forest roads in Brazilian Amazon is costly and has a significant environmental impact. Several practices and principles must be observed to comply with legislation, to preserve the remaining forest, and to ensure sustainable exploitation. Road planning is complex in this context, based on the number of aspects and variables that must be considered. This research aimed to evaluate computational methods' effectiveness in planning forest roads, optimizing resources to reduce damage to the remaining forest, compared to traditional planning methods. The study area was a native forest under a sustainable forest management regime located in municipalities of Terra Santa and Oriximiná, in Pará, in Brazilian Amazon. Data obtained from area made it possible formulate six instances of different sizes. A binary integer linear programming model was used, solved using CPLEX software, and Dijkstra, Bellman-Ford, Dial, and D'Esopo-Pape shortest path algorithm, implemented in C programming language. During processing of instances, the time taken to obtain the solution increased according to size of instance, however, time difference was not significant. Among the evaluated algorithms, the D'Esopo-Pape algorithm showed the best performance. The evaluated methods were effective in obtaining an optimal solution for proposed forest road planning. The solutions obtained using computational methods more effectively considered the restrictions associated with sustainable forest management, in contrast to those derived from the traditional planning by forestry company.

An optimization model for course scheduling in Undergraduate Industrial Engineering Program of Universitas Sebelas Maret

Course timetabling is a common problem in many universities. With different number of students enrolled in every course, the number of lecturers, and various size of room’s capacity, then it would be difficult for scheduler to assign courses manually. The assigning process must meet all of educational rules in order to satisfy students and lecturers for a better educational quality. There are sets of time slot, courses, and rooms. The room efficiency and the effectiveness needed due to limited available room. The problem is formulated in the form of binary integer linear programming. The objective function of the model is to maximise the room utility. The model also considers probability of a course taken by different student groups in order to avoid clash. The results show a significant difference between manual scheduling and optimization results can satifsy more constraints than manual scheduling.

Wide area monitoring and measurements using mixed integer linear programming in deregulated power system for smart grid

This paper deals with different methods involved in the determination of complete observability of power system under wide area monitoring using Phasor Measurement Unit (PMU). There are numerous methods available in literature for the determination of optimal locations of PMU for complete system observability, but out of all those methods, fast selection of best suitable with minimum number of PMUs at optimal location for complete observability, is still a challenge to power engineers for applying online in Smart Grid under deregulation environment. After detail analysis with various methods, this paper proposes an algorithm for selecting best possible method for determining optimal locations of PMUs. The analysis compares performance of the available methods, e.g., Binary Integer Linear Programming, Admittance Bus Matrix Method and Mixed Integer Linear Programing using General Algebraic Modelling System. To investigate the effectiveness of the proposed method for complete observability using system observability redundancy index (SORI), Indian Northern Regional Power Grid (NRPG-246 bus system) has also been considered here.

Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus.

Background: Food consumption is one of the most important drivers of the relation between human well-being and Earth's ecosystems. The current production level is difficult to sustain without compromising environmental integrity or public health. This calls for a decisive change in food consumption patterns in order to improve nutrition quality while respecting biodiversity and ecosystems. This change will produce some effect only if it is also culturally acceptable, accessible, economically fair and affordable. The design of food plans is traditionally carried out using mathematical optimization models, such as linear programming. This method has proved to be successful in providing nutritionally adequate diets while minimizing their economic and environmental impact. Nevertheless, cultural habits as well as attractiveness and variety of meals is very difficult to deal with, and no fully satisfactory way to include these issues in linear programming has been found.Objective: The aim of this paper is to move from traditional linear programming to a new programming methodology in order to cope also with acceptability in the design of meal plans.Method: Binary integer linear programming is the new modeling paradigm. In the proposed model, meal plans consist of providing the sequence and composition of daily meals over a given period of time and each meal can be composed using dishes from a given set. Therefore, instead of defining just a level of consumption of food groups or food items, the proposed model provides a realistic menu. To cope with sustainability, the energy and nutritional content of each dish is calculated together with its price and environmental impact. Furthermore, acceptability can be explicitly taken into account in a very natural way, that is bounding the daily, weekly, or total repetitions of single dishes and of dishes in the same food groups.Results: The paper reviews three successful studies with increasing complexity considering lunch plans for schools and full-board menus for nursing homes. The case studies show a great reduction of the environmental impact of the meal plans while ensuring an adequate nutritional intake, affordable prices and most importantly the plans are varied and culturally acceptable.

