Combinatorial Optimization Algorithm Research Articles

Evaluation of student failure in higher education by an innovative strategy of fuzzy system combined optimization algorithms and AI

This research suggests two novel metaheuristic algorithms to enhance student performance: Harris Hawk's Optimizer (HHO) and the Earthworm Optimization Algorithm (EWA). In this sense, a series of adaptive neuro-fuzzy inference system (ANFIS) proposed models were trained using these methods. The selection of the best-fit model depends on finding an excellent connection between inputs and output(s) layers in training and testing datasets (e.g., a combination of expert knowledge, experimentation, and validation techniques). The study's primary result is a division of the participants into two performance-based groups (failed and non-failed). The experimental data used to build the models measured fourteen process variables: relocation, gender, age at enrollment, debtor, nationality, educational special needs, current tuition fees, scholarship holder, unemployment, inflation, GDP, application order, day/evening attendance, and admission grade. During the model evaluation, a scoring system was created in addition to using mean absolute error (MAE), mean squared error (MSE), and area under the curve (AUC) to assess the efficacy of the utilized approaches. Further research revealed that the HHO-ANFIS is superior to the EWA-ANFIS. With AUC = 0.8004 and 0.7886, MSE of 0.62689 and 0.65598, and MAE of 0.64105 and 0.65746, the failure of the pupils was assessed with the most significant degree of accuracy. The MSE, MAE, and AUC precision indicators showed that the EWA-ANFIS is less accurate, having MSE amounts of 0.71543 and 0.71776, MAE amounts of 0.70819 and 0.71518, and AUC amounts of 0.7565 and 0.758. It was found that the optimization algorithms have a high ability to increase the accuracy and performance of the conventional ANFIS model in predicting students' performance, which can cause changes in the management of the educational system and improve the quality of academic programs.

Robust Design of BLDC Motor Considering Driving Cycle

With growing environmental concerns and the limitations of fuel cell resources, replacing petrol-based engines with electric machines as the traction motor for electric vehicles (EVs) is gaining attention. Among the different electric machines topology, for lower power applications such as three-wheel motorcycle, the Brushless Direct Current (BLDC) motors are the most favorable due to their simple structure, simple control algorithm, etc. One of the key aspects of developing BLDC motors in EV applications is utilizing the fast and efficient optimization algorithm over driving cycles. Another aspect is considering manufacturing tolerances to eliminate the failure product rate in mass production. The combination of optimization algorithms with consideration of manufacturing tolerances leads to a complex and time-consuming optimization procedure. To overcome this problem, the robust design by utilizing the Design of Experiment (DOE) method can be utilized. In this study, first, a developed systematic multi-physics multi-level optimization algorithm with consideration of manufacturing tolerances and driving cycles is proposed. Then, to evaluate the accuracy of the optimization process, a prototype of the optimized motor is manufactured. The efficiency and accuracy of the optimization algorithm are compared through Finite Element Method (FEM) and experimental results, showing the effectiveness of the proposed algorithm.

Decomposition with adaptive composite norm for evolutionary multi-objective combinatorial optimization

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective problem into a series of single-objective subproblems for collaborative optimization. The weighted sum (WS) method and the Tchebycheff (TCH) method are the two most popular scalarization methods. They have pros and cons in solving multi-objective combinatorial optimization problems (MOCOPs) the WS method allows MOEA/D to converge faster than the TCH method; the WS-based MOEA/D cannot obtain unsupported non-dominated vectors, while the TCH-based one can overcome this shortcoming. This inspired us to use the WS method to drive the population towards the Pareto front and then switch to the TCH method to maintain a more diverse population. To better balance convergence and diversity, we propose a new scalarization strategy called adaptive composite norm (ACN). The ACN strategy can combine the WS and the TCH with dynamic weighting. The experiments consider 16 instances including 4 MOCOPs and run on the PlatEMO. Results reveal that MOEA/D-ACN can rank first and significantly outperform the other evolutionary multi-objective combinatorial optimization algorithms on almost all instances.

