Combinatorial Optimization Method Research Articles

Smart Grid Dispatching Optimization for System Resilience Improvement

A large number of modern communication technologies and sensing technologies are incorporated into the smart grid, which makes its structure unique. The centralized optimized dispatch method of traditional power grids is difficult to achieve effective dispatch of smart grids. Based on the analysis of power generation plan and maintenance plan optimization model, this paper establishes a smart grid power generation and maintenance collaborative optimization model with distributed renewable energy. The objective function of this collaborative optimization problem is the operating cost of conventional units, the cost of wind power generation, and the cost of overhauling units; the constraints considered mainly include system constraints and overhaul constraints. The solution method of combinatorial optimization is analyzed, and the genetic optimization algorithm adopted in this paper is selected and discussed. According to the characteristics of the system, various loads are modeled, and power supply constraints are considered. By establishing an effective objective function, the adjustable load scheduling problem is transformed into a solvable optimal control problem. Taking into account the uncertain factors in the system, the advantage of the real-time control system is that it can realize the dynamic update scheduling of the load, so it is more in line with the requirements of the actual system. The real-time algorithm proposed in the paper is based on a distributed control strategy, which can not only realize dynamic compensation for random fluctuations in renewable energy power generation but also satisfy the load curve optimization under the premise of making full use of power supply resources. In addition, simulation experiments compare the load dispatching capabilities of the proposed algorithm with the existing algorithms, thereby verifying the performance of the proposed method.

Research on combinatorial optimization of multidirectional sheet postures for forming thickness uniformity

To solve the problem of the uneven thickness distribution of a formed part caused by a large difference between the forming angles and the different curvatures of the surfaces in CNC incremental forming, a combinatorial optimization method of multidirectional sheet postures was proposed based on particle swarm optimization. In this method, an infinite number of optional sheet postures at each point in the forming area are taken as the combined object. The optimization goal is to make the forming angles of the entire sheet part be smaller than the forming limit angle and to minimize the difference between them; then find the optimal combination of the multidirectional sheet postures that can be selected at each point in the forming area. Case studies of the algorithm and the actual forming experiment show that not only can the optimized multidirectional sheet metal postures determined by the proposed method realize the non-fracture forming of the sheet metal parts with different forming angles and different curvature of the surface, but also obtain a more uniform thickness distribution of the formed parts.

On the Problem of a Linear Function Localization on Permutations

Combinatorial optimization problems and methods of their solution have been a subject of numerous studies, since a large number of practical problems are described by combinatorial optimization models. Many studies consider approaches to and describe methods of solution for combinatorial optimization problems with linear or fractionally linear target functions on combinatorial sets such as permutations and arrangements. Studies consider solving combinatorial problems by means of well-known methods, as well as developing new methods and algorithms of searching a solution. We describe a method of solving a problem of a linear target function localization on a permutation set. The task is to find those locally admissible permutations on the permutation set, for which the linear function possesses a given value. In a general case, this problem may have no solutions at all. In the article, we propose a newly developed method that allows us to obtain a solution of such a problem (in the case that such solution exists) by the goal-oriented seeking for locally admissible permutations with a minimal enumeration that is much less than the number of all possible variants. Searching for the solution comes down to generating various permutations and evaluating them. Evaluation of each permutation includes two steps. The first step consists of function decreasing by transposing the numbers in the first n – 3 positions, and the second step is evaluation of the permutations for the remaining three numbers. Then we analyze the correlation (which is called balance) to define whether the considered permutation is the solution or not. In our article, we illustrate the localization method by solving the problem for n = 5. Keywords: localization, linear function, permutation, transposition, balance, position.

