Solving Optimization Problems Research Articles

A review of nature-inspired algorithms on single-objective optimization problems from 2019 to 2023

The field of nature inspired algorithm (NIA) is a vital area of research that consistently aids in solving optimization problems. One of the metaheuristic algorithm classifications that has drawn attention from researchers in recent decades is NIA. It makes a significant contribution by addressing numerous large-scale problems and achieving the best results. This research aims to identify the optimal NIA for solving single-objective optimization problems. The NIA discovered between 2019 and 2023 is presented in this study with a brief description. About 83 distinct NIAs have been studied in this study in order to address the optimization issues. In order to accomplish this goal, we have taken into consideration eight real-world single-objective optimization problems: the 3-bar truss design problem, the rolling element bearing, the pressure vessel, the cantilever beam, the I beam, the design of a welded beam, and the design of a spring. Based on a comparative study and bibliographic analysis, we have determined that two algorithms—the flow direction algorithm, and prairie dog optimization—give us the best results and optimal solutions for all eight of the engineering problems listed. Lastly, some perspectives on the limitations, difficulties, and future course are provided. In addition to providing future research guidelines, this will assist the novice and emerging researcher in providing a more comprehensive perspective on advanced NIA.

A revised Liu–Storey conjugate gradient parameter for unconstrained optimization problems with applications

ABSTRACT Conjugate Gradient (CG) methods are renowned for their efficiency and low memory requirements when solving optimization problems. However, certain formulations of CG methods that switch between two or more CG parameters often overlook specific values that could have been integrated. Moreover, the demonstration of the sufficient descent property in these methods usually relies on a strategy that assumes the possible exclusion of certain function values. To alleviate this assumption, this article introduces a structured Liu–Storey spectral CG method. This method extends the formulation of the spectral Fletcher conjugate descent method, enabling it to maintain fast convergence and inherit a good restart property. Therefore, the method ensures that the sufficient descent property holds without additional requirements and converges globally via some standard assumptions. Additionally, the method proves useful in solving robotic and image reconstruction models. Finally, it demonstrates robustness when compared to some standard algorithms.

Optimization based on the smart behavior of plants with its engineering applications: Ivy algorithm

This study presents a powerful and new modeling variant of bio-inspired algorithms, namely, the Ivy algorithm (IVYA), drawn from the growth patterns of Ivy plants. The algorithm simulates the coordinated and ordered population growth and the spreading and evolution of Ivy plants. The growth rate of Ivy plants is modeled using a differential equation and a data-intensive experimental process. The algorithm utilizes the knowledge of nearby Ivy plants to determine the direction of growth. Additionally, the algorithm mimics the behavior of Ivy plants in nature by choosing the closest and most vital neighbor for self-improvement. The IVYA's unique characteristics of preserving population diversity and its simplicity and flexibility allow for easy modification and extension, thus enabling researchers and practitioners to explore various modifications and techniques to enhance its performance and capabilities. These are the basic needs in optimizing engineering problems. The IVYA is compared with ten other algorithms on 26 classical test functions, demonstrating superior performance. Furthermore, the effectiveness of IVYA is shown by solving 12 engineering optimization problems and comparing the results with various optimization algorithms. The experimental results highlight the efficacy and competitiveness of the IVYA in solving optimization problems. Consider that the source code of the IVYA is publicly available at https://www.optim-app.com/projects/ivya.

Remark on Algorithm 1012: Computing projections with large data sets

In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum of squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD . This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world data sets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE , due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.

Improved Energy Valley Optimizer with Levy Flight for Optimization Problems

Energy Valley Optimizer (EVO) is one of the recent metaheuristic algorithms. It draws inspiration from advanced principles in physics related to particle stability and decay modes. This paper presents a new Energy Valley Optimizer (EVO) and levy flights that are hybrid to improve the EVO in solving optimization problems. Levy flight is one of the most important randomization techniques. Fifteen mathematical test functions (five unimodal functions, four multimodal functions, and six composite functions) are solved with the proposed algorithm. We also compare our results with previous results of metaheuristic algorithms. The statistical results show that the results of the Levy Energy Valley Optimizer (LEVO) outperform other algorithms in almost all mathematical test functions.

