Combinatorial Optimization Algorithm Research Articles

Multi-Objective Combinatorial Optimization Algorithm Based on Asynchronous Advantage Actor–Critic and Graph Transformer Networks

Multi-objective combinatorial optimization problems (MOCOPs) are designed to identify solution sets that optimally balance multiple competing objectives. Addressing the challenges inherent in applying deep reinforcement learning (DRL) to solve MOCOPs, such as model non-convergence, lengthy training periods, and insufficient diversity of solutions, this study introduces a novel multi-objective combinatorial optimization algorithm based on DRL. The proposed algorithm employs a uniform weight decomposition method to simplify complex multi-objective scenarios into single-objective problems and uses asynchronous advantage actor–critic (A3C) instead of conventional REINFORCE methods for model training. This approach effectively reduces variance and prevents the entrapment in local optima. Furthermore, the algorithm incorporates an architecture based on graph transformer networks (GTNs), which extends to edge feature representations, thus accurately capturing the topological features of graph structures and the latent inter-node relationships. By integrating a weight vector layer at the encoding stage, the algorithm can flexibly manage issues involving arbitrary weights. Experimental evaluations on the bi-objective traveling salesman problem demonstrate that this algorithm significantly outperforms recent similar efforts in terms of training efficiency and solution diversity.

Optimized Selective Assembly using Hungarian Algorithm

Assembly of discrete parts guided by hardware design specification constitutes the final phase in product manufacturing. In the course of mass production of components, mating parts with geometric or dimensional deviation from their intended design can be made acceptable by the identification of suitable pairs after analysing design fit and tolerance limits. By transforming this application-specific problem into a unified mathematical model, an optimal solution can be achieved that minimizes the rejection of non-conforming fabricated parts. Regardless of the type and range of a design fit, the problem can be mapped into a matrix using a ranking function defined by the user. The ranking function is modifiable as per the user requirements and may vary based on the selection criteria for an assembly. Based on the type of ranking function used, the tabulated matrix is solved using the Hungarian minimization/maximization algorithm, which is a powerful combinatorial optimization algorithm that solves the classical assignment problem in mathematics. This approach ensures maximum number of suiting pairs as well as nominal suiting of parts with each other resulting in high-quality products and maximum utilization of fabricated resources.

Computational design of residential units’ floor layout: A heuristic algorithm

Computer-aided intelligent design can improve the quality and efficiency of residential building design. However, the design conditions are diverse, and numerous combinations of spatial elements exist. We propose a heuristic algorithm—the combined Monte Carlo tree search (MCTS) and particle swarm optimization (PSO) algorithm (PSO-MCTS)—for the automated design of residential floor layouts. The MCTS algorithm deals with discrete variables (room locations). It considers architectural design experience and design standards during node pruning to compress the search space and simplify the computation. The PSO algorithm deals with continuous variables (room sizes) and accelerates the computing speed due to parallel processing. The PSO-MCTS algorithm achieves a good balance between computational efficiency and accuracy. It is suitable for various design conditions and requirements. The input parameters include the daylight façade, boundary scope, entrance location, room type and size, and relationships with adjacent rooms. The PSO-MCTS provides 100 %, 80 %, and 75 % better results than heuristic algorithms, designs by architects, and a state-of-the-art deep learning model, respectively.

An economic-environmental energy management system design for MT-HVDC networks via a semi-definite programming approximation with robust analysis

This research deals with the economic-environmental dispatch problem (EEDP) in multi-terminal high-voltage direct-current (MT-HVDC) systems by proposing a convex approximation based on semi-definite programming (SDP). The exact formulation of the EEDP corresponds to a non-convex, nonlinear programming problem due to the presence of a nonlinear quadratic constraint regarding the products between voltage variables. The thermal plants' economic and objective functions are modeled using typical quadratic functions. The SDP approach allows reaching a convex approximation that ensures the global optimal solution for each objective function independently or the construction of the optimal Pareto front via the weighting-factor optimization methodology. The proposed SDP approach also considers uncertainties in the demand and in the available power of renewable sources, which makes it robust. The main contribution of this research is a multi-period analysis that includes large-scale renewable generation sources and a robust analysis regarding demand and variations in renewable generation. Numerical results in two MT-HVDC systems demonstrate the effectiveness of the proposed SDP approach when compared to combinatorial optimization algorithms. All numerical simulations were carried out using the CVX convex disciplined tool, with the help of the SEDUMI and SDPT solvers, in the MATLAB programming environment.