Personalized manufacturing service composition recommendation: combining combinatorial optimization and collaborative filtering

Owing to the rapid proliferation of service technologies in cross-enterprise manufacturing collaborations, manufacturing service composition (MSC) has attracted much attention from both academia and industries. However, the existing service composition is often constructed by the combination of off-line and on-line services, quality of service (QoS) attributes are not appropriate for satisfying the specific demands of MSC. Moreover, there are very few historical QoS invocations of manufacturing service, leading to difficulty in recommending appropriate service composition to a target user. In order to find the personalized MSC mode from a complex service network more accurately, we combine combinatorial optimization with collaborative filtering in this paper to figure out two questions: (1) how to construct a QoS description model of manufacturing service composition; (2) how to enhance the effectiveness of personalized QoS-aware service composition recommendations. First, the new QoS model of MSC is proposed by considering both traditional characteristics (e.g. availability, performance and reliability), variability of service composition and enterprise dimensional QoS attributes. Second, the service combination optimization is constructed based on combinatorial optimization method. Third, the collaborative filtering is employed to calculate the missing QoS values of the candidate manufacturing services. Finally, with both available objective functions and predicted QoS values, optimal service composition recommendation can be generated by using combinatorial optimization model with QoS constraints.

Identification of conserved evolutionary trajectories in tumors.

As multi-region, time-series and single-cell sequencing data become more widely available; it is becoming clear that certain tumors share evolutionary characteristics with others. In the last few years, several computational methods have been developed with the goal of inferring the subclonal composition and evolutionary history of tumors from tumor biopsy sequencing data. However, the phylogenetic trees that they report differ significantly between tumors (even those with similar characteristics). In this article, we present a novel combinatorial optimization method, CONETT, for detection of recurrent tumor evolution trajectories. Our method constructs a consensus tree of conserved evolutionary trajectories based on the information about temporal order of alteration events in a set of tumors. We apply our method to previously published datasets of 100 clear-cell renal cell carcinoma and 99 non-small-cell lung cancer patients and identify both conserved trajectories that were reported in the original studies, as well as new trajectories. CONETT is implemented in C++ and available at https://github.com/ehodzic/CONETT. Supplementary data are available at Bioinformatics online.

Learning to Delay in Ride-Sourcing Systems: A Multi-Agent Deep Reinforcement Learning Framework

Ride-sourcing services are now reshaping the way people travel by effectively connecting drivers and passengers through mobile internets. Online matching between idle drivers and waiting passengers is one of the most key components in a ride-sourcing system. The average pickup distance or time is an important measurement of system efficiency since it affects both passengers’ waiting time and drivers’ utilization rate. It is naturally expected that a more effective bipartite matching (with smaller average pickup time) can be implemented if the platform accumulates more idle drivers and waiting passengers in the matching pool. A specific passenger request can also benefit from a delayed matching since he/she may be matched with closer idle drivers after waiting for a few seconds. Motivated by the potential benefits of delayed matching, this paper establishes a two-stage framework which incorporates a combinatorial optimization and multi-agent deep reinforcement learning methods. The multi-agent reinforcement learning methods are used to dynamically determine the delayed time for each passenger request (or the time at which each request enters the matching pool), while the combinatorial optimization conducts an optimal bipartite matching between idle drivers and waiting passengers in the matching pool. Four tailored reinforcement learning methods, delayed multi-agent deep Q learning (Delayed-M-DQN), delayed multi-agent actor-critic (Delayed-M-A2C), delayed multi-agent Proximal Policy Optimization (Delayed-M-PPO), and delayed multi-agent actor-critic with experience replay (Delayed-M-ACER), are developed. Through extensive empirical experiments with a well-designed simulator, we show that the proposed framework is able to remarkably improve system performances, by well balancing the trade-off among pick-up time, matching time, successful matching rate.

Theory and Methods of Euclidian Combinatorial Optimization: Current Status and Prospects

Euclidean combinatorial optimization problems are considered as discrete optimization problems on a set of combinatorial configurations mapped into an arithmetic Euclidean space. Modern methods of Euclidean combinatorial optimization are reviewed. The properties of the corresponding images of combinatorial sets are described. A theory of continuous functional representations and convex extensions is proposed for solving this class of problems. Areas of practical application and promising research areas are indicated.