Slender loris optimization algorithm for solving optimization problems

Over the years, numerous optimization problems have been addressed utilizing meta-heuristic algorithms. Continuing initiatives have always been to create and develop new, practical algorithms. This work proposes a novel meta-heuristic approach employing the slender Loris optimization algorithm (SLOA), miming slender Loris behavior. The behavior includes foraging, hunting, migration and communication with each other. The ultimate goal of the devised algorithm is to replicate the food-foraging behaviour of Slender Loris (SL) and the quick movement of SL when threatened (i.e.) their escape from predators and also mathematically modelled the special communication techniques of SL using their urine scent smell. SLOA modelled SL’s slow food foraging behaviour as the exploitation phase, and moving between the tree and escaping from a predator is modelled as the exploration phase. The Eyesight of slender Loris plays a vital role in food foraging during nighttime in dim light. The operator’s Eyesight is modelled based on the angle of inclination of SL. The urine scent intensity is used here to be instrumental in preventing already exploited territory activities, which improves algorithm performance. The suggested algorithm is assessed and tested against nineteen benchmark test operations and evaluated for effectiveness with standard widely recognized meta-heuristics algorithms. The result shows SLOA performing better and achieving near-optimal solutions and dominance in exploration–exploitation balance in most cases than the existing state-of-the-art algorithms.

A CMOS-compatible oscillation-based VO2 Ising machine solver

Phase-encoded oscillating neural networks offer compelling advantages over metal-oxide-semiconductor-based technology for tackling complex optimization problems, with promising potential for ultralow power consumption and exceptionally rapid computational performance. In this work, we investigate the ability of these networks to solve optimization problems belonging to the nondeterministic polynomial time complexity class using nanoscale vanadium-dioxide-based oscillators integrated onto a Silicon platform. Specifically, we demonstrate how the dynamic behavior of coupled vanadium dioxide devices can effectively solve combinatorial optimization problems, including Graph Coloring, Max-cut, and Max-3SAT problems. The electrical mappings of these problems are derived from the equivalent Ising Hamiltonian formulation to design circuits with up to nine crossbar vanadium dioxide oscillators. Using sub-harmonic injection locking techniques, we binarize the solution space provided by the oscillators and demonstrate that graphs with high connection density (η > 0.4) converge more easily towards the optimal solution due to the small spectral radius of the problem’s equivalent adjacency matrix. Our findings indicate that these systems achieve stability within 25 oscillation cycles and exhibit power efficiency and potential for scaling that surpasses available commercial options and other technologies under study. These results pave the way for accelerated parallel computing enabled by large-scale networks of interconnected oscillators.

A multi-objective optimization framework for determining optimal chemotherapy dosing and treatment duration

Traditional randomized clinical trials are regarded as the gold standard for assessing the efficacy of chemotherapy. However, this procedure has drawbacks such as high cost, time consumption, and limited patient exploration of treatment regimens. We develop a multi-objective optimization-based framework to address these limitations and determine the best chemotherapy dosing and treatment duration. The proposed framework uses patient-specific biological parameters to create a mathematical model of cell population dynamics in the patient’s body. The framework employs evolutionary heuristic search methods (simulated annealing and genetic algorithms) and a prescriptive analytics approach to optimize therapy sessions that transition from treatment to relaxation. We carefully adjust the chemotherapy dose during treatment to reduce tumor cells while preserving host cells (such as effector-immune cells). We strategically time the relaxation sessions to aid recovery, considering the ability of tumors and healthy cells to regenerate. We use a combined optimization method to determine the length of the session and the amount of drug to be administered. We compare quadratic and linear optimal control solvers for drug administration while genetic algorithms and simulated annealing are used to optimize session length. This approach is especially important in limited healthcare resources, ensuring efficient allocation while accurately identifying high-risk patients to optimize resource allocation and utilization.