Carbon trading price forecasting based on parameter optimization VMD and deep network CNN–LSTM model

To meet carbon peak and neutrality targets, accurate carbon trading price forecasting is very important for enterprises making emission reduction decisions. By fusing convolutional neural network (CNN) and long short-term memory network (LSTM), the CNN–LSTM model is constructed. After variational mode decomposition (VMD), several intrinsic mode functions (IMFs) components are obtained and input into the CNN–LSTM model, thus constructing the combined sooty tern optimization algorithm (STOA)–VMD–CNN–LSTM forecasting model. To test this model, the carbon trading prices of the carbon emission trading markets of Hubei, Guangdong and Shenzhen were forecast. The prediction performance of the STOA–VMD–CNN–LSTM model is compared with ARIMA, BP, CNN and LSTM benchmark models and models combining different decomposition technologies. The international carbon trading price (EUR and CER) is used for prediction. Compared with other methods, the developed model makes fewer errors and achieves superior performance. Several important implications are provided for investors and risk managers involved in carbon financial products.

Applicability of Neural Combinatorial Optimization: A Critical View

Neural Combinatorial Optimization has emerged as a new paradigm in the optimization area. It attempts to solve optimization problems by means of neural networks and reinforcement learning. In the last few years, due to their novelty and presumably good performance, many research papers have been published introducing new neural architectures for a variety of combinatorial problems. However, the incorporation of such models in the conventional optimization portfolio raises many questions related to their performance compared to other existing methods, such as exact algorithms, heuristics or metaheuristics. This paper aims to present a critical view of these new proposals, discussing their benefits and drawbacks with respect to the tools and algorithms already present in the optimization field. For this purpose, a comprehensive study is carried out to analyse the fundamental aspects of such methods, including performance, computational cost, transferability and reusability of the trained model. Moreover, this discussion is accompanied by the design and validation of a new neural combinatorial optimization algorithm on two well-known combinatorial problems, the Linear Ordering Problem and the Permutation Flowshop Scheduling Problem. Finally, new directions for future work in the area of Neural Combinatorial Optimization algorithms are suggested.

Boosting aquila optimizer by marine predators algorithm for combinatorial optimization

Abstract In this study, an improved version of aquila optimizer (AO) known as EHAOMPA has been developed by using the marine predators algorithm (MPA). MPA is a recent and well-behaved optimizer with a unique memory saving and fish aggregating devices mechanism. At the same time, it suffers from various defects such as inadequate global search, sluggish convergence, and stagnation of local optima. However, AO has contented robust global exploration capability, fast convergence speed, and high search efficiency. Thus, the proposed EHAOMPA aims to complement the shortcomings of AO and MPA while bringing new features. Specifically, the representative-based hunting technique is incorporated into the exploration stage to enhance population diversity. At the same time, random opposition-based learning is introduced into the exploitation stage to prevent the optimizer from sticking to local optima. This study tests the performance of EHAOMPA’s on 23 standard mathematical benchmark functions, 29 complex test functions from the CEC2017 test suite, six constrained industrial engineering design problems, and a convolutional neural network hyperparameter (CNN-hyperparameter) optimization for Corona Virus Disease 19 (COVID-19) computed tomography-image detection problem. EHAOMPA is compared with four existing optimization algorithm types, achieving the best performance on both numerical and practical issues. Compared with other methods, the test function results demonstrate that EHAOMPA exhibits a more potent global search capability, a higher convergence rate, increased accuracy, and an improved ability to avoid local optima. The excellent experimental results in practical problems indicate that the developed EHAOMPA has great potential in solving real-world optimization problems. The combination of multiple strategies can effectively improve the performance of the algorithm. The source code of the EHAOMPA is publicly available at https://github.com/WangShuang92/EHAOMPA.

