Classical Optimization Methods Research Articles

A multi-theoretical approach to supply chain management

The article examines the supply chain as a modeling object. The multi-criteria and contradictory goals in supply chain management are: on the one hand, the maximum level of service, on the other hand, minimizing logistics costs. Solving strategic optimization problems for this class of objects using classical optimization methods is difficult. The theoretical and methodological basis of the supply chain was considered from the perspective of a set-theoretic approach. The purpose of the study is to analyze the behavior of many different agents (suppliers, clients, etc.) with different needs and goals when making decisions. An agent is an active element of the system, possessing a certain autonomy and the ability to make independent decisions, relying on the information it has about the state of the environment and the actions of other agents. In turn, supply chains are a complex organizational (active) system, i.e. associated with human participation. The study of behavioral aspects and interorganizational interaction, the formation of new organizational forms are an extremely important aspect in the management and modeling of supply chains, a factor in the dynamic behavior of the logistics system. The conducted research represents an important contribution to the development of knowledge about the application of the set-theoretic approach in supply chain management. It demonstrates the applicability of this approach in practice through an analysis of a specific company, LLP «Knauf», on the Kazakhstan market.

GABoost: Graph Alignment Boosting via Local Optimum Escape

Heterogeneous graphs provide a universal data structure for representing various kinds of structured data in numerous domains. The graph alignment problem aims to find the correspondences of vertices in different graphs, playing a fundamental role in many downstream tasks of heterogeneous graph mining. In recent years, many graph alignment methods have been proposed, ranging from classical optimization methods , spectral methods , to embedding learning based-methods . Due to the problem's complexity, the result found by most existing methods is either a heuristic solution or a critical point in the solution space. In this paper, we propose GABoost, a graph alignment boosting algorithm that takes as input an initial alignment between two heterogeneous graphs and outputs a boosted alignment via an iterative local-optimum-escape process. One of the distinctive features of GABoost is that it can be sequentially composed with any graph alignment methods to improve the output of upstream methods. To examine the effectiveness of GABoost, we select 7 upstream methods of graph alignment as well as 6 real-world datasets, and quantitatively investigate the degree to which GABoost boosts these methods. The results show that GABoost improves the alignment accuracy of the 7 upstream methods by 25.25% on average with acceptable time overhead.

A Conceptual Framework for Optimizing Performance in Sustainable Supply Chain Management and Digital Transformation towards Industry 5.0

The economic growth of developed or emerging countries through globalization has prompted them to increase their supply chain performance. A large number of concepts, tools, and methodologies have been proposed in support of this performance improvement. They are mainly based on the use of classical optimization or enterprise modeling methods. However, environmental and social issues, not to mention digital transformation, are often ignored or not sufficiently integrated. Indeed, the world geopolitical situation, the increase in oil prices, and the commitment to protect our earth require the integration of sustainability aspects and Industry 4.0 concepts like digital twin and artificial intelligence in transforming the supply chain. This paper focuses on defining a conceptual framework to support sustainable supply chain management and digital transformation. It aims to exploit the sustainability and digital maturity of companies to transform their supply chains and enhance their performance to meet the challenges of Industry 5.0. Several practices related to sustainability, as well as two use cases on optimization and digital twin, are presented to illustrate this framework. Finally, based on the previous practices and use cases, an adapted framework for the supply chain manager to support the transition from Industry 4.0 to Industry 5.0 has been developed, as well as a performance dashboard.

A waste reduction strategy through autonomation under a closed-loop supply chain management

Currently, apart from manufacturing processes, the remanufacturing of products is considerably important. Appropriate remanufacturing requires the operation of long-run manufacturing systems. However, in long-run processes, the production system may convert to an out-of-control state due to machine breakdowns. Then, defective products are frequently produced; this increases wastage and disrupts environmental sustainability. In this model, a smart autonomation policy is deliberated for an error-free inspection in separating defective products during production. The autonomation policy facilitates waste reduction through remanufacturing. This paper concentrates on customer awareness and service-dependent demand, which directly improves the overall profitability of the system. A discrete investment to reduce setup cost, continuous investment to collect used goods, and cap-and-trade strategy to limit carbon emission are considered to obtain a more realistic model. Classical optimization method is applied for global maximum profit test of the profit function with respect to cycle length, customer awareness, service investment, discrete investment to reduce setup cost, number of shipments, and container capacities. Numerical testing, sensitivity to total profit in different cost parameters, and comparisons with previous research are explained. Some special scenarios including graphical representations are discussed to prove that a large investment is more beneficial than the cost of specific setup and collection.