Life prediction for proton exchange membrane fuel cell based on experimental results and combinatorial optimization algorithm

The durability is a key factor of fuel cell in large-scale application of automobiles. It is great important to real the lifetime and health status of fuel cells, especially in vehicle driving conditions. Based on the experimental data, this paper used the model-based method and data-driven method to predict the life of fuel cells, respectively. The model-based method established the equivalent circuit model according to the mapping law of electrochemical impedance spectroscopy (EIS) and the parameters of the equivalent circuit model were identified by newly considering the phenomenon of voltage recovery, revealing the strong linear correlation between impedance and voltage. The data-driven method selected a combinatorial optimization PSO-LSSVM algorithm and compared it with the prediction results of MATLAB's time series toolbox. The results show the mean square error (MSE), End of Life (EOL) of the model-based method, the time series toolbox and PSO-LSSVM algorithm are 0.019, 8.2 × 10−3 and 4.42 × 10−5, the 260h, 438h and 427h, respectively. Comparing with the real EOL of 421h, the error of PSO-LSSVM algorithm is only 6 h, which means the remaining useful life can be predicted with high accurately. Thus this study provides a reference for fault identification and life prediction of fuel cell health management.

Optimized Hierarchical Sliding Mode Control for the Swing-up and Stabilization of a Rotary Inverted Pendulum

This paper presents a study on controlling a rotary inverted pendulum (RIP) system using a hierarchical sliding mode control (HSMC) approach. The objective is to swing up and stabilize the pendulum at a desired position. The proposed HSMC controller addresses the underactuation challenge through a hierarchical structure of sliding surfaces. The particle swarm optimization (PSO) algorithm is used to optimize the controller parameters. Simulations were performed to evaluate the performance of the HSMC controller at different initial pendulum angles, demonstrating its effectiveness in achieving swing-up and stabilization. The integration of the PSO algorithm enhances the controller’s adaptability and robustness, emphasizing the benefits of combining optimization algorithms with controller parameter tuning for underactuated systems like the RIP.

Development of an evaluation method using a combined cat swarm optimization algorithm

The object of the study is complex dynamic objects with a hierarchical structure. The problem solved in the study is to increase the efficiency of decision-making while ensuring the given reliability. The subject of the study is the process of decision-making in management problems using an improved cat swarm optimization algorithm (CSO), an improved genetic algorithm and evolving artificial neural networks. The proposed method, due to additional and improved procedures, allows you: – to take into account the type of uncertainty of the initial data for setting CA for the local search procedure; – to implement adaptive strategies for finding food sources by CA; – to take into account the experience of the most authoritative CA while conducting local and global search; – to take into account the available computing resources of the state analysis system of complex dynamic objects and determine their required amount for involvement; – to take into account the CA search priority; – to determine the best CA using an improved genetic algorithm; – to conduct training of knowledge bases, which is carried out by training the synaptic weights of the artificial neural network, the type and parameters of the membership function, and architecture of individual elements and the architecture of the artificial neural network as a whole; – to avoid the local extremum problem by using the jump procedure. The proposed method was tested on the example of solving the problem of determining the composition of an operational group of troops (forces) and elements of its operational structure. An example of using the method showed an increase in the efficiency of data processing at the level of 14–19 % by using additional improved procedures. The proposed approach should be used to solve the problems of evaluating complex and dynamic processes characterized by a high degree of complexity

A benchmarking study of quantum algorithms for combinatorial optimization

We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr–Høyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use MaxCut problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of MaxCut problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from −1 to 1; and randomly generated Sherrington–Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven Õ2n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{{{\\mathcal{O}}}}}\\left(\\sqrt{{2}^{n}}\\right)$$\\end{document} scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving MaxCut problems.

