Combinatorial Optimization Method Research Articles

Ensemble Technique of Deep Learning Model for Identifying Tomato Leaf Diseases Based on Choquet Fuzzy Integral

As tomato leaves are often attacked by various microorganisms, pests and bacterial diseases, the yield of tomato is seriously reduced. Accurate and timely identification of tomato leaf diseases is of great significance to reduce farmers’ economic losses. Ensemble learning as a combinatorial optimization method, which can improve the generalization ability and model stability, is widely used in the field of plant leaf disease identification. However, commonly used ensemble methods such as majority voting, weighted averaging, etc. do not consider the interaction between inputs when aggregating the inputs of multiple models, such that they do not produce representative outputs. To solve this problem, this paper adds fuzzy algorithms to the ensemble method, i.e., five pre-trained deep learning models, namely VGG16, VGG19, Xception and InceptionV3 and InceptionResnet V2, are integrated using Choquet integral fuzzy integrals for four classes of tomato disease identification and classification. The experimental results show that the proposed method achieves encouraging results, with the best single deep learning model achieving 98.63% accuracy on the PlantVillage dataset and the proposed fuzzy ensemble method achieving 99.80% accuracy. For the identification of tomato diseases in natural scenarios, the proposed method achieves 97% accuracy. The method can effectively identify tomato diseases.

DockingGA: enhancing targeted molecule generation using transformer neural network and genetic algorithm with docking simulation.

Generative molecular models generate novel molecules with desired properties by searching chemical space. Traditional combinatorial optimization methods, such as genetic algorithms, have demonstrated superior performance in various molecular optimization tasks. However, these methods do not utilize docking simulation to inform the design process, and heavy dependence on the quality and quantity of available data, as well as require additional structural optimization to become candidate drugs. To address this limitation, we propose a novel model named DockingGA that combines Transformer neural networks and genetic algorithms to generate molecules with better binding affinity for specific targets. In order to generate high quality molecules, we chose the Self-referencing Chemical Structure Strings to represent the molecule and optimize the binding affinity of the molecules to different targets. Compared to other baseline models, DockingGA proves to be the optimal model in all docking results for the top 1, 10 and 100 molecules, while maintaining 100% novelty. Furthermore, the distribution of physicochemical properties demonstrates the ability of DockingGA to generate molecules with favorable and appropriate properties. This innovation creates new opportunities for the application of generative models in practical drug discovery.

Learning Encodings for Constructive Neural Combinatorial Optimization Needs to Regret

Deep-reinforcement-learning (DRL) based neural combinatorial optimization (NCO) methods have demonstrated efficiency without relying on the guidance of optimal solutions. As the most mainstream among them, the learning constructive heuristic (LCH) achieves high-quality solutions through a rapid autoregressive solution construction process. However, these LCH-based methods are deficient in convergency, and there is still a performance gap compared to the optimal. Intuitively, learning to regret some steps in the solution construction process is helpful to the training efficiency and network representations. This article proposes a novel regret-based mechanism for an advanced solution construction process. Our method can be applied as a plug-in to any existing LCH-based DRL-NCO method. Experimental results demonstrate the capability of our work to enhance the performance of various NCO models. Results also show that the proposed LCH-Regret outperforms the previous modification methods on several typical combinatorial optimization problems. The code and Supplementary File are available at https://github.com/SunnyR7/LCH-Regret.

К ВОПРОСУ О ФОРМАЛИЗАЦИИ ЗАДАЧИ РАНЖИРОВАНИЯ ТРЕБОВАНИЙ ИНФОРМАЦИОННОЙ БЕЗОПАСНОСТИ

The article is devoted to the issue of requirements fulfillment aimed at ensuring information security in an organization. The main contradiction of the subject area concerned is pointed out, which consists in the presence of a huge number of different variants of requirements fulfillment in the absence of a possibility to choose their correct and optimal order. The task of requirements ranking is set and the idea of the proposed solution is described in the form of seven provisions aimed at coordinated recording of heterogeneous requirements in a single notation, and an intuitive scheme of the idea is synthesized (with all seven provisions indicated on it).
 To represent the idea, the following entities are introduced: an object-organization and its elements to which requirements are imposed; generalized conditions for satisfying requirements that do not depend on the specifics of the organization; variations of sets of conditions that take into account a particular organization; basic conditions that check the presence/absence of elements 
 of the object and the values of their parameters; algorithms of activities in the organization to satisfy the conditions; priorities of requirements and resources needed by the algorithms. It is concluded that such formalization will lead organically to the algorithmic solution of the ranking problem and, eventually, to automation.
 The most suitable automated ways of solving the problem of ranking information security requirements – algorithmic application of combinatorial optimization and machine learning methods – are specified. Their high efficiency in comparison with «manual» methods used in modern information protection practice is predicted.
 The novelty, theoretical and practical significance of the obtained results are noted, as well as the prospect of further research – the construction of an analytical model of requirements fulfillment, which could be the basis of an appropriate method, followed by its program implementation and conducting of necessary experiments.

