Integer Linear Programming Problem Research Articles

Modeling and analysis of crosstalk-avoided and crosstalk-aware approaches in spectrally-spatially elastic optical networks

Inter-core crosstalk (Ic-Xt) and inter-mode crosstalk (Im-Xt) occur during the transmission of optical signals through multi-core multi-mode fibers in spectrally-spatially elastic optical networks (SS-EONs), which degrade the signal quality. Xt-Avoided (Xt-Av) and Xt-Aware (Xt-Aw) approaches, respectively, are used in SS-EONs for dealing with Ic-Xt and Im-Xt. From the network deployment perspective, network operators need to understand which approach, Xt-Av or Xt-Aw, is better in order to deal with Ic-Xt and Im-Xt in SS-EONs. To address the above issue, this paper models and analyzes Xt-Av and Xt-Aw approaches by considering Ic-Xt and Im-Xt simultaneously in SS-EONs. We formulate the optimization problems as the integer linear programming (ILP) problem for both Xt-Av and Xt-Aw approaches. When the ILP problems are intractable, we introduce heuristics for Xt-Av and Xt-Aw approaches. We compare ILP and heuristic approaches using Xt-Av and Xt-Aw in terms of the maximum allocated spectrum slot index, blocking ratio, and computation time. Numerical results indicate that the Xt-Aw approach for all Xt threshold values performs better than the Xt-Av approach in terms of resource utilization. At the same time, the Xt-Av approach has the advantage of using less computation time than the Xt-Aw approach. The analysis reveals that, in the Xt-Aw approach, the behavior of the maximum allocated spectrum slot index and blocking ratio on Xt threshold is reciprocal, and hence a suitable Xt threshold that enhances the network performances is required for network management.

Multi-source multicast service chaining model guaranteeing reliability of network services

Service chaining provides network services to users by processing packets with a series of virtualized network functions (VNFs). Multicast communication can suppress the network load compared to unicast communication when the same service is provided to multiple users simultaneously. Network providers need to ensure that services are provided to users under reliability requirements. Existing service chaining models can cause failure-intolerant or cost-inefficient resource allocation for multicast services. This paper proposes a multi-source multicast service chaining model that guarantees the reliability of network services with flexible routing and VNF placement. The proposed model determines the routing and VNF placement for each service chain request with redundancy so as to minimize the total resource utilization cost while satisfying the reliability requirement. In order to obtain cost-efficient feasible solutions, we introduce two heuristic algorithms. One is an algorithm that iteratively solves an integer linear programming problem until the reliability requirements are satisfied for all requests. The other is an algorithm that determines the VNF placement by using a metric based on the betweenness centrality and server failure rate. Numerical results show that the proposed model allocates the network and computation resources for services with lower total cost compared to the existing model. We also show illustrative examples of the resource allocation to compare the characteristics of two heuristic algorithms.

Mobility-aware task offloading in MEC with task migration and result caching

Numerous computation-intensive applications have emerged, demanding lower delay and energy consumption. Multi-access Edge Computing (MEC) provides task offloading services for mobile users (MUs) through proximate MUs, effectively minimizing service delay and energy consumption. However, the challenges of supporting MUs’ mobility persist, and ensuring uninterrupted task offloading services from MEC servers still needs to be solved. Additionally, applications like autonomous driving generate repetitive tasks, introducing unnecessary computational overhead. This paper adopts a task migration strategy to tackle these issues, specifically addressing task offloading failure due to MU mobility. Simultaneously, a computation-result cache-assisted technique is leveraged to alleviate the burden of repetitive computation. The objective is to minimize the system cost, which consists of the processing delay and energy consumption of tasks for all MUs. The problem is modeled as an integer linear programming problem, and the optimal solution is meticulously derived. In response to the high computational complexity inherent in obtaining the optimal solution, a low-complexity heuristic algorithm (CMHA) is introduced. Simulation results demonstrate that optimal and heuristic schemes significantly reduce the overall system delay and energy consumption.

Enhancing target benefits of power system stakeholders: A columns and constraint generation-based power-to-gas linked economic dispatch

Economic dispatch (ED) plays a crucial role in optimizing power plant output to minimize the cost of electricity production and ensure economic efficiency in complex power systems. However, with the growing emphasis on carbon neutrality policies and the increased use of renewable energy sources (RES), traditional ED models may lead to economic losses for independent power producers (IPP) and renewable energy providers (REP). To address this challenge, a new ED model is proposed in this study, which integrates power-to-gas (P2G) technology and takes into account the perspectives of all stakeholders, including independent system operator (ISO) IPP, and REP. The proposed approach is tested in the context of the cost based pool (CBP) market structure in S. Korea, where a mixed integer linear programming (MILP) problem is solved for each target benefit using columns and constraint generations (C&CG). By ensuring the target benefits of each stakeholder group, this improved ED model aims to encourage their participation in the power system and support economic efficiency. The simulation results of the P2G-linked ED proposed in this paper verify that as the capacity of the integrated P2G increases, there is an increase in the improvement rate of each target benefit for ISO, IPP, and REP.

