Solving Optimization Problems Research Articles

ОЦІНКА ОБЧИСЛЮВАЛЬНОЇ СКЛАДНОСТІ ГЕНЕТИЧНОГО АЛГОРИТМУ

The article is devoted to the estimation of computational complexity of a genetic algorithm as one of the key tools for solving optimisation problems. The theoretical aspects of computational complexity of algorithms and the interrelation of elements of a genetic algorithm are considered. The main types of computational complexity of algorithms are described: time, simple and asymptotic. Five basic rules for calculating the asymptotic complexity are given. A mathematical apparatus for estimating the asymptotic complexity of a genetic algorithm is presented, which takes into account the costs of forming the initial population and performing evolution. Evolution occurs through iterations, during which generations of individuals are subjected to certain operations in order to find an optimal solution (crossing, mutation, chromosome decoding, etc.). GA, as a global search algorithm, is considered to find the optimal path without getting stuck in local minima. To assess the computational complexity of GA, we consider solving the traveling salesman problem (TSP) for 28 cities of Ukraine using a modified TSPLIB library and the DEAP platform created in the Python programming language. A block diagram of the GA is presented, the main elements of which are the tournament selection operator, the ordered crossover operator, and the inversion mutation operator. The influence of the population size and the number of generations on the asymptotic complexity of the genetic algorithm in solving the TSP problem is studied. The study considered changing the size of the GA population from 50 to 500 with a step of 50, while for each such value four sets of the number of generations were modelled: from 50 to 200 with a step of 50. Based on the obtained results, we show a linear dependence of the GA execution time on the size of the considered input data. It is shown that the smallest time complexity of the presented GA for the given TSP problem is 0.33848 seconds with a population size of 50 and a similar number of generations, while the largest value is 3.752734 seconds with a population size of 500 and a number of generations of 200. The obtained results can be used to optimise the performance of a GA in the TSP problem.

Learning search algorithm: framework and comprehensive performance for solving optimization problems

In this study, the Learning Search Algorithm (LSA) is introduced as an innovative optimization algorithm that draws inspiration from swarm intelligence principles and mimics the social learning behavior observed in humans. The LSA algorithm optimizes the search process by integrating historical experience and real-time social information, enabling it to effectively navigate complex problem spaces. By doing so, it enhances its global development capability and provides efficient solutions to challenging optimization tasks. Additionally, the algorithm improves the collective learning capacity by incorporating teaching and active learning behaviors within the population, leading to improved local development capabilities. Furthermore, a dynamic adaptive control factor is utilized to regulate the algorithm’s global exploration and local development abilities. The proposed algorithm is rigorously evaluated using 40 benchmark test functions from IEEE CEC 2014 and CEC 2020, and compared against nine established evolutionary algorithms as well as 11 recently improved algorithms. The experimental results demonstrate the superiority of the LSA algorithm, as it achieves the top rank in the Friedman rank-sum test, highlighting its power and competitiveness. Moreover, the LSA algorithm is successfully applied to solve six real-world engineering problems and 15 UCI datasets of feature selection problems, showcasing its significant advantages and potential for practical applications in engineering problems and feature selection problems.

Using Improved Hybrid Grey Wolf Algorithm Based on Artificial Bee Colony Algorithm Onlooker and Scout Bee Operators for Solving Optimization Problems

Grey Wolf optimization (GWO) is a newly developed stochastic meta-heuristic technique motivated by nature. It shows potential in diverse optimization challenges. It replicates grey wolf hunting behaviour and social hierarchy, exploring the solution space similar to their natural process. The algorithm efficiently explores and converges to the optimal solution. However, a drawback of the standard GWO is its limited exploitation capability due to its exploration-focused iterations. This may hinder finding the optimal solution nearby, leading to lower local convergence rates and degraded solution quality. To address this, the GWO-Employed-Onlooker model suggests incorporating the onlooker and scout bee operators from the artificial bee colony algorithm (ABC) during the position-changing stage of the grey wolves. This enhances exploitation capability, resulting in improved local convergence rates and better solution quality. The proposed method’s performance is evaluated on various optimization functions and compared their convergence rate to standard GWO, Genetic Algorithm (GA), Firefly Algorithm (FA), ABC, and Ant Colony Optimization (ACO) techniques. The results demonstrate that the proposed strategy GWO-Employed-Onlooker is better, indicating that it is valuable in solving optimization problems.