Research on Morphological Innovation Design of Industrial Products Based on Combinatorial Genetic Algorithm

Abstract This paper applies the combinatorial genetic algorithm to the design of industrial product forms to achieve the effect of industrial product form design innovation. The standard genetic algorithm is applied to industrial product design, and the optimal order of genetic optimization is constructed through continuous population genetics, combined with the minimum value of the objective function to construct the constraints of the innovative design of industrial products. Using the method of combinatorial optimization to integrate different elements in industrial product design, a coding method based on rows and columns is proposed for the set coverage problem of design elements. Analyzing the user’s preference for industrial product form design allows us to explore the demand direction of industrial product innovation design and formulate a suitable innovation design scheme. The results show that the consensus satisfaction of hair dryer form design in genetic optimization 2nd and 9th are higher than 0.8. When users are stimulated by like and dislike sample pictures, there is no significant difference in the average response time, p=0.337>0.05, and the difference in the average response time of the users is more significant p=0.020<0.05 when they are confronted with the preferred design shape.

Genetic Algorithm Based Combinatorial Optimization for the Optimal Design of Water Distribution Network of Gurudeniya Service Zone, Sri Lanka

This paper brings an in-detail Genetic Algorithm (GA) based combinatorial optimization method used for the optimal design of the water distribution network (WDN) of Gurudeniya Service Zone, Sri Lanka. GAmimics the survival of the fittest principle of nature to develop a search process. Methodology employs fuzzy combinations of pipe diameters to check their suitability to be considered as the cost-effective optimal design solutions. Furthermore, the hydraulic constraints were implicitly evaluated within the GA itself in its aim for reaching the global optimum solution. Upon analysis, the results of GA approach delivered satisfactory design outputs.

A Combinatorial Optimization Analysis Method for Detecting Malicious Industrial Internet Attack Behaviors

Industrial Internet plays an important role in key critical infrastructure sectors and is the target of different security threats and risks. There are limitations in many existing attack detection approaches, such as function redundancy, overfitting and low efficiency. A combinatorial optimization method Lagrange multiplier is designed to optimize the underlying feature screening algorithm. The optimized feature combination is fused with random forest and XG-Boost selected features to improve the accuracy and efficiency of attack feature analysis. Using both the UNSW-NB15 and Natural gas pipeline datasets, we evaluate the performance of the proposed method. It is observed that the influence degrees of the different features associated with the attack behavior can result in the binary classification attack detection increases to 0.93, and the attack detection time reduces by 6.96 times. The overall accuracy of multi-classification attack detection is also observed to improve by 0.11. We also observe that nine key features of attack behavior analysis are essential to the analysis and detection of general attacks targeting the system, and by focusing on these features one could potentially improve the effectiveness and efficiency of real-time critical industrial system security. In this paper, CICDDoS2019 dataset and CICIDS2018 dataset are used to prove the generalization. The experimental results show that the proposed method has good generalization and can be extended to the same type of industrial anomaly data sets.

Optimal transport methods for combinatorial optimization over two random point sets

We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in Rd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^d$$\\end{document} where the edge cost between two points is given by a pth power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and d≥3,1≤p<d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d \\ge 3, 1\\le p<d$$\\end{document}. Previous results were limited to the range p<d/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p<d/2$$\\end{document}. Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques.

VeLP: Vehicle Loading Plan Learning from Human Behavior in Nationwide Logistics System