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a prescription for choosing the variational parameters of the circuit. We propose modifications to both. First, we define the Gibbs objective function and show that it is superior to the energy expectation value for use as an objective function in tuning the variational parameters. Second, we describe an Ansatz Architecture Search (AAS) algorithm for searching the discrete space of quantum circuit architectures near the QAOA to find a better ansatz. Applying these modifications for a complete graph Ising model results in a $244.7\%$ median relative improvement in the probability of finding a low-energy state while using $33.3\%$ fewer two-qubit gates. For Ising models on a 2d grid we similarly find $44.4\%$ median improvement in the probability with a $20.8\%$ reduction in the number of two-qubit gates. This opens a new research field of quantum circuit architecture design for quantum optimization algorithms.

Two-Phase Neural Combinatorial Optimization with Reinforcement Learning for Agile Satellite Scheduling

The agile Earth observing satellite (AEOS) scheduling problem consists of scheduling a set of image acquisitions and selecting the start time of each acquisition, satisfying the constraints and maximizing the gain. With the development of satellite technologies and higher requirements of users, the AEOS scheduling problem has to consider constraints and criteria that vary with the run-time on-orbit state, such as the transition time constraint and image quality criteria. These requirements increase the difficulty to model the problem. In this paper, a two-phase neural combinatorial optimization method with reinforcement learning is proposed for the AEOS scheduling problem. First, a neural combinatorial optimization with the reinforcement learning method is proposed to select a set of possible acquisitions and provide a permutation of them. Second, with the selected acquisition sequence, a reinforcement learning algorithm based on deep deterministic policy gradient is proposed to select the start time of each acquisition under the time constraints. The experimental results with artificial instances show that the proposed method is a viable candidate for the highly combinatorial AEOS scheduling problem; furthermore, it has the ability to cope with the run-time assessment, like the transition time calculation and the image quality evaluation.

Highly sensitive microgrid protection using overcurrent relays with a novel relay characteristic

Following the high penetration of synchronous generators (SGs) in the power network, optimal overcurrent coordination improvement under faulty conditions has become a crucial problem. To reduce the overcurrent relay operating time, a new overcurrent relay curve is proposed in this study. Then, the overcurrent coordination problem is overcome by using a robust combinatorial optimisation method. Additionally, SG sizing and location is performed to verify the merits of both the proposed relay curve and the applied optimisation algorithm. The proposed relay curve performance is compared with other non-standard relays characteristic available in the literature for a standard microgrid. Then, the proposed relay curve is applied to both the 8-bus transmission and the 33 kV distribution portion of the 30-bus IEEE standard power test systems. Then, the SG transient stability for different fault locations is analysed. Finally, an accurate comparison between the proposed relay curve and standard/non-standard curves available in the literature is provided by applying the same optimisation method and network topology. The simulation results confirm the superiority of the proposed relay curve.

The selection of a priority package of measures for technical re-equipment and reconstruction of the district of electrical grids

Making decisions on the technical re-equipment and reconstruction of electrical grids needs analyzing a large amount of information, comparing a variety of options, evaluating the impact of a decision in the long term. Therefore, the process of formation of the package of measures is complicated. In this regard, it is necessary to develop an automated decision support system for selecting a priority package of measures for the technical re-equipment and reconstruction of the electrical grid district. The article presents the structure of the decisionmaking process for the technical re-equipment and reconstruction of the district of electrical grids, the model of formation and the method for selecting a priority package of measures. It is proposed to use graph theory for compiling a decision tree and methods of combinatorial optimization for the formation and selection of a priority package of measures. A two-level structural scheme of the decision-making process for the selection of a priority package of measures for the technical re-equipment and reconstruction of the electrical grids at the local and global levels has been developed.

Reentrant random quantum Ising antiferromagnet

We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ and uniformly distributed random transverse fields ($\Gamma_0 \le \Gamma_i \le 2\Gamma_0$) in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (DMRG, combinatorial optimisation and strong disorder RG methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line ($h=0,\Gamma_0=1$) there is an infinite disorder quantum fixed point, while at the other end ($h=2,\Gamma_0=0$) there is a classical random first-order transition point. Close to this fixed point, for $h>2$ and $\Gamma_0>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.