Reinforcement learning assisted recursive QAOA

In recent years, variational quantum algorithms such as the Quantum Approximation Optimization Algorithm (QAOA) have gained popularity as they provide the hope of using NISQ devices to tackle hard combinatorial optimization problems. It is, however, known that at low depth, certain locality constraints of QAOA limit its performance. To go beyond these limitations, a non-local variant of QAOA, namely recursive QAOA (RQAOA), was proposed to improve the quality of approximate solutions. The RQAOA has been studied comparatively less than QAOA, and it is less understood, for instance, for what family of instances it may fail to provide high-quality solutions. However, as we are tackling NP-hard problems (specifically, the Ising spin model), it is expected that RQAOA does fail, raising the question of designing even better quantum algorithms for combinatorial optimization. In this spirit, we identify and analyze cases where (depth-1) RQAOA fails and, based on this, propose a reinforcement learning enhanced RQAOA variant (RL-RQAOA) that improves upon RQAOA. We show that the performance of RL-RQAOA improves over RQAOA: RL-RQAOA is strictly better on these identified instances where RQAOA underperforms and is similarly performing on instances where RQAOA is near-optimal. Our work exemplifies the potentially beneficial synergy between reinforcement learning and quantum (inspired) optimization in the design of new, even better heuristics for complex problems.

Model predictive control of bidirectional heat transfer in prosumer-based solar district heating networks

District heating networks with decentralized heat production are ideally suited to include a high share of renewable energy sources for heat production in urban areas with limited space. A new concept is a prosumer-based district heating network in which some or even all buildings are equipped with decentralized building-level heat storages and heat generation plants. To exploit the full potential of the interconnected heating network, buildings with surplus heat are intended to transfer heat to buildings with heating demands to prevent the activation of the central heating plant. This work presents an initial feasibility study on using a model predictive control strategy to manage bidirectional heat transfer between buildings in a district heating network. We formulate this problem as an optimal control problem, incorporating binary decision variables for each potential heat transfer connection. This results in a mixed-integer nonlinear optimization problem that is hard to solve. The problem is solved with a fast gradient-based optimization algorithm in combination with a combinatorial integral approximation strategy. A case study concerning a residential heating network with building-level solar thermal collectors and storage tanks is carried out. The optimized operation is compared to the real operation obtained from one month of measurements. The results show that the optimized strategy with bidirectional heat transfer can exploit the total heat generated in the whole network. The central heating provider is only required when the heat produced or stored by all the buildings is insufficient to meet the total heat demand within the network. In the case study, this leads to a reduction of almost 75% of the required thermal energy from the central heat provider.

Transfer learning for bearing fault diagnosis: adaptive batch normalization and combined optimization method

Bearings are crucial components in rotating machinery equipment. Bearing fault diagnosis plays a significant role in the maintenance of mechanical equipment. This study aims to enhance the practicality of bearing fault diagnosis to meet real-world engineering requirements. In real industrial environments, the continuously changing operating conditions such as equipment speed and load pose challenges in collecting data for bearing fault diagnosis, as it is challenging to gather data for all operational conditions. This paper proposes a transfer learning approach for bearing fault diagnosis based on adaptive batch normalization (AdaBN) and a combined optimization algorithm. Initially, a ResNet neural network is trained using source domain data. Subsequently, the trained model is transferred to the target domain, where AdaBN is applied to mitigate domain shift issues. Furthermore, a combined optimization algorithm is employed during model training to enhance fault diagnosis accuracy. Experimental validation is conducted using bearing data from the Case Western Reserve University dataset and Northeast Forestry University (NEFU) dataset. Comparison shows that AdaBN and the combined optimization algorithm improve bearing fault diagnosis accuracy effectively. On the NEFU dataset, the diagnostic accuracy exceeds 95%.