On the Simplex Method for 0/1-Polytopes

We present three new pivot rules for the Simplex method for Linear Programs over 0/1-polytopes. We show that the number of nondegenerate steps taken using these three rules is strongly polynomial, linear in the number of variables, and linear in the dimension. Our bounds on the number of steps are asymptotically optimal on several well-known combinatorial polytopes. Our analysis is based on the geometry of 0/1-polytopes and novel modifications to the classical steepest-edge and shadow-vertex pivot rules. We draw interesting connections between our pivot rules and other well-known algorithms in combinatorial optimization. Funding: A. E. Black and J. A. De Loera are grateful for the support received through the National Science Foundation [Grants DMS-1818969 and NSF GRFP]. L. Sanita is grateful for the support received from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Vidi.193.087].

Wear parameters identification of hydrodynamic bearing based on operational modal analysis and on-rotor sensing technology

Abrasive wear is a predominant fault in hydrodynamic bearings that can deteriorate bearing performance and damage the rotating machine eventually. The present work proposes a novel wear parameters identification method for hydrodynamic bearings based on operational modal analysis (OMA) and on-rotor sensing (ORS) technology. With this framework, the objective function is defined as the sum of squared errors between the theoretical modal frequencies and the identified modal frequencies. For the experiment verification, the ORS technology is used to collect rotor vibration directly. Additionally, the cepstrum editing procedure (CEP) is applied to enhance modal information. The different wear parameters are successfully identified using combined stochastic subspace identification (SSI) and particle swarm optimization (PSO) algorithms in both simulation and experimental signals.

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

As 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.

Automated Pricing and Replenishment Decisions for Vegetable Products Based on Data Analysis

This study delves into the critical factors for the successful operation of vegetable products supermarkets: efficient inventory management and accurate market demand analysis. Given the perishability of vegetables, their variety, and the complexity of supply chains, a linear regression model and the method of least squares have been developed to estimate model parameters. Additionally, the ARIMA model is utilized to forecast the unit prices of commodities. In a more comprehensive approach, considering various influencing factors, a combinatorial optimization algorithm (integrating linear regression and greedy algorithm) is employed to determine the optimal replenishment strategy. Based on this, the study forecasts the sales volume and unit prices for various categories over the next seven days, and accordingly, establishes the pricing strategy and predicted replenishment volume for each category. The research underscores the necessity for retailers to precisely analyze sales data and market trends, optimize supply chain management, and formulate effective pricing strategies to cope with seasonal variations and limited sales space. These measures are essential to satisfy consumer demand and enhance profitability.

Multidisciplinary design and optimization of journal bearing for high-power wind turbine speed increaser

With the increasing power of wind turbine generators (WTG), the failure rate of rolling bearings in wind turbines due to insufficient bearing capacity increases with the increase of bearing size. To overcome these challenges, this paper proposes a design optimization method for the rectangular groove elliptical sliding bearing (RGEB) of the WTG output shaft. This method can maximize the radial bearing capacity under the premise of ensuring that the oil film pressure is large, the end leakage and the temperature rise are small. The multidisciplinary design and modeling of RGEB are carried out according to the structure and working conditions of WTG. Based on computational fluid dynamics (CFD), the influence of the number of rectangular dynamic pressure grooves on the bearing performance is analyzed. The kriging model, BP neural network model, and SSA-BP model are constructed for each performance index of RGEB, to establish a high-precision combined surrogate model based on global error criterion. After establishing the optimization equation, the PSO and SQP combined optimization algorithm is used to optimize the optimal structural parameters. The results show that the bearing capacity of the optimized RGEB is 95.9% higher than that of the ordinary elliptical bearing (EB) without increasing the size and quality of the bearing. In addition, the combined surrogate model can effectively replace the expensive finite element model to deal with the WTG sliding-bearing optimization problem.

Quantum-Informed Recursive Optimization Algorithms

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm, solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization. Published by the American Physical Society 2024

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.