Generalization of the method based on parameterization developed for solving integer programming problems

This study presents the generalization of methods based on parameterization proposed for solving integer programming problems with linear objectives and linear constraints. Initially, the method based on parameterization, proposed for solving 2, 3, and 4-variable integer linear programming problems, is generalized to n-variable integer linear programming problems. The proposed method relies on the parameterization obtained from Diophantine equations. Using this parameterization, the original problem is reformulated as another integer linear programming problem that can be solved more efficiently using simple mathematical programming. The method can be used regardless of the number of constraints of the problem and also provides all alternative solutions to the decision maker. It is demonstrated with some examples that this method provides an efficient algorithm.

Optimal routing and heterogeneous resource allocation for computing-aware networks

Computing-aware networking (CAN) is introduced to unite the computing resources distributed in different platforms. This paper proposes a joint routing and resource allocation model to minimize the total operational cost in CAN. We formulate the problem as an integer linear programming problem. We introduce a polynomial-time algorithm for larger-size problems. The numerical results reveal that the introduced algorithm reduces the computation time 9.18 times, with increasing the objective no more than 4% compared to the optimal solution; the proposed model can reduce 70% of the total cost compared to a baseline adopting a two-stage strategy in our examined cases.

Total Unimodularity and Strongly Polynomial Solvability of Constrained Minimum Input Selections for Structural Controllability: An LP-Based Method

This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given an autonomous system and a prescribed set of input links, where each input link has a non-negative cost, the problems include selecting the minimum cost of input links and selecting the input links with the smallest possible cost while bounding their cardinality to achieve system structural controllability. Current studies show that in the dedicated input case (i.e., each input can actuate only one state variable), the former problem is polynomially solvable by some graph-theoretic algorithms, while the general nontrivial constrained case is largely unexplored. We show that these problems can be formulated as equivalent integer linear programming (ILP) problems. Subject to the 'source strongly-connected component grouped input constraint', which contains the dedicated input one as a special case, we demonstrate that the constraint matrices of these ILPs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">totally unimodular</i> . This property allows us to solve these ILPs efficiently via their linear programming (LP) relaxations, leading to a unifying algebraic method for these problems with polynomial time complexity. We further show that these problems can be solved in strongly polynomial time, independent of the size of the costs and cardinality bounds. Finally, we provide an example to illustrate the power of the proposed method.

Optimal scheduling of park electric and cooling system considering multi-energy synergy

The park’s electric refrigeration system exhibits complex coupling relationships and heterogeneous operational characteristics, making it difficult to achieve optimal operation. Therefore, a strategy for optimizing the park’s electric refrigeration system, considering the potential for mutual assistance from multiple energy sources, is proposed. Firstly, an introduction to the structure of the park’s electric refrigeration system is provided. Subsequently, operational constraints for the park’s units are established through quantitative analysis of the operational characteristics of systems such as the photovoltaic power generation system. Based on this, an optimization scheduling strategy for the park’s electric refrigeration system is proposed to minimize system operating costs. Finally, the model is transformed into a Mixed Integer Linear Programming (MILP) problem by employing linearization techniques. Simulation results demonstrate the effectiveness of the proposed strategy.

A Tool to Optimize the Participation of BESS to the UK Ancillary Services Market

In the last decade, several applications and studies have demonstrated that, thanks to their fast response time, Battery Energy Storage Systems (BESSs) are a promising technology to incorporate operational flexibility in grids and plants, opening to the possibility of providing a set of different grid services. In this context, this paper defines an optimization model to encode UK market rules and output the optimal set of offers on day-ahead and intraday markets, dynamic frequency response services and imbalance settlement, with a specific focus on a BESS. The proposed mathematical model includes BESS technical constraints and market temporal sequencing, also modelling the State Of Energy Management. Limitations on the number of cycles per day and optimization of the battery use are implemented. A Mixed Integer Linear Programming problem is defined to reduce the computational burden and to integrate the model in the Energy Management System (EMS) developed by the University of Genoa. Specific tests have been performed, allowing to compare scenarios in which ancillary services are enabled or not. According to the results, Dynamic Frequency Response services are the most profitable market. The integration in the EMS of the constraints related to the encoded market sections allows to exploit this tool to evaluate the profitability of investments involving a BESS over long time horizon.