For a nationwide logistics transportation system, it is critical to make the vehicle loading plans (i.e., given many packages, deciding vehicle types and numbers) at each sorting and distribution center. This task is currently completed by dispatchers at each center in many logistics companies and consumes a lot of workloads for dispatchers. Existing works formulate such an issue as a cargo loading problem and solve it by combinatorial optimization methods. However, it cannot work in some real-world nationwide applications due to the lack of accurate cargo volume information and effective model design under complicated impact factors as well as temporal correlation. In this paper, we explore a new opportunity to utilize large-scale route and human behavior data (i.e., dispatchers' decision process on planning vehicles) to generate vehicle loading plans (i.e., plans). Specifically, we collect a five-month nationwide operational dataset from JD Logistics in China and comprehensively analyze human behaviors. Based on the data-driven analytics insights, we design a &lt;u&gt;Ve&lt;/u&gt;hicle &lt;u&gt;L&lt;/u&gt;oading &lt;u&gt;P&lt;/u&gt;lan learning model, named VeLP, which consists of a pattern mining module and a deep temporal cross neural network, to learn the human behaviors on regular and irregular routes, respectively. Extensive experiments demonstrate the superiority of VeLP, which achieves performance improvement by 35.8% and 50% for trunk and branch routes compared with baselines, respectively. Besides, we deployed VeLP in JDL and applied it in about 400 routes, reducing the time by approximately 20% in creating plans. It saves significant human workload and improves operational efficiency for the logistics company.

KaryoNet: Chromosome Recognition with End-to-End Combinatorial Optimization Network.

Chromosome recognition is a critical way to diagnose various hematological malignancies and genetic diseases, which is however a repetitive and time-consuming process in karyotyping. To explore the relative relation between chromosomes, in this work, we start from a global perspective and learn the contextual interactions and class distribution features between chromosomes within a karyotype. We propose an end-to-end differentiable combinatorial optimization method, KaryoNet, which captures long-range interactions between chromosomes with the proposed Masked Feature Interaction Module (MFIM) and conducts label assignment in a flexible and differentiable way with Deep Assignment Module (DAM). Specially, a Feature Matching Sub-Network is built to predict the mask array for attention computation in MFIM. Lastly, Type and Polarity Prediction Head can predict chromosome type and polarity simultaneously. Extensive experiments on R-band and G-band two clinical datasets demonstrate the merits of the proposed method. For normal karyotypes, the proposed KaryoNet achieves the accuracy of 98.41% on R-band chromosome and 99.58% on G-band chromosome. Owing to the extracted internal relation and class distribution features, KaryoNet can also achieve state-of-the-art performances on karyotypes of patients with different types of numerical abnormalities. The proposed method has been applied to assist clinical karyotype diagnosis. Our code is available at: https://github.com/xiabc612/KaryoNet.

Optimal Pole-Swapping in Bipolar DC Networks With Multiple CPLs Using an MIQP Model

This express brief presents a mixed-integer quadratic programming (MIQP) model to address the problem of optimal pole-swapping in asymmetric bipolar DC networks. The exact mixed-integer nonlinear programming model is convexified by using two stages. Using Taylor’s series expansion, the first stage corresponds to linearizing the hyperbolic relationship between voltage and powers in the constant power loads. The second stage applies the concept of the big-M number in order to obtain a linear equivalent for the product between binary and continuous variables. The proposed MIQP model is solved using the MATLAB programming environment, with the convex disciplined tool known as CVX and the Gurobi solver. Numerical results in the 21-and 85-bus grids demonstrate the effectiveness of the proposed MIQP formulation when compared to combinatorial optimization methods. The MIQP model ensures reductions of about 3.7609 and 49.7928kW in the total grid power losses for the 21-and 85-bus grids, respectively, when the neutral wire is assumed to be floating in all the nodes of the network except for the substation bus.

RL-CSL: A Combinatorial Optimization Method Using Reinforcement Learning and Contrastive Self-Supervised Learning

Reinforcement learning-based methods have shown great potential in solving combinatorial optimization problems. However, the related research has not been mature in terms of both models and training methods. This paper proposes a method based on reinforcement learning and contrastive self-supervised learning. To be specific, the proposed method uses an attention model to learn a policy for generating solutions and combines a contrastive self-supervised learning model to learn the attention encoder in the way of node-by-node. Correspondingly, a two-phase learning method, including node-wise learning and solution-wise learning, is adopted to train the attention model and the contrastive self-supervised model jointly and collaboratively. The performance of the proposed method has been verified by numerical experiments on various combinatorial optimization problems.

A novel neural network model with distributed evolutionary approach for big data classification

The considerable improvement of technology produced for various applications has resulted in a growth in data sizes, such as healthcare data, which is renowned for having a large number of variables and data samples. Artificial neural networks (ANN) have demonstrated adaptability and effectiveness in classification, regression, and function approximation tasks. ANN is used extensively in function approximation, prediction, and classification. Irrespective of the task, ANN learns from the data by adjusting the edge weights to minimize the error between the actual and predicted values. Back Propagation is the most frequent learning technique that is used to learn the weights of ANN. However, this approach is prone to the problem of sluggish convergence, which is especially problematic in the case of Big Data. In this paper, we propose a Distributed Genetic Algorithm based ANN Learning Algorithm for addressing challenges associated with ANN learning for Big data. Genetic Algorithm is one of the well-utilized bio-inspired combinatorial optimization methods. Also, it is possible to parallelize it at multiple stages, and this may be done in an extremely effective manner for the distributed learning process. The proposed model is tested with various datasets to evaluate its realizability and efficiency. The results obtained from the experiments show that after a specific volume of data, the proposed learning method outperformed the traditional methods in terms of convergence time and accuracy. The proposed model outperformed the traditional model by almost 80% improvement in computational time.