An optimal control approach to scheduling and production in a process using decaying catalysts

This article presents a novel approach to optimise scheduling and production planning to meet seasonal demand in an industrial process using decaying catalysts, based on its formulation as a multistage mixed-integer optimal control problem (MSMIOCP). Unlike existing methodologies, the MSMIOCP formulation allows to solve this problem as a standard nonlinear optimisation problem without combinatorial optimisation methods, which can be advantageous in providing reliable, robust and efficient solutions. Using this formulation, four case studies of this problem, differing in reaction or deactivation kinetics, are investigated. Two different solution implementations are used, each having their own relative advantages. The first implementation demonstrates a bang-bang behaviour for the linear scheduling controls, consistent with a theoretical analysis, but faces integration problems and does not always produce high quality solutions. The second implementation, while not demonstrating the bang-bang property, always produces high quality solutions and shows the advantages of the MSMIOCP formulation over existing methodologies.

Synthesis of the topological structure of a self-healing and scalable data network segment

An approach is proposed to reduce the load on the backbone channels of the data network. The scientific novelty lies in the improvement of the method for reducing the load of backbone channels by synthesizing the topological structure of its segments, which have the properties of local self-healing and scalability, and segment recovery and scaling occur without access to the backbone channels of the main network. The following tasks were solved: the structure of the primary regular communication network was formed, assuming the possibility of self-recovery; an algorithm for the formation of a secondary communication network of a local segment based on the existing primary regular network has been developed; the principles of local scaling are formulated; a method for local scaling of the topological structure of data transmission network segments is proposed; the comparative analysis of the load of the main channels of the data transmission network was carried out using the standard and the proposed variants of the synthesis of its local components. A regular graph with a given connectivity is used as the initial structure. Further transformations were carried out using a modified combinatorial optimization method. The topological features of the "grid" type graph are used to scale the segment. With a large number of segment switching nodes, the additional load on the trunk channels increases with the proposed approach more slowly than with the standard one. The main computational difficulties arise when applying the method of indefinite Lagrange multipliers. Therefore, the development of this study may consist in reducing the computational complexity of the algorithm for forming a secondary communication network of the segment under consideration.

Configuration-Making Algorithm for the Smart Machine Controller Based on the Internet of Things Concept

This article focuses on the approaches of selecting cost-effective solutions to configurations of hardware components in digital systems (in particular, smart machines) by the combinatorial optimization method. A search for the solution to the application of cross-functional or special-purpose hardware components for LoT devices is a multi-criteria objective. The proposed selection algorithm for the configuration of hardware components feeds on rigorous formalization and ranking of qualitative indicators, parameters and key features of the components in question. The authors have applied the algorithm in the MatLab environment in order to choose the best configuration of hardware components for the smart machine intended to be a core of an intelligent control unit for an analysis of AC network parameters and control over the actuating electromechanical devices. The results of the analysis have become a ground for the development of the special-purpose controller for an intelligent module of the smart machine. The synthetic solution to a configuration of the smart controller provides an analysis of monitoring data. It can also make it possible for the smart machine to transfer data via a service interface to an external automation controller, which remotely disconnects the machine at the command of a user. The result of the design procedure is the advisable configuration of the special-purpose smart machine controller intended to analyze the AC network parameters obtained using the proposed design methodology.