Chaotic-Based Mountain Gazelle Optimizer for Solving Optimization Problems

The Mountain Gazelle Optimizer (MGO) algorithm has become one of the most prominent swarm-inspired meta-heuristic algorithms because of its outstanding rapid convergence and excellent accuracy. However, the MGO still faces premature convergence, making it challenging to leave the local optima if early-best solutions neglect the relevant search domain. Therefore, in this study, a newly developed Chaotic-based Mountain Gazelle Optimizer (CMGO) is proposed with numerous chaotic maps to overcome the above-mentioned flaws. Moreover, the ten distinct chaotic maps were simultaneously incorporated into MGO to determine the optimal values and enhance the exploitation of the most promising solutions. The performance of CMGO has been evaluated using CEC2005 and CEC2019 benchmark functions, along with four engineering problems. Statistical tests like the t-test and Wilcoxon rank-sum test provide further evidence that the proposed CMGO outperforms the existing eminent algorithms. Hence, the experimental outcomes demonstrate that the CMGO produces successful and auspicious results.

Learning to Optimize Contextually Constrained Problems for Real-Time Decision Generation

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this paper, we combine ideas from both fields to address the problem of learning to generate decisions to instances of optimization problems with potentially nonlinear or nonconvex constraints where the feasible set varies with contextual features. We propose a novel framework for training a generative model to produce provably optimal decisions by combining interior point methods and adversarial learning, which we further embed within an iterative data generation algorithm. To this end, we first train a classifier to learn feasibility and then train the generative model to produce optimal decisions to an optimization problem using the classifier as a regularizer. We prove that decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Furthermore, the learning models are embedded in an active learning loop in which synthetic instances are iteratively added to the training data; this allows us to progressively generate provably tighter optimal decisions. We investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields advantages over predict-then-optimize and supervised deep learning techniques, respectively. In particular, our framework is more robust to parameter estimation error compared with the predict-then-optimize paradigm and can better adapt to domain shift as compared with supervised learning models. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2020.03565 .

A once-through artificial neural network approach for used nuclear fuel inverse depletion analysis: A comparative study

This work addresses the challenge of identifying the origins and burnup history of used nuclear fuel, which is crucial for safeguarding and non-proliferation analysis. It presents a comparative evaluation of two distinct computational approaches to bundles at the same in-core position: the first entails building a forward Artificial Neural Networks (ANN) surrogate model for fuel inventory prediction followed by solving the inverse depletion problem using an optimization solver. The second approach is to build an inverse ANN model that relates the used nuclear fuel inventory to its initial and burnup conditions (a once-through approach), eliminating the need for the inverse optimization solver step which results in better accuracy, less computational costs, and renders the application of such approach practical. KENO VI depletion model is utilized to deplete a VVER assembly model generating the necessary datasets for the ANN inverse model training and validation. The inverse model is then employed to estimate the initial composition and the burnup for several test cases. The results are then compared to the known initial and burnup conditions as well as to the estimations made by benchmark results from an existing ANN forward surrogate model combined with the Particle Swarm Optimization (PSO) solver. Comparative analyses across eight scenarios consistently reveal that the once-through ANN inverse model has superior accuracy and consistency in terms of estimating the actual burnup and initial fuel enrichment with a relative root mean squared error (RMSE) of 1.20×10-2 compared to the benchmark approach (ANN-PSO) which yielded a relative RMSE of 2.18×10-2. Moreover, the once-through inverse approach has a significantly lower computational cost as it requires 1 inverse model run compared to the 9,450,000 model runs required by the benchmark approach (ANN-PSO). Overall, the results demonstrate that the proposed once-through approach simplifies and enhances the efficiency of solving the inverse fuel depletion problem while outperforming the benchmark approach in terms of predictive accuracy computational cost.

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.

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.

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.

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.