Diversity Design of Traditional Cultural Elements in Interior Design Based on Combinatorial Optimization Algorithm

Abstract There are great limitations in the imagination and play space of traditional interior design methods, and it is very costly to make changes after the design is completed. For this reason, this paper combines and optimizes SIFT and image splicing methods to recognize traditional cultural elements in images. Gray scale processing is performed on the image, unstable edge response points are removed and low contrast feature points are filtered, and the Gaussian pyramid is established by convolving the image with the Gaussian kernel function under different scale factors to establish the dimensions of the feature points. On this basis, an image splicing optimization algorithm that combines the two-dimensional information entropy of the image is proposed to divide the image into detail regions and flat regions, assign corresponding weights to the feature points in the optimization stage of the uni-responsive matrix, and minimize the residual sum to obtain the optimal uni-responsive matrix using the Levenberg-Marquardt algorithm, to improve the splicing quality. In the actual design test, the Chinese chair has the lowest success rate of 94.1%, and the output quality is 0.9215 and 0.9527. The output quality decreases as the scene becomes more complex. The SSIM and DoEM values for the Chinese chair are 0.9582 and 0.9682 for a simple scenario and decrease to a minimum of 0.8543 and 0.8472 as the number of interior pieces and other items in the scenario increases. By proposing the approach in this paper, labor costs and expenses can be saved and a new direction for interior design development can be taken.

Spatial layout and optimization of e-commerce logistics management based on combinatorial optimization algorithm

Abstract Warehousing space layout is crucial for e-commerce logistics. A refined and scientific approach to warehouse design enhances space utilization and operational efficiency. This minimizes unused space and idle time, lowers inventory costs, and strengthens the competitive edge of e-commerce logistics. In this study, we conceptualize the logistics space layout issue as a crate problem, harnessing the rapid optimization capabilities of genetic algorithms (GA) and simulated annealing (SA). We propose a hybrid algorithm where SA forms the core, using GA to generate initial solutions and new iterations. Design parameters for the combined operation process are systematically developed. This algorithm is evaluated using both datasets and real arithmetic cases, demonstrating superior performance in large-scale combinatorial optimization problems. It achieves a search accuracy of 0.5% to 3% higher than GA alone, converging more reliably to the global optimum, thus reducing search time and operational scope. This research offers vital theoretical insights for optimizing space layouts in e-commerce logistics management.

Исследование методов решения задач смешанного целочисленного линейного программирования

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

A method combining optimization algorithm and inverse-deformation design for improving the injection quality of box-shaped parts

A method combining optimization algorithm and inverse-deformation design for improving the injection quality of box-shaped parts

A novel network security situation assessment model based on multiple strategies whale optimization algorithm and bidirectional GRU.

The rapid development of the internet has brought about a comprehensive transformation in human life. However, the challenges of cybersecurity are becoming increasingly severe, necessitating the implementation of effective security mechanisms. Cybersecurity situational awareness can effectively assess the network status, facilitating the formulation of better cybersecurity defense strategies. However, due to the low accuracy of existing situational assessment methods, situational assessment remains a challenge. In this study, a new situational assessment method, MSWOA-BiGRU, combining optimization algorithms and temporal neural networks, was proposed. Firstly, a scientific indicator system proposed in this research is used to calculate the values of each indicator. Then, the Analytic Hierarchy Process is used to derive the actual situation values, which serve as labels. Taking into account the temporal nature of network traffic, the BiGRU model is utilized for cybersecurity situational assessment. After integrating time-related features and network traffic characteristics, the situational assessment value is obtained. During the evaluation process, a whale optimization algorithm (MSWOA) improved with a mix of strategies proposed in this study was employed to optimize the model. The performance of the proposed MSWOA-BiGRU model was evaluated on publicly available real network security datasets. Experimental results indicate that compared to traditional optimization algorithms, the optimization performance of MSWOA has seen significant enhancement. Furthermore, MSWOA-BiGRU demonstrates superior performance in cybersecurity situational assessment compared to existing evaluation methods.