A Multi-Start Gradient Combination Method for High-Performance Global Search

The gradient descent is one of the most common methods to modify the gradient parameters of the neural network, however, it may fall into the local optimum in the training process. As we all know, genetic algorithm can find the global optimal solution through global search, but it may not be efficient, always takes a lot of running time. These two methods are complementary in the running time and the cost, which inspired us to consider the combination of gradient descent and genetic algorithm. In this paper, a multi-start combinatorial optimization method based on the genetic algorithm and the gradient descent is proposed. First, the initial point is selected through the genetic algorithm. Then the combination of multi-start and gradient descent is used, which can quickly achieve the global search and improve the performance with relatively less running time and cost. Compared with the traditional genetic algorithm and gradient descent method, this proposed algorithm has a better performance in computing the global optimum efficiently.

Efficient Integration of Photovoltaic Solar Generators in Monopolar DC Networks through a Convex Mixed-Integer Optimization Model

The problem regarding the optimal siting and sizing of photovoltaic (PV) generation units in electrical distribution networks with monopolar direct current (DC) operation technology was addressed in this research by proposing a two-stage convex optimization (TSCO) approach. In the first stage, the exact mixed-integer nonlinear programming (MINLP) formulation was relaxed via mixed-integer linear programming, defining the nodes where the PV generation units must be placed. In the second stage, the optimal power flow problem associated with PV sizing was solved by approximating the exact nonlinear component of the MINLP model into a second-order cone programming equivalent. The main contribution of this research is the use of two approximations to efficiently solve the studied problem, by taking advantage of convex optimization models. The numerical results in the monopolar DC version of the IEEE 33-bus grid demonstrate the effectiveness of the proposed approach when compared to multiple combinatorial optimization methods. Two evaluations were conducted, to confirm the efficiency of the proposed optimization model. The first evaluation considered the IEEE 33-bus grid without current limitations in all distribution branches, to later compare it to different metaheuristic approaches (discrete versions of the Chu and Beasley genetic algorithm, the vortex search algorithm, and the generalized normal distribution optimizer); the second simulation included the thermal current limits in the model’s optimization. The numerical results showed that when the maximum point power tracking was not regarded as a decision-making criterion, the expected annual investment and operating costs exhibited better performances, i.e., additional reductions of about USD 100,000 in the simulation cases compared to the scenarios involving maximum power point tracking.

A mixed-integer conic approximation for optimal pole-swapping in asymmetric bipolar DC distribution networks

This paper deals with the optimal pole-swapping problem in bipolar asymmetric distribution networks by proposing a mixed-integer conic approximation (MICA) model to minimize the total grid power losses for a particular load condition. The non-convex relation between voltage and power in the constant power loads is relaxed through equivalent cones. The effect of the neutral wire’s connection is considered in the proposed MICA model via an auxiliary variable associated with the total current drained to the earth in the case of a solidly grounded connection. Numerical comparisons with three combinatorial optimization methods (black-hole optimization, sine-cosine algorithm, and the Chu & Beasley genetic algorithm) and a mixed-integer quadratic approximation in two test feeders composed of 21 and 85 buses demonstrate the effectiveness of the proposed MICA model. Reductions of about 3.9411 and 10.1706% were obtained after applying the MICA model to the optimal pole-swapping problem. All numerical validations were carried out in the MATLAB programming environment, using the convex disciplined tool known as CVX with the Gurobi solver.

