Real-world Engineering Problems Research Articles

Solving multi-objective robust optimization problems via Stakelberg-based game model

Real-world multi-objective engineering problems frequently involve uncertainties stemming from environmental factors, production inaccuracies, and other sources. A critical aspect of addressing these problems, termed Multi-Objective Robust Optimization (MORO) problems, is the development of solutions that are both optimal and resilient to uncertainties. This paper proposes addressing these uncertainties through the application of Stackelberg game models, a novel approach involving the interaction of two players. The Leader searches for optimal and robust solutions and the Follower generates uncertainties based on the Leader’s chosen solutions. The Follower seeks to tackle the most challenging uncertainties associated with the Leader’s candidate solutions. Additionally, this paper introduces a novel metric to assess the robustness of a given set of solutions concerning specified uncertainties.Based on the proposed approach, a co-evolutionary algorithm is developed. A numerical study is then conducted to evaluate the algorithm by comparing its performance with those obtained by four benchmark algorithms on nine benchmark MORO problems. The numerical study also aims to assess its sensitivity to run parameter variations. The experimental results demonstrate the proposed approach’s effectiveness in identifying a non-dominated robust set of solutions.

A Multi-Strategy Improved Northern Goshawk Optimization Algorithm for Optimizing Engineering Problems

Northern Goshawk Optimization (NGO) is an efficient optimization algorithm, but it has the drawbacks of easily falling into local optima and slow convergence. Aiming at these drawbacks, an improved NGO algorithm named the Multi-Strategy Improved Northern Goshawk Optimization (MSINGO) algorithm was proposed by adding the cubic mapping strategy, a novel weighted stochastic difference mutation strategy, and weighted sine and cosine optimization strategy to the original NGO. To verify the performance of MSINGO, a set of comparative experiments were performed with five highly cited and six recently proposed metaheuristic algorithms on the CEC2017 test functions. Comparative experimental results show that in the vast majority of cases, MSINGO’s exploitation ability, exploration ability, local optimal avoidance ability, and scalability are superior to those of competitive algorithms. Finally, six real world engineering problems demonstrated the merits and potential of MSINGO.

Multi-objective group learning algorithm with a multi-objective real-world engineering problem

The concern of multi-objective optimization is to deal with optimization problems with more than one objective that should be optimized at the same time. In this paper, a new multi-objective optimization algorithm called multi-objective group learning algorithm is examined. The algorithm is based on the effect of group leaders on the group members and the effect that the group members have on each other. The algorithm is evaluated against the five Zitzler, Deb and Thiele (ZDT) benchmark functions, two standard functions of the DTLZ benchmarks, and a real-world engineering problem. To quantitatively examine the ability of the algorithm four metrics are utilized. Additionally, to statistically confirm the results, standard deviation and the average metrics are used. Moreover, the Wilcoxon rank sum test is used to examine the importance of the results statistically. Finally, the results of the algorithm are evaluated against multi-objective ant lion optimizer, multi-objective evolutionary algorithm based on decomposition, Pareto envelop-based selection algorithm-II, and multi-object moth swarm algorithm. The results of the benchmark functions showed that the proposed work produced better results in most of the metrics for three out of five ZDT benchmarks, and for the rest of the benchmarks it produced better results in at least one of the metrics compared to the participated algorithms. Moreover, the result of the real world engineering problem proved the ability of the proposed algorithm in producing acceptable and better Pareto front in almost all the metrics. For the proposed algorithm, the result of the generational distance for the speed reducer design problem is 0.8002, whereas it is 7.9375710, and 61.98134 for the multi-objective evolutionary algorithm based on decomposition, multi-objective ant lion optimizer, respectively. Additionally, the produced result for the spacing metric by the proposed algorithm was smaller than the result of the other algorithms for the same metric by at least 100 points. The result of the aforementioned metric proves the good distribution of the non-dominated solutions by the proposed algorithm.