A new filled function method for solving constrained global optimization problems

ABSTRACT Filled function methods have been considered as effective algorithms for solving global optimization problems. However, their effectiveness is greatly affected by the selection of parameters, the noncontinuous or non-differentiable properties of the constructed filled function. In addition, many of the constructed filled functions are only for unconstrained optimization problems, and they are unable to solve constrained optimization problems. In this paper, a new filled function is constructed for solving constrained global optimization problems. The new filled function has only one parameter which needs to be adjusted, and, when the objective functions and constrained functions are all continuously differentiable functions, the constructed filled function is also a continuously differentiable function. Then, the classical local optimization methods can be used to find a better minimum of the proposed filled function and a few parameter adjustments are needed. At last, a new filled function algorithm for constrained global optimization is developed based on the proposed filled function. The new algorithm is applied to several test examples. The results of the numerical experiments show that the new filled function algorithm is effective and efficient.

Non-probabilistic reliability-based multi-scale topology optimization of thermo-mechanical continuum structures with stress constraints

A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β=3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method.

A model for optimizing an investment portfolio in modern conditions

Subject. This article discusses the issues of improving the methodology for optimizing an investment portfolio in modern conditions. Objectives. The article aims to develop a model for optimizing the investment portfolio, taking into account the investor's risk profile and the limited budget. Methods. For the study, I used a comparative analysis, mathematical modeling in economics, machine learning methods, genetic algorithms, and the Python programming language. Results. The article presents the author-developed model of optimizing the investment portfolio of an enterprise, based on the symbiosis of individual elements and principles of the most effective methods of optimizing the investment portfolio, algorithms for their implementation, mathematical model and practical recommendations. Conclusions and Relevance. The combination of classical methods of investment portfolio optimization and machine learning in the model helps improve the accuracy of assessing the future return of assets and determine their weights in the investor's portfolio. The theoretical significance of the work lies in the fact that the scientific provisions that actualize the task of improving existing or developing new approaches to optimizing the investment portfolio are proved. The practical significance of the study lies in the fact that the presented model is of an applied nature, taking into account the risk profile of the investor, tactical and strategic goals of investment, and budget constraints. The results of the study may be of interest to novice stock market participants, experienced investors, IT specialists engaged in the creation of programs and robots for trading on the stock market using machine learning tools.

Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

This paper examines the performance of three binary metaheuristic algorithms when applied to two distinct knapsack problems (0–1 knapsack problems (KP01) and multidimensional knapsack problems (MKP)). These binary algorithms are based on the classical mantis search algorithm (MSA), the classical quadratic interpolation optimization (QIO) method, and the well-known differential evolution (DE). Because these algorithms were designed for continuous optimization problems, they could not be used directly to solve binary knapsack problems. As a result, the V-shaped and S-shaped transfer functions are used to propose binary variants of these algorithms, such as binary differential evolution (BDE), binary quadratic interpolation optimization (BQIO), and binary mantis search algorithm (BMSA). These binary variants are evaluated using various high-dimensional KP01 examples and compared to several classical metaheuristic techniques to determine their efficacy. To enhance the performance of those binary algorithms, they are combined with repair operator 2 (RO2) to offer better hybrid variants, namely HMSA, HQIO, and HDE. Those hybrid algorithms are evaluated using several medium- and large-scale KP01 and MKP instances, as well as compared to other hybrid algorithms, to demonstrate their effectiveness. This comparison is conducted using three performance metrics: average fitness value, Friedman mean rank, and computational cost. The experimental findings demonstrate that HQIO is a strong alternative for solving KP01 and MKP. In addition, the proposed algorithms are applied to the Merkle-Hellman Knapsack Cryptosystem and the resource allocation problem in adaptive multimedia systems (AMS) to illustrate their effectiveness when applied to optimize those real applications. The experimental findings illustrate that the proposed HQIO is a strong alternative for handling various knapsack-based applications.