Solving the three-dimensional open-dimension rectangular packing problem: A constraint programming model

This paper addresses the three-dimensional open-dimension rectangular packing problem (3D-ODRPP). This problem addresses a set of rectangular boxes of given dimensions and a rectangular container of open dimensions. The objective is to pack all boxes orthogonally into the container while minimizing the container volume. Real-world applications of the 3D-ODRPP arise in production systems with operations of shipping or moving. The literature has presented mainly mixed-integer programming (MIP) formulations and their linearization techniques for the problem allied with general-purpose optimization solvers. To model and solve the 3D-ODRPP, we propose a constraint programming model based on a position-free modeling approach with logic operators. We ran computational experiments to assess the performance of the proposed model compared to the benchmark MIP models from instances of the literature. The results show our approach is competitive in different sets of problem instances in terms of reaching optimality as well as providing satisfactory feasible solutions quickly.

A new early warning system based on metaheuristics in CPS architecture

ABSTRACT Cyber security is the most studied in recent years by the association of metaheuristic techniques thanks to their ability to solve optimization problems in a limited time and NP-hard problems. The Early Warning System (EWS) can identify malicious exercises and anomalies in the CPS and provide robust network systems protection. In addition, grouping attacks in EWS is important for defining defense policies. Information security in the CPS architecture is about securing information during data aggregation, large-scale processing and sharing in the network environment, especially low-linkage open networks. Motivated by these considerations, we propose a new security approach based on the Artificial Bee Colony (ABC) metaheuristic algorithm to strengthen the security framework of the CPS architecture against the system and within CPS attacks. In this work, we propose a new Early Warning System approach based on metaheuristics. Based on two fundamental concepts of clustering, coherence and separation, an integrated index was proposed based on Davies-Bouldin (DB) and Silhouette Index (SI). An improved ABC algorithm was proposed based on these indices. After having identified two different types of an objective function, based on the above concepts, and after having tested the algorithm on DBSI, the results of the experiments found are auspicious.

Oscillatory Neural Network-Based Ising Machine Using 2D Memristors.

Neural networks are increasingly used to solve optimization problems in various fields, including operations research, design automation, and gene sequencing. However, these networks face challenges due to the nondeterministic polynomial time (NP)-hard issue, which results in exponentially increasing computational complexity as the problem size grows. Conventional digital hardware struggles with the von Neumann bottleneck, the slowdown of Moore's law, and the complexity arising from heterogeneous system design. Two-dimensional (2D) memristors offer a potential solution to these hardware challenges, with their in-memory computing, decent scalability, and rich dynamic behaviors. In this study, we explore the use of nonvolatile 2D memristors to emulate synapses in a discrete-time Hopfield neural network, enabling the network to solve continuous optimization problems, like finding the minimum value of a quadratic polynomial, and tackle combinatorial optimization problems like Max-Cut. Additionally, we coupled volatile memristor-based oscillators with nonvolatile memristor synapses to create an oscillatory neural network-based Ising machine, a continuous-time analog dynamic system capable of solving combinatorial optimization problems including Max-Cut and map coloring through phase synchronization. Our findings demonstrate that 2D memristors have the potential to significantly enhance the efficiency, compactness, and homogeneity of integrated Ising machines, which is useful for future advances in neural networks for optimization problems.

Enhancing forest optimization algorithm with gravitational search for nonlinear continuous optimization

Meta-heuristic algorithms have great role in solving problems related to optimization. Meta-heuristic method cannot solve problems related to optimization due to No Free Lunch theory. Hence different optimization methods are proposed by various researchers each year in order to solve optimization problems. Forest Optimization Algorithm (FOA) is an evolutionary optimization algorithm that is appropriate for continuous nonlinear optimization problems. The algorithm drawbacks include entrapment in local optimum and failure in achieving global optimum. The paper proposes hybrid algorithm called FOAGSA, in which the Gravitational Search Algorithm (GSA) is employed to improve the FOA performance in order to solve nonlinear continuous problems. The FOAGSA was evaluated through 39 benchmark optimization functions and two engineering problems. The experimental results proved that the FOAGSA exhibited acceptable results compared to state-of-art and well-known Meta-heuristic algorithms. Friedman ranking algorithm was utilized to compare FOAGSA with existing methods. The FOAGSA was ranked first on that basis.

