Combinatorial Optimization Method Research Articles

Modeling and solving time-sensitive task allocation for USVs with mixed capabilities

Efficient task allocation for Unmanned Surface Vehicles (USVs) in maritime operations is crucial for optimal resource utilization and mission success. This paper introduces a task assignment model that accounts for the capabilities and time constraints associated with the heterogeneity of USVs. An Extended-Restriction Multiple Traveling Salesmen Problem (ER-MTSP) model is formulated, encapsulating the diverse capabilities of USVs and time restrictions. To solve this problem, a Fuzzy Enhanced Non-Dominated Sorting Genetic Algorithm (FENSGA-II) is developed, incorporating adaptive random testing initialization and customized hierarchical operators to generate high-quality Pareto frontiers. The fuzzy-linguistic satisfactory degree then re-evaluates the linguistic importance preferences of the objectives within the Pareto set, aiding in reasonable decision-making. Additionally, a two-phase refinement strategy balances individual task values and structure topology, enabling flexible task selection in emergency situations. Simulations and lake trials conducted across various problem variants demonstrate the effectiveness of the model. The results highlight the superiority of our approach compared to current combinatorial optimization methods, providing enhanced solutions across different problem variations.

A New Grey Prediction Model and Its Application in Renewable Energy Consumption

Renewable energy is an energy resource that can be used continuously. At present, international oil prices continue to rise, the problem of global climate change is becoming increasingly prominent, and renewable energy and clean energy have ushered in a new round of development opportunities. Based on the new gray prediction model, this paper forecasts the consumption of renewable energy and further analyzes the sustainable development of renewable energy. In this paper, the combinatorial optimization method of cumulative order, background value coefficient, and initial conditions, parameter optimization combination, parameter combinatorial optimization process of the gray prediction model, and parameter optimization mechanism based on the PSO algorithm are proposed, and the reduction error analysis is carried out. The consumption of wind power and photovoltaic renewable energy is forecasted, and three different forecasting methods as exponential smoothing method, time series analysis method, and new gray forecasting method are compared, and the wind speed, irradiation intensity, and load are forecasted by these three different forecasting methods. Compared with the time series analysis method and the exponential smoothing method, the RMSE of the new grey prediction method is reduced by 127.12% and 160.59%, and the error rate is reduced by 3.16% and 4%, respectively. Based on the consumption forecast of renewable energy, this paper analyzes its sustainability from three directions economy, resource supply, and environment, and finally gives energy policy recommendations.

Spatial phase distortion compensation technology based on combinatorial optimization method in heterodyne detection

The spatial phase distortion caused by turbulent atmosphere, target speckle, or optical system aberration causes decoherence of heterodyne signals. The decoherence effect is the key problem that imposes restrictions on the application of laser heterodyne techniques. We propose an approach for spatial phase distortion correction based on a genetic algorithm by establishing a one-to-one correspondence between combination of spatial phase compensation amounts and heterodyne efficiency of the system. The spatial phase distortion compensation problem is converted into a combinatorial optimization problem. The experiment results show that the method achieves excellent compensation performance for the spatial phase distortion, significantly contributing to the applications of heterodyne techniques.

Selecting fast algorithms for the capacitated vehicle routing problem with machine learning techniques

AbstractWe present machine learning (ML) methods for automatically selecting a “best” performing fast algorithm for the capacitated vehicle routing problem (CVRP) with unit demands. Algorithm selection is to automatically choose among a portfolio of algorithms the one that is predicted to work best for a given problem instance, and algorithm configuration is to automatically select algorithm's parameters that are predicted to work best for a given problem instance. We present a framework incorporating both algorithm selection and configuration for a portfolio that includes the automatically configured “Sweep Algorithm,” the first generated feasible solution of the hybrid genetic search algorithm, and the Clarke and Wright algorithm. The automatically selected algorithm is shown here to deliver high‐quality feasible solutions within very small running times making it highly suitable for real‐time applications and for generating initial feasible solutions for global optimization methods for CVRP. These results bode well to the effectiveness of utilizing ML for improving combinatorial optimization methods.

Power system fault diagnosis with quantum computing and efficient gate decomposition

Power system fault diagnosis is crucial for identifying the location and causes of faults and providing decision-making support for power dispatchers. However, most classical methods suffer from significant time-consuming, memory overhead, and computational complexity issues as the scale of the power system concerned increases. With rapid development of quantum computing technology, the combinatorial optimization method based on quantum computing has shown certain advantages in computational time over existing methods. Given this background, this paper proposes a quantum computing based power system fault diagnosis method with the quantum approximate optimization algorithm. The proposed method reformulates the fault diagnosis problem as a Hamiltonian by using Ising model, which completely preserves the coupling relationship between faulty components and various operations of protective relays and circuit breakers. Additionally, to enhance problem-solving efficiency under current equipment limitations, the symmetric equivalent decomposition method of multi-z-rotation gate is utilized. Furthermore, the small probability characteristics of power system events is utilized to reduce the number of qubits. Simulation results based on the test system show that the proposed methods can achieve the same optimal results with a faster speed compared with the classical higher-order solver provided by D-Wave.

Adaptive Space Search-based Molecular Evolution Optimization Algorithm.

In drug development process, a significant portion of budget and research time are dedicated to the lead compound optimization procedure in order to identify potential drugs. This procedure focuses on enhancing the pharmacological and bioactive properties of compounds by optimizing their local substructures. However, due to the vast and discrete chemical structure space and the unpredictable element combinations within this space, the optimization process is inherently complex. Various structure enumeration-based combinatorial optimization methods have shown certain advantages. However, they still have limitations. Those methods fail to consider the differences between molecules and struggle to explore the unknown outer search space. In this study, we propose an adaptive space search-based molecular evolution optimization algorithm (ASSMOEA). It consists of three key modules: construction of molecule-specific search space, molecular evolutionary optimization, and adaptive expansion of molecule-specific search space. Specifically, we design a fragment similarity tree in molecule-specific search space, and apply a dynamic mutation strategy in this space to guide molecular optimization. Then we utilize an encoder-encoder structure to adaptively expand the space. Those three modules are circled iteratively to optimize molecules. Our experiments demonstrate that ASSMOEA outperforms existing methods in terms of molecular optimization. It not only enhances the efficiency of the molecular optimization process, but also exhibits a robust ability to search for correct solutions. The code is freely available on the web at https://github.com/bbbbb-b/MEOAFST. Supplementary data are available at Bioinformatics online.

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.

Numerical analysis of quantization‐based optimization

AbstractWe propose a number‐theory‐based quantized mathematical optimization scheme for various NP‐hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization‐based optimization proposal also depends on stochastic features (i.e., the white‐noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization‐based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

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.