Multi-agent reinforcement learning method for cutting parameters optimization based on simulation and experiment dual drive environment

Improving production efficiency while ensuring product surface quality is a constant focus of manufacturers. Cutting parameter optimization is an important technique for ensuring high-efficiency and high-quality production. In this paper, a novel method for cutting parameter optimization that integrates multi-agent reinforcement learning with a dual-drive virtual machining environment is proposed. First, a feature extraction, fusion and generation model for cutting simulation and experimental data is proposed to solve the problem of incomplete data acquisition in the production process. Second, a Markov decision model for optimizing cutting parameters is defined, and a virtual machining environment driven by both simulation and experimental data is constructed. Third, a novel multi-agent reinforcement learning method called Q-MIX-MATD3, in which a twin delay deep deterministic policy gradient, value function decomposition and a teacher model are combined, is proposed to explore the cutting parameter optimization policy by interacting with the virtual machining environment. Finally, the proposed method is verified on a commutator production line. Moreover, the results show that the accuracy of the virtual machining environment driven by both simulation and experiment increases by more than 5 %, response efficiency increases by 31 %, and Q-MIX-MATD3-based cutting parameter optimization method reduces time cost by 98 % and achieves the optimization effect of the classical optimization method.

Mathematical modeling of minimization of electricity consumption by industrial enterprises with continuous production

Relevance. Determined by the importance of minimizing electrical power consumption in industrial enterprises with continuous production, considering the specific characteristics of their technological processes and the requirements to maintain the output volume of their products. Aim. To solve the task of minimizing electrical power consumption based on a mathematical model and gradient method under optimal planning of the production volume of the industrial enterprises with continuous production; to develop a mathematical model for optimal distribution of production over a time cycle (month, quarter, year) across departments, taking into account both simple and functional constraints, derived from the condition of ensuring minimal electrical power consumption in industrial enterprises with continuous production. Methods. When developing the mathematical model for ensuring minimal electrical power consumption while preserving the production volume, classic Lagrange optimization methods were used. To ensure sufficient calculation accuracy, iterative methods were also applied. For the task under consideration, a calculation error margin of ε=0,1 was assumed and established. It is known that the choice of calculation error margin depends on the specifics of the problem at hand and the decision-maker. To verify the adequacy of the developed model, the method of finding the relative extremum of a function of several variables was used. Results. The use of the mathematical model, which takes into account the nature of the technological process and boundary conditions in both simple and integral forms, demonstrated the feasibility of optimal planning of electrical power consumption by the enterprise. The effectiveness of the developed approaches was verified using a metallurgical enterprise as an example of an industrial enterprise with continuous production, in solving the task of minimizing electrical power consumption for products produced during the reporting period. The use of the proposed model allowed for a reduction in annual electrical power consumption by 2.5% while maintaining the same production volume. One of the classic optimization methods – the method of finding the relative extremum of functions of several variables – showed almost identical results upon verification. This serves as further evidence of the adequacy of the proposed model.

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

Human–structure interaction effects on lightweight footbridges with tuned mass dampers

The aim of the work is to explore how the interaction between pedestrians and a bridge deck could affect the effectiveness of tuned mass dampers (TMD) in suppressing the vibrations of lightweight footbridges. To this end, a human–structure interaction (HSI) model is built in a modal dynamic analysis framework, and it is applied to a lightweight footbridge subject to a large number of pedestrian arrangements with near-resonant walking frequencies. Compared with the response ignoring HSI, the results show that the interaction between the dynamic response of the pedestrians and the structure can reduce the vibrations in the deck, but they exceed comfort limits based on peak and root mean square (RMS) acceleration criteria. In order to reduce the oscillations to a comfortable level, a TMD located at midspan has been designed following classical optimisation methods that neglect HSI. The efficiency of the damper in resonant conditions is demonstrated in the time and frequency domains, even under a large number of synchronised pedestrians interacting with the structure, suggesting that crowds do not introduce important detuning effects in the TMD.

Green Probabilistic Inventory Model with Shortage Backordering, Carbon Emission Cost, and Imperfect Quality Items: A Newton-Raphson Method Approach Using Python

In this paper, a green inventory model has been developed to explain the relationship between a single manufacturer and many retailers in a multiplayer supply chain system. It is assumed that there exist some imperfect items in a quantity lot. In green inventory, one of the important issues is carbon emission with its cost to inventory management. Some troubles in the transportation process yield imperfect quality items. This trouble is the potential to increase the amount of carbon emission and some imperfect quality items. It also affects the cost of the inventory. Therefore, these two aspects will be analyzed under the shortage backorder policy. Due to the complexity of the model, the classical optimization methods cannot be used to determine the optimum values exactly. Therefore, formulation optimization is predominantly conducted using a numerical approach for finding partial derivatives and Newton-Raphson's method for finding the optimal solution. These methods are assisted by the Python programming language, operated within the Google Colab environment and Spyder (Python 3.8) using Anaconda environment.