Solving Mixed Integer Linear Programming Problems with bounded variables by the Adaptive Method

Solving Mixed Integer Linear Programming Problems with bounded variables by the Adaptive Method

A distributionally robust energy management of microgrid problem with ambiguous chance constraints and its tractable approximation method

As the penetration of intermittent renewable energy increases in microgrid systems, flexible power generation resources cause the power imbalance problem. To improve the absorption of renewable energy and to deal with its uncertainty more effectively, this paper proposes a distributionally robust approximate model for microgrid with ambiguous chance constraints (DR-CCP). First, the distributionally robust model with ambiguous chance constraints is a semi-infinite chance constrained planning problem, which is computationally difficult and inefficient, so the use of Chernoff's inequality to derive a safe tractable approximation form for the ambiguous chance constraint on the basis of a probability distribution for ambiguous sets including bounded perturbations with mean zero, transforms it into a mixed integer linear programming problem that can be directly solved using CPLEX to solve it. Then, the optimal value of the proposed model is used to approximate equivalent conditional value at risk (CVaR), and the relationship with CVaR is established. The optimal solution of our model is employed to construct multiple sets of comparison models, enhancing the richness of numerical experiments. Finally, to validate the feasibility and effectiveness of our proposed model, a series of diverse tests are performed on the IEEE 33-bus power distribution system.

Tabu Search-Based Heuristic Solver for General Integer Linear Programming Problems

Tabu Search-Based Heuristic Solver for General Integer Linear Programming Problems

A genetics algorithms for optimizing a function over the integer efficient set

In this paper, we propose an algorithm called Directional Exploration Genetic Algorithm (DEGA) to resolve a function Phi over the efficient set of a multi-objective integer linear programming problem (MOILP). DEGA algorithm belongs to evolutionary algorithms, which operate on the decision space by choosing the fastest improving directions that improve the objectives functions and Phi function. Two variants of this algorithm and a basic version of the genetic algorithm (BVGA) are performed and implemented in Python. Several benchmarks are carried out to evaluate the algorithm's performances and interesting results are obtained and discussed.

Исследование методов решения задач смешанного целочисленного линейного программирования

The paper discusses mathematical methods and software designed to solve optimization problems with linear objective functions and constraints, subject to additional restrictions on the integrality of variables. The main algorithms for combinatorial optimization are outlined and a comparative analysis of current packages and solvers for solving mixed integer linear programming problems in Python is carried out.

Recovering sign bits of DCT coefficients in digital images as an optimization problem

Recovering unknown, missing, damaged, distorted, or lost information in DCT coefficients is a common task in multiple applications of digital image processing, including image compression, selective image encryption, and image communication. This paper investigates the recovery of sign bits in DCT coefficients of digital images, by proposing two different approximation methods to solve a mixed integer linear programming (MILP) problem, which is NP-hard in general. One method is a relaxation of the MILP problem to a linear programming (LP) problem, and the other splits the original MILP problem into some smaller MILP problems and an LP problem. We considered how the proposed methods can be applied to JPEG-encoded images and conducted extensive experiments to validate their performances. The experimental results showed that the proposed methods outperformed other existing methods by a substantial margin, both according to objective quality metrics and our subjective evaluation.

Project Portfolio Management in a Multi-project Environment

Creating a portfolio of projects is an important scientific and practical task that applies to all areas of human activity, and the field of information technology is no exception. Research has shown that there are multiple approaches to solving this task, each characterized by certain features. Known methods of resource allocation have been analyzed, classified, and shown to be primarily related to linear programming problems, resource distribution matrices, or based on empirical knowledge. The project portfolio formation model was presented as a fuzzy problem of integer linear programming. A structural approach was used to depict the functioning principles of the system and information flows. An analysis was conducted, and development tools were selected. The outcome of the work resulted in a prototype of the software. Further research will focus on verifying the system's performance and constructing related modules.

A novel state estimation method for distribution networks with low observability based on linear AC optimal power flow model

The state estimation (SE) problem is one of the key functions in real-time control and management of modern electrical distribution networks. However, due to the complex network configuration and the limited number of measuring devices in these networks, the SE problem faces many challenges. In this manuscript, a new state estimation methodology is proposed based on the AC optimal power flow (ACOPF) model for distribution networks with a small number of real-time measurements. The proposed method is formulated in the form of a mixed integer linear programming problem (MILP), where the estimated states are regarded as the decision variables in the optimization problem. The load consumption values are also assumed as the decision variables where the estimation limits of these variables are determined by pseudo-measurements taken from the historical data. The main objective function is to maximize the state estimation accuracy, while the power flow equations are defined as the problem constraints. The efficiency of the proposed methodology is evaluated by implementing on the test networks and comparing the estimation results accuracy with the conventional weighted least squares (WLS) method. The obtained numerical results show the superior performance of OPF-based SE model to WLS method. Moreover, linearizing the formulation demonstrates an acceptable precision while ensuring convergence and optimum solution in low observability conditions.