Application of DE-ELM Algorithm in SF6 Circuit Breaker Contact Ablation Evaluation

When assessing the ablation status of circuit breaker contacts, the average dynamic contact resistance of the arc contacts of high-voltage SF6 circuit breakers is crucial. The average dynamic contact resistance of arc contacts on circuit breakers under various current levels may be accurately predicted using a method based on a differential evolution algorithm and extreme learning machine (DE-ELM), which is suggested in this research. Combining optimization algorithms yields the ideal input weight and hidden layer bias of the ELM method. The DE-ELM approach has outstanding anticipation performance for anticipation data under various current levels when compared to other anticipation methods. Finally, an expert system for assessing the ablation state of contacts based on the DE-ELM algorithm is created using the average dynamic contact resistance data of arc contacts predicted by DE-ELM. As a guide for the upkeep of high-voltage SF6 circuit breakers, the ablation status of contacts is categorized into four grades: A-level ablation, B-level ablation, C-level ablation, and D-level ablation.

Topological optimization hybrid algorithm for the adhesive joint

The subject of this study is a topological optimization algorithm for a lapped symmetric adhesive joint. The purpose of this research is to create a hybrid optimization algorithm that combines the advantages of a genetic algorithm and a particle swarm algorithm and, at the same time, reduces the time required to solve the problem. Task: to create a methodology for solving the optimization problem for a symmetric double-sided lapped adhesive joint, which consists of a main plate and two patches (the main plate has a constant thickness, and the thickness of the patches varies along the length of the joint, this is required to reduce the stress concentration in the joint and reduce its weight) with satisfaction of the optimality criterion, namely, to minimize the mass of the structure with the strength and thickness restrictions for the patch. The optimization problem is that we must find the optimal patch form, namely, the length of the patch and the thickness-on-length dependence for the patch. Methods: the modified Goland-Reissner model was used to describe the deflected mode of the joint. The finite difference method was used to solve the direct stress state problem for the structure. For the numerical solution of the optimization problem, a combination of the multi-population model of the genetic optimization algorithm and the particle swarm algorithm was used. To improve the performance of the genetic algorithm, a multi-population model with migration of the best individuals between populations was applied. The introduction of individuals from other populations into the population avoids homogenization of the genotype in a separate population and premature stopping of the optimization process. To describe the shape of the patch, the Fourier series expansion of the patch thickness dependence was used. Results: A hybrid algorithm is proposed based on the sequential application of a genetic algorithm and a particle swarm algorithm for three populations of solutions. The particle swarm algorithm makes it possible to improve the value of the objective function achieved at the previous stage by 20%. Conclusions: the scientific novelty lies in the improvement of the optimization algorithm compared with the known ones. To reduce the calculation time, a one-dimensional adhesive joint stress state mathematical model was used in this paper. The methods used made it possible to create a combined topological optimization algorithm that combines the advantages of both methods and allows us to find a solution to the problem quite quickly. The Python program run time is only a few minutes.

Iterative quantum algorithm for combinatorial optimization based on quantum gradient descent

Combinatorial optimization has wide and high-value applications in many fields of science and industry, but solving general combinatorial optimization problems is non-deterministic polynomial time (NP) hard. Many such problems can be mapped onto the ground-state-search problems of the Ising model. Here, an iterative quantum algorithm based on quantum gradient descent to solve combinatorial optimization problems is introduced, where the initial state of a quantum register evolves over several iterations to a good approximation of the Ising-Hamiltonian ground state. We verified the effectiveness of the proposed algorithm in solving the MaxCut problem for different types of undirected graphs by numerical simulations, and analyzed the robustness of the algorithm to errors by simulating random error and Gaussian error. We compared the performance of the algorithm with the quantum approximate optimization algorithm, and the results indicate that the proposed algorithm has comparable convergence performance. We also verified the feasibility of the algorithm by conducting experiments on a real quantum computer through the quantum cloud platform. Our work provides a potential method for solving combinatorial optimization problems on future quantum devices without the use of complex classical optimization loops.