A novel hybrid method based MPP tracking design using boost converter for solar power systems

The convergence time is one of the key parameters for evaluating the energy conversion efficiency of PV power systems in the experimental process of tracking the maximum power point (MPP) in real-time. When the PV system is partially shaded, for example, MPP tracking easily slips into the local MPP and takes a long time. To overcome this drawback, a new solution for a stand-alone PV power system has been proposed that combines the incremental conductance (In-Cond) algorithm and the improved grey wolf optimization (GWO) approach. The improved GWO technique changed the methodology is used to find the global power area in this proposed method, and it is integrated with the In-Cond algorithm to fast obtain the global MPP. To demonstrate the efficacy of the suggested strategy, MATLAB/ Simulation and experiment results of the PV system are provided. The proposed hybrid method has a quick response time of 0.18 to 0.42 seconds for good transient oscillation and global power tracking, whereas the classic GWO and particle swarm optimization (PSO) methods take 0.82 to 2.1 seconds and 0.68 to 2.2 seconds, respectively. The global MPP was obtained not only with uniform irradiance intensity, but also with partial shade.

Machine learning methods for service placement: a systematic review

With the growth of real-time and latency-sensitive applications in the Internet of Everything (IoE), service placement cannot rely on cloud computing alone. In response to this need, several computing paradigms, such as Mobile Edge Computing (MEC), Ultra-dense Edge Computing (UDEC), and Fog Computing (FC), have emerged. These paradigms aim to bring computing resources closer to the end user, reducing delay and wasted backhaul bandwidth. One of the major challenges of these new paradigms is the limitation of edge resources and the dependencies between different service parts. Some solutions, such as microservice architecture, allow different parts of an application to be processed simultaneously. However, due to the ever-increasing number of devices and incoming tasks, the problem of service placement cannot be solved today by relying on rule-based deterministic solutions. In such a dynamic and complex environment, many factors can influence the solution. Optimization and Machine Learning (ML) are two well-known tools that have been used most for service placement. Both methods typically use a cost function. Optimization is usually a way to define the difference between the predicted and actual value, while ML aims to minimize the cost function. In simpler terms, ML aims to minimize the gap between prediction and reality based on historical data. Instead of relying on explicit rules, ML uses prediction based on historical data. Due to the NP-hard nature of the service placement problem, classical optimization methods are not sufficient. Instead, metaheuristic and heuristic methods are widely used. In addition, the ever-changing big data in IoE environments requires the use of specific ML methods. In this systematic review, we present a taxonomy of ML methods for the service placement problem. Our findings show that 96% of applications use a distributed microservice architecture. Also, 51% of the studies are based on on-demand resource estimation methods and 81% are multi-objective. This article also outlines open questions and future research trends. Our literature review shows that one of the most important trends in ML is reinforcement learning, with a 56% share of research.

Tracking an untracked space debris after an inelastic collision using physics informed neural network

With the sustained rise in satellite deployment in Low Earth Orbits, the collision risk from untracked space debris is also increasing. Often small-sized space debris (below 10 cm) are hard to track using the existing state-of-the-art methods. However, knowing such space debris’ trajectory is crucial to avoid future collisions. We present a Physics Informed Neural Network (PINN)—based approach for estimation of the trajectory of space debris after a collision event between active satellite and space debris. In this work, we have simulated 8565 inelastic collision events between active satellites and space debris. To obtain the states of the active satellite, we use the TLE data of 1647 Starlink and 66 LEMUR satellites obtained from space-track.org. The velocity of space debris is initialized using our proposed velocity sampling method, and the coefficient of restitution is sampled from our proposed Gaussian mixture-based probability density function. Using the velocities of the colliding objects before the collision, we calculate the post-collision velocities and record the observations. The state (position and velocity), coefficient of restitution, and mass estimation of un-tracked space debris after an inelastic collision event along with the tracked active satellite can be posed as an optimization problem by observing the deviation of the active satellite from the trajectory. We have applied the classical optimization method, the Lagrange multiplier approach, for solving the above optimization problem and observed that its state estimation is not satisfactory as the system is under-determined. Subsequently, we have designed Deep Neural network-based methods and Physics Informed Neural Network (PINN) based methods for solving the above optimization problem. We have compared the performance of the models using root mean square error (RMSE) and interquartile range of the predictions. It has been observed that the PINN-based methods provide a better estimation performance for position, velocity, mass and coefficient of restitution of the space debris compared to other methods.