THE METHOD OF EFFICIENT DISTRIBUTION OF DIFFERENT ELEMENTS OF A COMPLEX SYSTEM OF CONTROL

Context. An important prerequisite for reliable protection of the state border of Ukraine is the effective detection of violators of the border. For this purpose, various state-of-the-art systems and observation complexes are used at the border agency, and some border dresses are equipped with the latest technical means of border guarding. The diversity of possibilities of individual means of observation in their complex use makes it important to determine the effective location of observation points, taking into account the features of the terrain. Objective. The purpose of the work is to develop a method for effective placement of elements of complex surveillance systems of the border agency. Method. The work proposes a heuristic approach to solving the problem of determining the effective placement of different capabilities of technical means of observation. The developed method is based on the cyclic use of the known method of combinatorial optimization of placement of observation points for all components of a complex surveillance system of the border agency with adjustment after each iteration of the overburden. At the same time, with the use of geo-processing takes into account the barrier to the negative impact of terrain and the possibility of different technical means of surveillance in different conditions. To assess the effectiveness of the functioning of the components of the surveillance system, an indicator is used reflecting the share of the area of the strip of overlap, which provides the identification of objectives. Results. As a result of using the proposed methodology, a rational structural construction of a complex surveillance system of the border guard body and a set of uncontrolled points of the area are obtained. This plurality can be used in planning the service of the units of the border guard. The description of algorithmic and program realization of the proposed method is given. Using the developed software, the optimization of the placement of three types of elements of a complex observation system (towers of the system of optoelectronic observation, mobile thermal imaging complexes, observation posts) was carried out. Conclusions. Modern construction of complex surveillance systems of the border agency in many cases is not optimal. To increase the efficiency of their operation, it is possible to use the proposed method of placement of elements of these systems on the ground.

Optimal partial clique edge covering guided by potential energy minimization

For given integers k, n, r we aim at families of k sub-cliques called blocks, of a clique with n vertices, such that every block has r vertices, and the blocks together cover a maximum number of edges. We demonstrate a combinatorial optimization method that generates such optimal partial clique edge coverings. It takes certain packages of columns (corresponding to vertices) in the incidence matrix of the blocks, considers the number of uncovered edges as an energy term that has to be minimized by transforming these packages. As a proof of concept we can completely solve the above maximization problem in the case of kle 4 blocks and obtain optimal coverings for all integers n and r with r/nge 5/9. This generalizes known results for total coverings to partial coverings. The method as such is not restricted to kle 4 blocks, but a challenge for further research (also on total coverings) is to limit the case distinctions when more blocks are involved.

IMPROVEMENT OF THE MECHANISM OF SELECTION OF SUBSOIL PLOTS TO TRANSFER TO TAX ON ADDITIONAL INCOME FROM THE EXTRACTION OF HYDROCARBONS

Since 2019, in pilot mode (a list of pilot projects — 35 subsoil plots, the volume of production of which is about 4% of Russia’s annual oil production), a federal tax on additional income from the extraction of hydrocarbon raw materials (TAI) has come into effect. TAI refers to tax mechanisms based on economic results, in contrast to the current mineral extraction tax, where taxable items are gross indicators of the amount or cost of hydrocarbons produced. The transition from tax mechanisms based on gross figures to taxation based on economic results has been the global trend of the last fifty years. TAI can be an effective tax incentive mechanism that can ensure the involvement in the development of low-margin hydrocarbon reserves in the current taxation, as well as the introduction of promising methods to increase oil recovery. Currently, according to the Tax Code of the Russian Federation, the TAI can be applied to IV groups of subsoil plots (indicating their location and the degree of depletion of reserves). At the same time, the selection criteria for these plots do not fully take into account the tasks facing the state (budget, public, technological, etc.). Considering that the Ministry of Finance of Russia, based on the results of the implementation of pilot projects, envisages a gradual transition of the oil industry to TAI, an urgent task is to improve the selection mechanism of mining projects to provide this tax preference, including by developing a comprehensive system of selection criteria and a transparent methodology for ranking projects. The proposed approach to competitive selection of subsoil plots for transfer to TAI is based on weighted sum and combinatorial optimization methods.