A comparative study on the performance of Gray Wolves Optimization and Multi-Free Dynamic Schema

In this paper, we present a comparison study on the performance of Gray Wolves Optimization (GWO) and Multi-free dynamic schema (MFDS) algorithms. The Multi-free Dynamic Schema (MFDS) algorithm is a sophisticated optimization method created for solving optimization problems. It contains different operators (dynamic schema operator, dissimilarity operator, similarity operator and free dynamic schema operator). Where, The Grey Wolf Optimization (GWO) algorithm is a metaheuristic optimization algorithm inspired by the social behavior of grey wolves in a pack. This study focused on the run time and the number of iterations to reach the optimal solutions. The sample of this comparison was on ten functions. The results showed the superiority of an algorithm (MFDS) on (GWO) algorithm in most test functions, especially at the run time.

Navigating uncertain distribution problem: a new approach for resolution optimization of transportation with several objectives under uncertainty

Amidst uncertainty, decision-making in manufacturing becomes a central focus due to its complexity. This study explores complex transportation constraints and uses novel ways to guide manufacturers. The Multi-objective Stochastic Linear Fractional Transportation Problem (MOSLFTP) is a crucial tool for managing supply chains, manufacturing operations, energy distribution, emergency routes, healthcare logistics, and other related areas. It adeptly addresses uncertainty, transforming efficiency and effectiveness in several domains. Stochastic programming is the process of converting theoretical probabilities into concrete certainties. The artistic compromise programming technique acts as a proficient mediator, reconciling opposing objectives and enabling equitable decision-making. This novel approach also addresses the Multi-objective Stochastic Linear plus Linear Fractional Transportation Problem (MOSLPLFTP), which involves two interconnected issues. The effectiveness of these principles is clearly shown with the help of the LINGO® 18 optimization solver. This study uses a ranking method to compare the similar methods to solve the current problems. A meticulously designed example acts as a significant achievement, shedding light on our method in a practical setting. It serves as a distinctive instrument, leading manufacturers through the maze of uncertainty and assisting them in determining the most advantageous course of action. This journey involves subtle interactions between complexity and simplicity, uncertainty is overcome by decisiveness, and invention is predominant.

An improved sparrow search algorithm using chaotic opposition‐based learning and hybrid updating rules

SummaryMetaheuristic algorithms have special effects in solving optimization problems in real life and have become the focus of researchers. The sparrow search algorithm (SSA) is a newly proposed swarm‐based metaheuristic algorithm that has shown excellent optimization performance. Although compared with other algorithms, SSA shows good performance, the original SSA algorithm still has problems such as weak optimization ability, leading to falling into the local optimum, and being unable to balance exploration and exploitation well. Therefore, this paper proposes an improved SSA using chaotic opposition‐based learning and hybrid updating rules (CHSSA). First, chaotic opposition‐based learning is proposed to improve the diversity of the population. Second, two strategies, including adaptive weights and spiral search, are adopted to update the position. Finally, to evaluate the performance of the proposed CHSSA, this paper uses 23 benchmark functions, IEEE CEC 2017 functions and 4 practical engineering optimization problems to evaluate the algorithm performance. The experimental results show that compared with other advanced optimization algorithms, CHSSA has the characteristics of fast convergence speed, high search accuracy, and strong robustness.