Quantum computer based feature selection in machine learning

AbstractThe problem of selecting an appropriate number of features in supervised learning problems is investigated. Starting with common methods in machine learning, the feature selection task is treated as a quadratic unconstrained optimisation problem (QUBO), which can be tackled with classical numerical methods as well as within a quantum computing framework. The different results in small problem instances are compared. According to the results of the authors’ study, whether the QUBO method outperforms other feature selection methods depends on the data set. In an extension to a larger data set with 27 features, the authors compare the convergence behaviour of the QUBO methods via quantum computing with classical stochastic optimisation methods. Due to persisting error rates, the classical stochastic optimisation methods are still superior.

A deep Q-learning approach to optimize ordering and dynamic pricing decisions in the presence of strategic customers

In this paper, we present an optimization method to analyze the simultaneous decisions on dynamic pricing and ordering quantities for seasonal products, by a retailer in monopolistic condition. Customers are assumed to be strategic and may postpone their purchase to get a lower price in future. The problem has been investigated in the context of multiple substitute products. We have developed a model based on deep neural networks to estimate customers’ demand. The problem is complex and cannot be solved using classical optimization methods. Therefore, we have developed a reinforcement learning algorithm called deep Q-learning algorithm (DQL) to solve the problem. The proposed algorithm is a combination of a Q-learning algorithm and two deep neural networks for the primary and discount sales periods, which uses the neural network to estimate the Q-values in a large space of states and actions. The performances of the demand model and the proposed optimization algorithm have been tested using a real-world dataset taken from the clothing industry. The results of our experiments demonstrate that the proposed demand model performs better than a fully connected neural network-based model and a latent class model tested in this paper. Furthermore, the performance of the DQL algorithm is significantly superior to those of two simulated annealing and genetic algorithms. In addition, the results of a comparison between the DQL algorithm and another reinforcement learning algorithm called State-Action-Reward-State-Action (SARSA) indicate that the proposed algorithm results in higher revenues and takes less time to converge. Consequently, the proposed algorithm has a high potential for solving such a large scale integrated pricing and ordering optimization problem.

Allocation and Sizing of DSTATCOM with Renewable Energy Systems and Load Uncertainty Using Enhanced Gray Wolf Optimization

Over the last decade, flexible alternating current transmission systems (FACTS) have been crucial in ensuring optimal power distribution within modern power systems. A vital component of FACTS devices is the distribution static compensator (DSTATCOM), which is essential for maintaining a reliable power supply. It is commonly used for reactive power compensation, voltage regulation, and harmonic reduction. Determining the appropriate size and placement of DSTATCOMs is vital to ensuring their efficiency. This study introduces the improved gray wolf optimizer (I-GWO), a refined version of the classical gray wolf optimization (GWO) method. The I-GWO incorporates a dimension learning-based hunting (DLH) strategy to preserve population diversity, balance exploration and exploitation, and prevent the premature convergence of classical GWO. In this research, the I-GWO was applied to determine the optimum allocation and sizing of the DSTATCOMs, considering system constraints, including those presented by the intermittent and stochastic nature of the load and renewable energy resources, specifically wind and solar energy. The suggested approach was successfully tested on 33-, 69-, and 85-bus distribution systems and then compared with existing studies. The results demonstrated the I-GWO-based approach’s superiority in terms of reducing power losses, improving voltage profiles, and enhancing voltage stability.

Improved Hedge Fund Portfolio Optimization Using 2-Step Covariance Matrix and Fund Transaction Costs

This study focuses on fund portfolio investments in the Chinese market. The application of classic portfolio optimization methods encounters several issues when applied to fund portfolios. For example, issues such as the non-normal distribution of returns on funds or fund portfolios, turnover rate limitations in fund investments, and liquidity constraints of fund assets, which can lead to transaction costs and opportunity costs, are prevalent challenges. The existence of these issues can compromise the effectiveness of classic portfolio optimization methods like Mean-Variance Optimization. This may result in a reduction of accuracy in determining the portfolios optimal weights, a deviation of actual trading results from the models optimal expectation, and may even render the optimal weights impractical in real-world scenarios. To address these challenges, this paper integrates the 2-Step covariance matrix method (2-Step method) and the measurement of fund transaction costs into the portfolio optimization process. The paper finds that the 2-Step method, compared to the baseline, can indeed improve the risk-return indicators of the potimal fund portfolio. The inclusion of the transaction cost can effectively control the turnover frequency of the portfolio. Even after accounting for these costs, the 2-Step method continues to exhibit a significant improvement effect compared to the baseline.