Combinatorial Optimization Algorithm Research Articles

Surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

AbstractAs potent approaches for addressing computationally expensive optimization problems, surrogate-assisted evolutionary algorithms (SAEAs) have garnered increasing attention. Prevailing endeavors in evolutionary computation predominantly concentrate on expensive continuous optimization problems, with a notable scarcity of investigations directed toward expensive combinatorial optimization problems (ECOPs). Nevertheless, numerous ECOPs persist in practical applications. The widespread prevalence of such problems starkly contrasts the limited development of relevant research. Motivated by this disparity, this paper conducts a comprehensive survey on SAEAs tailored to address ECOPs. This survey comprises two primary segments. The first segment synthesizes prevalent global, local, hybrid, and learning search strategies, elucidating their respective strengths and weaknesses. Subsequently, the second segment furnishes an overview of surrogate-based evaluation technologies, delving into three pivotal facets: model selection, construction, and management. The paper also discusses several potential future directions for SAEAs with a focus towards expensive combinatorial optimization.

Explanations for combinatorial optimization problems

We introduce a representation for generating explanations for the outcomes of combinatorial optimization algorithms. The two key ideas are (A) to maintain fine-grained representations of the values manipulated by these algorithms and (B) to derive explanations from these representations through merge, filter, and aggregation operations. An explanation in our model presents essentially a high-level comparison of the solution to a problem with a hypothesized alternative, illuminating why the solution is better than the alternative. Our value representation results in explanations smaller than other dynamic program representations, such as traces. Based on a measure for the conciseness of explanations we demonstrate through a number of experiments that the explanations produced by our approach are small and scale well with problem size across a number of different applications.

Retraction Note: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Retraction Note: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Metaheuristic-driven extended exergy accounting for sustainable closed-loop food supply chain management

In this research, an exergetic mathematical model is proposed for closed-loop food supply chain network design considering economic, environmental, and social aspects. The studded closed-loop food supply chain consists of six echelons, four echelons for forwarding the products (suppliers, factory, distribution centers, and customers), and two echelons for returning the products (collecting centers and disposal centers). The exergetic model is based on the extended exergy accounting method, which calculates the consumed exergy in all six echelons by considering the equivalents of labor and capital exergy. This model aims to minimize both the economic and exergetic costs associated with the food supply chain. To solve the proposed mathematical model, an ensemble global–local search metaheuristic algorithm utilizing a combined whale optimization algorithm (WOA) and simulated annealing (SA), called CWOASA, is proposed. In the CWOASA algorithm, first, WOA is used to search the entire search space. Next, SA is applied to further improve the best solution obtained by WOA. A real dataset of a dairy supply chain is used to evaluate the efficiency of the proposed metaheuristic-driven exergy analysis model and claim its benefits over the existing methods. Simulation results revealed that the proposed method leads to a 6.74% reduction in the total exergy consumption of the supply chain. The proposed methodology offers valuable insights, shedding light on the prospective gains in terms of mitigated environmental impact for each incremental economic expenditure, thus laying the foundation for promising avenues of future research.

A novel near infrared spectroscopy analytical strategy for soil nutrients detection based on the DBO-SVR method

Soil is the basis of agricultural production and accessing accurate information on soil nutrients is essential. Traditional methods of soil composition detection, which are based on chemical analysis, are characterized by being costly and polluting. Spectroscopic analysis has proven to be a rapid, non-destructive and effective technique for predicting soil properties in general and potassium, phosphorus and organic matter in particular. However, previous research on soils has rarely combined optimization algorithms with machine learning techniques, which has led to suboptimal model accuracy and convergence speed. In this study, a total of 184 soil samples were collected from three cities of Linhai, Yueqing and Longyou County, Zhejiang Province, China. After measuring pH values, alkali-hydrolyzable nitrogen (SAN), available phosphorus (SAP), available potassium (SAK) and soil organic matter (SOM) contents, along with their corresponding spectroscopic measurements, nine pretreatment methods and their combinations are adopted. A novel assessment model, integrating support vector machine and dung beetle optimization algorithm (DBO-SVR), is proposed to predict pH values and SAN, SAP, SAK, SOM content. Meanwhile, the DBO algorithm is compared with three mainstream optimization algorithms (particle swarm optimization (PSO), whale optimization algorithm (WOA) and grey wolf optimizer (GWO)). Results showed that the DBO-SVR model was shown best performance with Rp, RMSEP and RPD of 0.9842, 0.1306, 5.6485 respectively for prediction of pH value, with Rp, RMSEP and RPD of 0.8802, 15.0574 mg/kg and 2.0508, respectively for assessment of SAN content, with Rp, RMSEP and RPD of 0.9790, 12.8298 mg/kg, and 4.5132, respectively for assessment of SAP content, with Rp, RMSEP and RPD of 0.8677, 22.5107 mg/kg, and 1.9546, respectively for assessment of SAK content, and with Rp, RMSEP and RPD of 0.9273, 2.6427g/kg , and 2.1821, respectively for assessment of SOM content. This study demonstrates that the combination of near-infrared (NIR) spectroscopy and the DBO-SVR algorithm is capable of predicting soil nutrient composition with greater accuracy and efficiency.

Quantum dueling: an efficient solution for combinatorial optimization

In this paper, we present a new algorithm for generic combinatorial optimization, which we term quantum dueling. Traditionally, potential solutions to the given optimization problems were encoded in a ‘register’ of qubits. Various techniques are used to increase the probability of finding the best solution upon measurement. Quantum dueling innovates by integrating an additional qubit register, effectively creating a ‘dueling’ scenario where two sets of solutions compete. This dual-register setup allows for a dynamic amplification process: in each iteration, one register is designated as the ‘opponent,’ against which the other register’s more favorable solutions are enhanced through a controlled quantum search. This iterative process gradually steers the quantum state within both registers toward the optimal solution. With a quantitative contraction for the evolution of the state vector, classical simulation under a broad range of scenarios and hyper-parameter selection schemes shows that a quadratic speedup is achieved, which is further tested in more real-world situations. In addition, quantum dueling can be generalized to incorporate arbitrary quantum search techniques and as a quantum subroutine within a higher-level algorithm. Our work demonstrates that increasing the number of qubits allows the development of previously unthought-of algorithms, paving the way for advancement of efficient quantum algorithm design.

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.

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.

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.

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.

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.