Оптимизация размещения трансформаторных подстанций в городских микрорайонах с использованием генетического алгоритма и алгоритмов трассировки ЛЭП на карте

To define the placement of electric substations when designing power supply schemes in urban neighborhood is a challenging task since it is necessary to consider spatial restrictions when choosing routes for electric power lines. Thus, the selection of the substation distribution is usually limited by comparison of several variants. In the scientific literature, problems of optimization are usually considered without taking into account real environmental restrictions for the electric power transmission lines. And it significantly reduces the adequacy of the models used. Thus, the study of the possibilities to use both combinatorial optimization methods and the construction of minimum cost routes in the GIS environment to select the optimal layout of electrical substations when designing power supply schemes for urban neighborhood is relevant. The methods to determine the shortest paths on the graphs and the genetic algorithm search are used for the research. The map of the electric lines of Ivanovo city has been used as base data for calculation. A new method has been developed to determine the optimal number and placement of transformer substations to power a lot of buildings on the digital city map. A wave algorithm of cost surfaces is used to estimate the cost of laying cable electric power transmission lines from the consumer to any location of the transformer substation. A genetic algorithm is used to select the network structure. The research results have confirmed the possibility to determine the best transformer substation distribution using GIS with given spatial restrictions.

The Efficiency of an Optimized PID Controller Based on Ant Colony Algorithm (ACO-PID) for the Position Control of a Multi-articulated System

In this article, a robot manipulator is controlled by the PID controller in a closed loop system with unit feedback. The difficulty of using the controller is parameter tuning, because the tuning parameters still use the trial and error method to find the PID parameter constants, namely Proportional Gain (Kp), Integral Gain (Ki) and Derivative Gain (Kd). In this case the Ant colony Optimization algorithm (ACO) is used to find the best gain parameters of the PID. The Ant algorithm is a method of combinatorial optimization, which utilizes the pattern of ants search for the shortest path from the nest to the place where the food is located, this concept is applied to tuning PID parameters by minimizing the objective function such that the robot manipulator has improved performance characteristics. This work uses the Matlab Simulink environment, First, after obtaining the system model, the ant colony algorithm is used to determine the proper coefficients 𝐾p, 𝐾i, and Kd in order to minimize the trajectory errors of the two joints of the robot manipulator. Then, the parameters will implement in the robot system. According to the results of the computer simulations, the proposed method (ACO-PID) gives a system that has a good performance compared with the classical PID.

Efficient Integration of Fixed-Step Capacitor Banks and D-STATCOMs in Radial and Meshed Distribution Networks Considering Daily Operation Curves

The problem regarding the optimal integration of efficient reactive power compensation in radial and meshed distribution networks using fixed-step capacitor banks and distribution static compensators (D-STATCOMs) is addressed in this research paper by proposing a master–slave optimization methodology. Radial and meshed distribution topologies are considered for the grid structure while including variable active and reactive demand curves. An economic analysis is performed, considering the net present value of the optimization plan, as well as the costs of energy losses and the capacitor banks’ acquisition, installation, and operation. In the case of the D-STATCOMs, an annualized costs analysis is presented. In the master stage, the discrete version of the generalized normal distribution optimization (GNDO) algorithm selects the nodes and the sizes of the capacitor banks. In the slave stage, the successive approximations power flow approach is implemented. Numerical results in the IEEE 33-bus grid (with both radial and meshed topologies) and the IEEE 85-bus grid (with a radial configuration) demonstrated the proposed master–slave optimization’s effectiveness in minimizing the project’s expected net present value for a planning period of five years. Moreover, a simulation in the IEEE 69-bus grid under peak operation conditions showed that the GNDO approach is an excellent optimization technique to solve the studied problem when compared to combinatorial and exact optimization methods. In addition, numerical validations considering D-STATCOMs in the IEEE 85-bus grid confirmed the effectiveness and robustness of the GNDO approach in addressing problems associated with optimal reactive power compensation in medium-voltage distribution systems.

Optimizing planning and operation of renewable energy communities with genetic algorithms

Renewable Energy Communities (REC) have the potential to become a key agent for the energy transition. Since consumers have different consumption patterns depending on their habits, their grouping allows for a better use of the resource. REC provide both economic and environmental benefits. However, its potential drastically diminishes when grouping of prosumers and energy al- location is performed improperly, as the energy generated ends up not being consumed. Given the importance of extracting the maximum potential of REC, this study presents a tool to assist in both the planning and the operation phases. We present a combinatorial optimization method for participant selection and a multi-objective (MO) optimization of solar energy allocation. Specific Ge- netic Algorithms (GA) were developed including problem-specific approaches for reducing the search space, encoding, techniques for space ordering, fitness functions, special operators to replace duplicate individuals and decoding for equality constraints. The performance of the novel solution approach was exper- imentally proved with an electrical solar installation and electricity consumers from Northern east Spain. The results show that the developed tool achieves energy sharing in REC with low solar energy excess, high self-consumption and high avoided CO2 emissions while assuring low payback periods for all partic- ipants. This tool will be essential to increase revenues of REC schemes and boost their beneficial environmental impact.