Cooperative Optimization Model of BRT Speed and Timing Based on Dual Station at an Intersection

This paper presents a binary integer linear programming model based on a dual station at an intersection to make BRT (Bus Rapid Transit) go through the intersection without stopping. This paper first gives the setting of the BRT dual station at the intersection and compares the average BRT delay of the single and dual station at the intersection. Through comparison, it is found that dual station can optimize BRT operations, but there is still room for further optimization. Therefore, this paper establishes a 01 linear programming model based on a dual station. The model takes the shortest travel time of BRT as the optimization objective, and takes the selection of the dual station, green light time of the intersection and cycle time as optimization variables. The case analysis and results show that, compared with the current situation, the average intersection delay of signal priority method, simple dual station method and method proposed in this paper are reduced by 3.51 s (8.6%), 17.27 s (42.17%) and 35.99 s (87.89%); compared with the current situation, the average stopping times at intersection of the signal priority method, simple dual station method and the method proposed in this paper are reduced by −3 (−9.4%), 2 (6.2%) and 23 (71.8%), respectively. Under the control of the method proposed in this paper, the average intersection delay is 4.96 s, and the average stopping times at the intersection is 0.18. This shows that the optimization model proposed in this paper can greatly reduce BRT delay and parking times. The setting of dual station makes the two stations symmetrical to each other, which conforms to the name of the journal. This paper belongs to the field of Symmetry and other scientific disciplines and engineering.

Binary Code Optimized for Partial Encryption

A common technique for the partial encryption of compressed images and videos encrypts only the sign bits of some syntax elements such as the quantized transform coefficients or the motion vector differences. The sign bit can be interpreted as the most significant bit (MSB) in the binary representation of the syntax element. Our work is motivated by the key observation that the binary code used for this representation has an impact on the quality of the reconstruction at the eavesdropper and on the size of the stream to be encrypted. Therefore, we address the problem of optimal binary code design for partial encryption. Ideally, the goal is to simultaneously maximize the eavesdropper’s distortion and minimize the length of the compressed MSB stream. Since these two objectives are conflicting in general, we formulate the problem as the maximization of a weighted sum of the eavesdropper’s distortion and of the probability of the MSB being 0. We cast the problem as a binary integer linear program equivalent to a maximum weight matching problem, which has a polynomial-time solution algorithm. We show that when the source to be quantized and the quantizer are symmetric, the problem can be converted to a linear program of a smaller size, for a family of distortion metrics. Extensive experiments assess the performance of the optimized binary code in comparison with existing approaches. The results reveal that certain existing partial encryption schemes could benefit from the proposed design.

Satellite Constellation Pattern Optimization for Complex Regional Coverage

The use of regional-coverage satellite constellations is on the rise, urging the need for an optimal constellation design method for complex regional coverage. Traditional constellations are often designed for continuous global coverage, and the few existing regional constellation design methods lead to suboptimal solutions for periodically time-varying or spatially varying regional-coverage requirements. This paper introduces a new general approach to design an optimal constellation pattern that satisfies such complex regional-coverage requirements. To this end, the circular convolution nature of the repeating ground-track orbit and common ground-track constellation is formalized. This formulation enables a scalable constellation pattern analysis for multiple target areas and with multiple subconstellations. The formalized circular convolution relationship is first used to derive a baseline constellation pattern design method with the conventional assumption of symmetry. Next, a novel method based on binary integer linear programming is developed, which aims to optimally design a constellation pattern with the minimum number of satellites. This binary integer linear programming method is shown to achieve optimal constellation patterns for general problem settings that the baseline method cannot achieve. Five illustrative examples are analyzed to demonstrate the value of the proposed new approach.