Optimal operation of multiple energy system considering load management approach and uncertainty

In recent years, the advancement of technology has led to the development of energy networks' infrastructure, resulting in the transformation of conventional networks into smart networks. By incorporating communication equipment, each component of the network can now exchange information with other components, creating an environment where innovative ideas can be implemented. One such idea is the utilization of multi-carrier energy systems, also known as Energy Hubs. Integrating energy hubs into traditional networks used to be a challenging task. However, with the expansion and enhancement of smart networks, the potential for incorporating and locating energy hubs within the power grid has significantly increased. In these systems, the focus shifts from optimizing a single energy carrier to ensuring the optimal operation of a system that encompasses multiple energy carriers, such as natural gas, electric grid, and thermal energy. Energy hubs act as intermediaries between energy supply companies and various consumers, including residential, commercial, and industrial sectors. These energy suppliers can encompass different energy networks, such as electricity, gas, and local heating. The integration of residential and commercial energy hubs has become a crucial aspect of modern energy systems, particularly in the context of load response applications. This paper proposes a novel approach for effectively utilizing residential and commercial energy hubs, taking into account the time of use (ToU) load response program. In the proposed system, the inherent uncertainties of the system are addressed using the two-point estimation method of the model. To achieve the desired objective, the Cuckoo optimization algorithm, a well-established meta-heuristic algorithm for solving optimization problems, is employed. This algorithm aids in determining the optimal scheduling of energy resources while considering ToU tariffs and load management plan signals. The results demonstrate that the proposed approach can significantly reduce energy costs for the energy system.

Prediction and optimization of hobbing parameters for minimizing energy consumption and gear geometric deviations

Improving gear precision and achieving green sustainability in gear machining are two important aspects of the gear manufacturing process. However, to achieve these two goals simultaneously, it may be necessary to make trade-offs when selecting the gear processing parameters. In this work, both energy consumption and gear geometric deviations were considered simultaneously to optimize the hobbing parameters. The relationships between the hobbing parameters, energy consumption, and gear geometric deviations were modeled using the response surface method (RSM). The statistical significance of the model was tested using analysis of variance (ANOVA). An improved multi-objective particle swarm optimization (IMOPSO) was then performed to solve optimization problems that involved multiple and conflicting objectives in the hobbing process. The results obtained indicate that both the energy consumption ( E) and the gear geometric deviations are parameter-dependent. The feed rate ( f) and the spindle speed ( n) have opposing effects on both energy consumption E and the gear geometric deviations. The optimum hobbing parameter sets obtained from the calculated Pareto frontier can provide a feasible solution for manufacturers to solve the trade-off problems that occur in the hobbing process, and the experimental results confirmed the effectiveness of the IMOPSO approach.

Closed-form solutions of consistency ratio in best worst method minmax optimization model: max of edge error matrix and minmax edge error determinant methods

The Best Worst Method (BWM), a reduced version of the AHP, is a recent multi-criteria decision-making tool based on pairwise comparisons with reference to the best and worst criteria. Consistency Ratio (CR) measurement for the rating quality and prioritizations is still a controversial topic. Firstly, the computation for the current CR of BWM must rely on a software optimization solver to find the optimal values, and the solver may not always guarantee the exact optimal solutions, especially if the computational cost settings are not large enough for higher number of criteria. Secondly, much effort to evaluate optimization algorithms is needed to find the best solutions with the least computational resources due to diverse solvers possibly leading to different results with different performances. Thirdly, optimization programming code is not trivial to be implemented for general BWM users. To address these issues, this paper presents the closed-form solutions, Max of Edge Error Matrix (MEEM) (Eq. (44) of Theorem 4) and Minmax Edge Error Determinant (MEED) (Algorithm 1), to replace the BWM optimization models to directly calculate the CR values. Two simulations have been performed with a basic laptop using a single process. One simulation of twenty thousand random pairs of vectors took 26.34 h to perform to verify that the approximate results are higher than or very close to the exact closed-form values of both methods when high computational cost is allocated for the solver to increase the precision. Another simulation of one million random pairs of vectors only took 1.27 h to perform to verify that the MEED and MEEM methods always produce the same results for the number of criteria up to nine. The computational time for the exact results is dramatically reduced when the solver is not needed. The advantages of the proposed solutions include the following: the software to solve the optimization model to obtain CR is unnecessary, and the proposed calculation is extremely efficient to obtain the exact accuracy. The two-step optimization model can preserve the fixed Minmax Edge Error to find the weights which add up to one, which is the condition to determine if the model reaches exact optimal solutions. As the CR optimization model produces multiple versions of weights, which are recommended not to be used, the new method does not need to compute the unnecessary weight values to get the Minmax Edge Error. With the provision of equations leading to closed forms, users can understand the properties of CR in much clearer perspectives. Due to the computational efficiency and explainability, the proposed closed forms can replace the CR optimization model to compute CR efficiently and accurately for all diverse applications using BWM.