Optimization of power dispatching schedule of a charging station based on a micro grid with a photovoltaic module

The world is on a course toward total electrification of vehicles. In the near future, most vehicles will run on electric power. One of the main reasons for users' dissatisfaction with electric vehicles is the lack of public direct current charging stations. Since electric vehicles charging can cause an additional increase in peak load on the grid, the optimal solution is direct current charging stations with photovoltaic generation with a micro grid architecture. If the charging station has a connection to the public grid, then, provided that the solar energy and storage system are optimally utilized, the station aggregator's profit can be increased by selling excess energy to the grid. This paper analyzes the charging habits of customers at direct current charging stations. It was found that the peak demand for charging is observed around 9:00 and 14:00-17:00, the same time as the general peak load on the grid. Thus, the peak charging demand coincides with the peak grid load and increases the net peak of the system. However, this excess demand on the system in the form of charging load can be met by the installed solar photovoltaic system, as the output power of the photovoltaic system is sufficient to meet the charging demand during the peak hours of solar radiation. Thus, for the considered direct current charging station, the optimization problem of dynamic economic dispatch was formulated, since the generation and load schedules change over time. The goal of optimization is to minimize the cost of primary energy. This problem, formalized as a mixed integer linear programming problem, was solved using the interior-point solver of the GEKKO library in Python. Four scenarios for the operation of the station were worked out, in summer and winter, with a fixed and dynamic electricity tariff. According to the results of the study, it was found that in the conditions of a fixed tariff in the summer, the cost of primary energy can be reduced 2.5 times, in fact, increase profits, thanks to the sale of electricity to the public grid. In winter, the use of the optimization algorithm of the station will provide an insignificant cost savings due to low photovoltaic generation. Under the conditions of a dynamic tariff that corresponds to the prices on the day-ahead market, using the optimization algorithm, it was found that for this experimental variant of the station's operation, the maximum profit in summer will be 207.60 UAH, while in winter the cost of primary energy will be 177.47 UAH. The results obtained indicate that the operation of a charging station under dynamic tariffs in the day-ahead market in Ukraine is a promising direction for the development of charging infrastructure in the country and proves the possibility of efficient use of renewable energy sources. Thus, this paper analyzes the global experience of developing charging stations based on micro grids, the integration of renewable energy sources into them, and approaches to building electricity dispatch schedules. The financial feasibility of the station's operation in the context of the electricity market in Ukraine was also investigated

Simultaneous capacity configuration and scheduling optimization of an integrated electrical vehicle charging station with photovoltaic and battery energy storage system

The implementation of an optimal power scheduling strategy is vital for the optimal design of the integrated electric vehicle (EV) charging station with photovoltaic (PV) and battery energy storage system (BESS). However, traditional design methods always neglect accurate PV power modeling and adopt overly simplistic EV charging strategies, which might result in suboptimal and infeasible designs. This study proposes a novel simultaneous capacity configuration and scheduling optimization model for PV/BESS integrated EV charging stations, which combines hybrid modeling for PV power prediction and optimal scheduling method for charging piles. The original model is then converted to a mixed integer linear programming problem by the Big-M method to greatly reduce the computational complexity. A typical scenario of commercial region is employed to demonstrate the effectiveness of the proposed approach. The results indicate that the approach could improve economic benefits by 15.67 % and reduce carbon emissions by 37.14 % compared with the entire grid-based mode. Besides, integrating the PV hybrid modeling method and optimal charging scheduling strategy could achieve superior capacity configurations and greatly improve the comprehensive performance of the system. It is thus illustrated that the approach could provide a promising solution for the optimal design and scheduling of PV/BESS integrated EV charging stations.

Distributionally robust optimization model considering deep peak shaving and uncertainty of renewable energy

In order to achieve the goal of carbon neutrality, the capacity of renewable power generation is continuously expanding while thermal power units are transitioning from main power source to auxiliary power source. To alleviate the peak shaving burden of thermal power units under the uncertainty of renewable energy and improve the absorption level of renewable energy, a two-stage distributionally robust optimization (DRO) model considering deep peak shaving and the uncertainty of renewable energy is proposed. The day-ahead unit commitment solutions are determined in the first stage, and the detailed scheduling strategies are obtained in the second stage. Column-and-constraint generation (C&CG) algorithm is applied to solve the model, and the master problem and subproblem are reformulated as duality-free mixed integer linear programming problems. The results show that the scheduling strategy obtained based on the model can alleviate the peak shaving burden brought by the uncertainty of renewable energy and reduce the abandonment rate of wind resources and solar resources, and the proposed DRO model provides a good trade-off between economy and robustness compared to stochastic optimization (SO) and robust optimization (RO).