Multi-objective reinforcement learning for bi-objective time-dependent pickup and delivery problem with late penalties

This study addresses the bi-objective time-dependent pickup and delivery problem with late penalties (TDPDPLP). Incorporating time-dependent travel time into the problem formulation to model traffic congestion is critical, especially for problems with time-related costs, to decrease the difference in the projected quality of solutions when applying optimization methods in the real world. This study proposes a multi-objective reinforcement learning (MORL)-based method with hypernetwork and heterogeneous attention mechanism (HAM) with a two-stage training scheme to solve the bi-objective TDPDPLP. The proposed method can instantly generate an approximation of the Pareto optimal front (POF) after offline training. The conducted ablation study also showed that discarding coordinates from the features simplifies the model and saves several hours of training while improving the quality of the solutions. The performance of the trained model is evaluated on various instances, including real-world-based instances from Barcelona, Berlin, and Porto-Alegre. The performance of the proposed method is evaluated based on the hypervolume (HV) and additive epsilon (ϵ+) of the generated POF. We compare the performance of the proposed method to another MORL method, namely the preference-conditioned multi-objective combinatorial optimization (PMOCO) and several well-known multi-objective evolutionary algorithms (MOEAs). Experiments showed that the proposed method performs better than PMOCO and the employed MOEAs on various problem instances. The trained method only needs minutes to generate a POF approximation, while the MOEAs require hours. Furthermore, it also generalizes well on different characteristics of problem instances and performs well on instances from cities other than the city in the training instances.

G-Aligner: a graph-based feature alignment method for untargeted LC–MS-based metabolomics

BackgroundLiquid chromatography–mass spectrometry is widely used in untargeted metabolomics for composition profiling. In multi-run analysis scenarios, features of each run are aligned into consensus features by feature alignment algorithms to observe the intensity variations across runs. However, most of the existing feature alignment methods focus more on accurate retention time correction, while underestimating the importance of feature matching. None of the existing methods can comprehensively consider feature correspondences among all runs and achieve optimal matching.ResultsTo comprehensively analyze feature correspondences among runs, we propose G-Aligner, a graph-based feature alignment method for untargeted LC–MS data. In the feature matching stage, G-Aligner treats features and potential correspondences as nodes and edges in a multipartite graph, considers the multi-run feature matching problem an unbalanced multidimensional assignment problem, and provides three combinatorial optimization algorithms to find optimal matching solutions. In comparison with the feature alignment methods in OpenMS, MZmine2 and XCMS on three public metabolomics benchmark datasets, G-Aligner achieved the best feature alignment performance on all the three datasets with up to 9.8% and 26.6% increase in accurately aligned features and analytes, and helped all comparison software obtain more accurate results on their self-extracted features by integrating G-Aligner to their analysis workflow. G-Aligner is open-source and freely available at https://github.com/CSi-Studio/G-Aligner under a permissive license. Benchmark datasets, manual annotation results, evaluation methods and results are available at https://doi.org/10.5281/zenodo.8313034ConclusionsIn this study, we proposed G-Aligner to improve feature matching accuracy for untargeted metabolomics LC–MS data. G-Aligner comprehensively considered potential feature correspondences between all runs, converting the feature matching problem as a multidimensional assignment problem (MAP). In evaluations on three public metabolomics benchmark datasets, G-Aligner achieved the highest alignment accuracy on manual annotated and popular software extracted features, proving the effectiveness and robustness of the algorithm.

Automated Fiber Placement Laminate Level Optimization for Mitigation of Through Thickness Defect Stacking

Manufacturing composite structures with Automated Fiber Placement (AFP) requires detailed process planning that is rigorous and time consuming. To facilitate, accelerate and perpetuate process planning knowledge, the Computer Aided Process Planning (CAPP) tool was developed. CAPP assists process planners in identifying optimal layup strategies for each ply of a laminate. This paper expands the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: genetic algorithm, differential evolution, particle swarm, and greedy search. The algorithms identify optimal combinations of ply-level layup strategies by analyzing defect stacking using two objective functions. These approaches are evaluated through a digital case study performed on a complex tool surface. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack-up.