Comparison of finite element modeling approaches for Ti6Al4V porous bone implants

Additive technologies have made it possible to make a significant breakthrough in the development and production of personalized porous implants, which have clear advantages over monolithic predecessors. At the same time, engineers are faced with a number of new tasks, one of which is correct and effective numerical modeling of porous implants in the process of solving optimization problems. The study compares approaches to numerical modeling of porous titanium for bone implants, taking into account differences in the mechanical parameters of the material and the geometry of the models. The detailed geometry of the structure of 9 models is considered, for which two variants of material parameters are specified: pure Ti6Al4V alloy and experimental ones obtained for specimens printed from Ti6Al4V powder. As a proposed approach to homogenizing the structure, a continuum model of a cylinder is considered, for which the experimental properties of the specimen’s material are specified. The numerically obtained values of Young's moduli for each approach are compared with those obtained in the experiment. It has been established that when setting the properties of a pure alloy, the calculated Young's modulus exceeds the experimental one by 83–92 %. The closest thing to experiment is detailed modeling of geometry with setting the experimental properties of the material structure, while the calculated Young's modulus does not exceed the experimental one by more than 10 %. However, in this case the calculation takes from 2 to 8 hours. In the case of continuum modeling, the calculated Young's moduli exceed the calculated moduli in detailed modeling by no more than 11 %, while the calculation lasts no more than 1 minute. Based on this, it is proposed to use a continuum approach to modeling implants in the process of calculating the optimization of their shape, as an initial iteration before detailed modeling of the structure. As material properties, it is necessary to use the mechanical parameters of the structures, previously obtained from uniaxial compression experiments. Using the properties of a pure alloy will lead to results that significantly exceed the actual ones when calculating the porous structure.

Optimal with Respect to Accuracy Recovery of Some Classes Functions by Fourier Series

Introduction. Function approximation (approximation or restoration) is widely used in data analysis, model building, and forecasting. The goal of function approximation is to find the function that best approximates the original function. This can be useful when the original function is too complex to analyze or when a model needs to be simplified for more efficient computation or interpretation. Function approximation is an important tool in science, engineering, economics, and other fields where data analysis and modeling are required. It allows you to simplify complex functions, identify patterns in the behavior of the object of study, and predict the value of a function beyond the available data. The purpose of the paper is consider the problems of approximation of a function, which on some interval is given by its values in some set of nodal points and belongs to some class of functions by trigonometric Fourier series with a given accuracy and at fulfillment of given constraints on its execution time. The main attention is paid to obtaining estimates of computational complexity (implementation time) and solving the problem of function approximation by Fourier series with a given or maximum possible accuracy using efficient algorithms for solving optimization problems. Results. The general formulation of the problem of approximation of functions by Fourier series in accordance with the technology of solving problems of computational and applied mathematics with specified values of quality characteristics is presented. Estimates of the error of the proposed approximation algorithms using for the computation of Fourier coefficients the optimal in accuracy and close to them quadrature formulas for the computation of integrals from rapidly oscillating functions of the classes of Helder and Lipschitz with given fixed values in the nodes of a fixed grid are given. The corresponding quadrature formulas and constructive estimates of the error of the method of approximation of functions of the specified classes are given. Estimates of computational complexity of the given algorithms are obtained, which allow us to set real constraints on the time of algorithm implementation with a given or maximum possible accuracy. Conclusions. A comprehensive analysis of the quality of the considered algorithms for the approximation of functions by Fourier series using the accuracy-optimal (or close to them) quadrature formulas for the computation of Fourier coefficients for the computation of integrals from rapidly oscillating functions is presented. The estimates of their main characteristics – accuracy and computational complexity – are obtained. Keywords: function approximation, Fourier series, Fourier series coefficients, approximation error, computational complexity.