Fault Detection and Isolation System Based on Structural Analysis of an Industrial Seawater Reverse Osmosis Desalination Plant

Currently, the use of industrial seawater reverse osmosis desalination (ISROD) plants has increased in popularity in light of the growing global demand for freshwater. In ISROD plants, any fault in the components of their control systems can lead to a plant malfunction, and this condition can originate safety risks, energy waste, as well as affect the quality of freshwater. This paper addresses the design of a fault detection and isolation (FDI) system based on a structural analysis approach for an ISROD plant located in Lima (Peru). Structural analysis allows obtaining a plant model, which is useful to generate diagnostic tests. Here, diagnostic tests via fault-driven minimal structurally overdetermined (FMSO) sets are computed, and then, binary integer linear programming (BILP) is used to select the FMSO sets that guarantee isolation. Simulations shows that all the faults of interest (sensors and actuators faults) are detected and isolated according to the proposed design.

A mixed integer programming formulation for Smashed Sums puzzle: Generating and solving problem instances

Playing mind games and puzzles has 2500 years of known history. Puzzles and games constitute a research domain that is attracting the interest of scientists from numerous disciplines such as artificial and computational intelligence, neural networks etc. All types of puzzles and games contain their own logic and mathematics. Able to know the science behind them and modelling the logic that a person uses to solve them would shed light to some decisional concepts. This is particularly true from the perspective of computational intelligence. In this paper a logic-based puzzle game called Smashed Sums is considered. The binary integer linear programming formulation is proposed to use in solving and generating the puzzles. Illustrative examples are given to show the validity of the formulation. Some experimental computations are conducted to analyze the puzzle and its complexity. And several open problems are concluded for the further researches.

Lifetime optimization for partial coverage in heterogeneous sensor networks

In this work, we investigate the problem of lifetime optimization for partial coverage in heterogeneous sensor networks. This problem which is NP-Hard in its general form is known under the name of α-coverage, where α refers to a prescribed level of coverage threshold that we need to maintain. Sleep-Awake scheduling which turns sensors to On and Off, is the common and the well known technique that has been heavily studied in the literature to deal with energy management under coverage constraint. The question is how to orchestrate the clustering of the sensor nodes into disjoint or non-disjoint covers, and to schedule these covers, so that the total network’s lifetime is maximized. Unlike earlier works, we consider both global (whole targets) resp. local (individual target) monitoring thresholds to improve the coverage quality rather than dealing with a single global leveling threshold as in the literature. In addition, instead of employing a default covers’ activation which may lead to the starvation phenomenon, where targets may remain uncovered for a long time period, we provide a clairvoyant scheduling for the obtained covers to ensure fair smoothing for the cumulated target’s uncovered time periods during the network’s service. First, a novel mathematical Binary Integer Linear Programming (BILP) is proposed to solve the α-coverage problem to optimality. Then, provable guarantees of the upper bound for the number of partial cover sets are given. Next, we formulate the covers’ planning as a p-dispersion problem and due to the NP-Completeness of the former, an efficient Genetic Algorithm (GA) based approach is designed to achieve efficient covers’ scheduling with minimal execution time complexity. Finally, a series of experiments are conducted and several QoS metrics are evaluated to show the usefulness of our proposals.

On the Optimization of User Association and Resource Allocation in HetNets With mm-Wave Base Stations

This article investigates the problem of joint user association and resource allocation, defined by the number of allocated time-slots, in hybrid heterogeneous networks with the coexistence of sub-6-GHz base stations and millimeter wave (mm-Wave) base stations. To do so, we formulate a joint optimization problem to improve the efficiency of resource utilization by maximizing the number of associated users and minimizing the number of allocated time-slots. The optimization problem is formulated as a binary integer linear program and is proved to be NP-hard. Accordingly, we propose two efficient heuristic algorithms to solve it. The first one is centralized and relies on complete information, whereas the second one is distributed and is based on a reinforcement learning approach. The proposed distributed learning algorithm aims to find the best association for each user based on its past experience, automatically and independently from others. Simulation results show that the performances of both proposed algorithms are close-to-optimal with an important reduction in computational complexity.