OPTIMIZATIONAL TRACTION TASKS ON THE RAILWAY NETWORK

Purpose. The paper involves the development of information and algorithmic support for conducting the optimization traction and energy calculations on the railway network for their further use in decision-making systems – systems for efficient management of the transport process. Methodology. The system is based on the graph-analytic system, the model of the train with different types of traction, the methods of optimal control of the train and the fundamental algorithms on the weighted graphs with possible parallel ribs (arcs). In the complex, these components of the system provide finding the tracks on the chart-diagram according to the given criteria, conducting the optimization traction-energy calculations according to different criteria, as well as conducting a comparative analysis of the obtained results. The reliability of the results has been repeatedly checked by available methods for varying complexity of race according to the plan and profile of the course. For this purpose, data obtained as a result of control visits using dynamometric cars were used. Also a comparative analysis of the modes in operation of trains, calculated and received by qualified drivers on different races was conducted. Findings. The problem of efficient operation of various types and modifications of locomotives, involved in the implementation of trains schedules for different purposes and loads is considered. Presentations of direct and inverse optimization, according to various criteria, of the regime tasks on the railway network and variants of their effective solution are given. The analysis of the results of the developed mathematical support and the ideas of implemented algorithms is given. Originality. The paper proposes the establishment of the network optimization problems that arise at the stages of the developing the plan for the formation, construction of traffic schedules, transmission capacity assessment and the calculation of optimal parameters for the composite graphs of motion, etc. The system approach is important to ensure the combination of the developed network structure in the universal terms of the graph theory with the system of actualization of their parameters. Pull and energy efficiency calculations are carried out by combinatorial optimization methods, which ensured the maximum level of automation of the process in solving a large set of direct and inverse regime problems with different optimality criteria. Practical value. The information and algorithmic support for the automation of the process in solving the direct and reverse regime traction-energy problems on the railway network was developed. It was tested in the process of calculating the main components for the formation of traffic schedules, analysis of train driving modes, assessment in choosing the optimal parameters of the track reconstruction for high-speed and new types of trains (locomotives).

Development and use of a Cytoscape app for GRNCOP2

Background and Objective: Gene regulatory networks (GRNs) are essential for understanding most molecular processes. In this context, the so-called model-free approaches have an advantage modeling the complex topologies behind these dynamic molecular networks, since most GRNs are difficult to map correctly by any other mathematical model. Abstract model-free approaches, also known as rule-based extraction methods, offer valuable benefits when performing data-driven analysis; such as requiring the least amount of data and simplifying the inference of large models at a faster analysis speed. In particular, GRNCOP2 is a combinatorial optimization method with an adaptive criterion for the discretization of gene expression data and high performance, in contrast to other rule-based extraction methods for discovering GRNs. However, the analysis of the large relational structures of the networks inferred by GRNCOP2 requires the support of effective tools for interactive network visualization and topological analysis of the extracted associations. This need motivated the possibility of integrating GRNCOP2 in the Cytoscape ecosystem in order to benefit from Cytoscapes core functionality, as well as all the other apps in its ecosystem.Methods: In this paper, we introduce the implementation of a GRNCOP2 Cytoscape app. This incorporation to Cytoscape platform includes new functionality for GRN visualizations, dynamic user-interaction and integration with other apps for topological analysis of the networks.Results: In order to demonstrate the usefulness of integrating GRNCOP2 in Cytoscape, the new app was used to tackle a novel use case for GRNCOP2: the analysis of crosstalk between pathways. In this regard, datasets associated with Alzheimer’s disease (AD) were analyzed using GRNCOP2 app and other apps of the Cytoscape ecosystem by performing a topological analysis of the AD progression and its synchronization with the Ubiquitin Mediated Proteolysis pathway. Finally, the biological relevance of the findings achieved by this new app were evaluated by searching for evidence in the literature.Conclusions: The proposed crosstalk analysis with the new GRNCOP2 app focused on assessing the phase of the Alzheimer’s disease progression where the coordination with the Ubiquitin Mediated Proteolysis pathway increase, and identifying the genes that explain the signalling between these cellular processes. Both questions were explored by topological contrastive analysis of the GRNs generated for the GRNCOP2 app, where several facilities of Cytoscape were exploited. The topological patterns inferred by this new App have been consistent with biological evidence reported in the scientic literature, illustrating the effectiveness of using this new GRNCOP2 App in pathway analysis.Availability: The GRNCOP2 App is freely available at the official Cytoscape app store: http://apps.cytoscape.org/apps/grncop2