Economically efficient, environment friendly & power stack shed reduction energy management system by utilizing renewable energy resources for remote hilly areas of Pakistan

In the current era, Energy Management has now become one of the most vital aspects of the power or energy system all over the world. With the increase in the power demand, generation capacity can’t be increased due to various economic, ecological and climate changing factors. Due to the depletion of the non-renewable energy sources with time, it is the need of the time to manage the electricity usage in such a way so that it can be maintained and sustained well with the increasing demand. Pakistan is facing several power and energy crisis issues. Along with the increasing power generation capacity it is quite necessary to manage the energy generation and utilization so that the power demand can be met satisfactorily. Energy Management in hilly areas of the country zone is a crucial issue for economical hydro, solar, wind and agriculture sustainability. In this paper, effective energy management demonstration of Renewable Energy Resources is produced to guarantee continuous supply of energy for remote hilly areas. In the proposed plot, power should be produced through water, wind and solar energy. Different wellsprings of energy management are being utilized to deal with the discontinuous nature of sustainable assets and unpredicted power stack shedding. Furthermore, limiting the ecological effects and cost of power to customers by utilizing multi-objective streamlining method. The proposed multi-objective optimization problem will be solved by using Binary Integer Linear Programming (BILP) incorporated by Branch & Bound Algorithm on MATLAB.

Edge-Enabled V2X Service Placement for Intelligent Transportation Systems

Vehicle-to-everything (V2X) communication and services have been garnering significant interest from different stakeholders as part of future intelligent transportation systems (ITSs). This is due to the many benefits they offer. However, many of these services have stringent performance requirements, particularly in terms of the delay/latency. Multi-access/mobile edge computing (MEC) has been proposed as a potential solution for such services by bringing them closer to vehicles. Yet, this introduces a new set of challenges such as where to place these V2X services, especially given the limit computation resources available at edge nodes. To that end, this work formulates the problem of optimal V2X service placement (OVSP) in a hybrid core/edge environment as a binary integer linear programming problem. To the best of our knowledge, no previous work considered the V2X service placement problem while taking into consideration the computational resource availability at the nodes. Moreover, a low-complexity greedy-based heuristic algorithm named "Greedy V2X Service Placement Algorithm" (G-VSPA) was developed to solve this problem. Simulation results show that the OVSP model successfully guarantees and maintains the QoS requirements of all the different V2X services. Additionally, it is observed that the proposed G-VSPA algorithm achieves close to optimal performance while having lower complexity.

A multi-constrained binary ILP method for optimal allocation of PMUs in network

This paper proposes multi-constrained binary integer linear programming (MBILP) method for optimal installation of phasor measurement units in IEEE networks considering Fast Load Voltage Stability Index (FLVSI), branch weight and redundancy constraints to minimize the cost of installation and to accomplish complete network observability. The weak buses of IEEE network are sorted based on their severity through the proposed strategy. A new FLVSI is programmed along with branch weight and redundancy constraints in MBILP to place PMUs in network. As installation cost of PMU for different buses varies with the number of branches or number of channels connected, PMUs should be allotted at bus with minimum cost. Redundancy of bus is computed to measure redundancy of bus network. Priority of PMU placement is considered at weak bus with proposed FLVSI in such a way that the cost is minimized and redundancy is adequate considering both branch weight and redundancy constraints. Ranking is proposed for PMU placement to find weak load bus in network along with the consideration of branch weight and redundancy. Zero injection (ZI) constraint modeling is recommended to minimize allocations further in system without losing observability. Contingency constraints for single-line or PMU loss are considered for allocation of PMUs. The proposed method is compared with ZI and without ZI modeling under general and line-outage or PMU loss cases to show efficacy of method. To estimate observability performance of complete network, a Complete Network Bus Observability Index is suggested. IEEE 14-, 24-, 30- and 57-bus networks are programmed with MATLAB software and compared with standard approaches to validate their efficacy.