Two-dimensional problem for an infinite body of two coaxial cylinders under the action of a solenoidal body force in the theory of thermoelastic diffusion

This study investigates the dynamic response of an infinite structure comprising two coaxial cylinders employing the one-relaxation-time generalized thermoelastic diffusion model. The inner cylinder, serving as a cavity, possessing a radius a, while the outer cylinder has radius b. The inner cylinder is insulated and experiencing a localized thermal load with thickness 2 h. The outer cylinder, with radius b, is also experiencing to a localized thermal load with width 2 h, and its surface exhibits no traction. Additionally, the structure experiences the influence of a solenoidal body force. The analysis of this problem employs a combination of Laplace transform, inverse Laplace transform, and exponential Fourier transform techniques. Numerical analysis of the resulting solutions reveals the variations in temperature, displacement, radial stress, concentration, and potential fields as a function of the radial coordinate. Results indicate a minimal impact of the time interval on the temperature distribution, while displacement and radial stress exhibit significant time-dependent behavior. These findings highlight the significance of incorporating thermoelastic diffusion theory in the analysis of real-world engineering problems.

A Hybrid Intelligent Optimization Algorithm Based on a Learning Strategy

To overcome the limitations of single-type intelligent optimization algorithms prone to becoming stuck in local optima for complex problems, a hybrid intelligent optimization algorithm named SDIQ is proposed. This algorithm combines simulated annealing (SA), differential evolution (DE), quantum-behaved particle swarm optimization (QPSO), and improved particle swarm optimization (IPSO) into a unified framework. Initially, SA is used to explore the solution space and guide individuals toward preliminary optimization. The individuals are then ranked by fitness and divided into three subpopulations, each optimized by DE, QPSO, and IPSO, respectively. After each iteration, probabilistic learning based on fitness logarithms facilitates mutual learning among subpopulations, enabling global information sharing and improvement. The experimental results demonstrate that SDIQ exhibits strong global search capability and stability in solving both standard test functions and real-world engineering problems. Compared to traditional algorithms, SDIQ enhances global convergence and solution efficiency by integrating multiple optimization strategies and leveraging inter-individual learning, providing an effective solution for complex optimization problems.

Improved multi-strategy artificial rabbits optimization for solving global optimization problems

Artificial rabbits optimization (ARO) is a metaheuristic algorithm based on the survival strategy of rabbits proposed in 2022. ARO has favorable optimization performance, but it still has some shortcomings, such as weak exploitation capacity, easy to fall into local optima, and serious decline of population diversity at the later stage. In order to solve these problems, we propose an improved multi-strategy artificial rabbits optimization, called IMARO, based on ARO algorithm. In this paper, a roulette fitness distance balanced hiding strategy is proposed so that rabbits can find better locations to hide more reasonably. Meanwhile, in order to improve the deficiency of ARO which is easy to fall into local optimum, an improved non-monopoly search strategy based on Gaussian and Cauchy operators is designed to improve the ability of the algorithm to obtain the global optimal solution. Finally, a covariance restart strategy is designed to improve population diversity when the exploitation is stagnant and to improve the convergence accuracy and convergence speed of ARO. The performance of IMARO is verified by comparing original ARO algorithm with six basic algorithms and seven improved algorithms. The results of CEC2014, CEC2017, CEC2022 show that IMARO has a good exploitation and exploration ability and can effectively get rid of local optimum. Moreover, IMARO produces optimal results on six real-world engineering problems, further demonstrating its efficiency in solving real-world optimization challenges.

Spiral-refraction mutation prairie dog algorithm: Optimization framework for engineering design of interconnected multimachine power system

Many real-world engineering problems, characterized by high-dimensionality, nonlinearity, nonconvexity, and multi-modality, demand advanced optimization methods. Traditional algorithms may struggle with these challenges. Prairie dog optimization (PDO) was proposed for function optimization but faces limitations in balancing exploration and exploitation due to two reasons. The first one is related to diversity features which may not be efficient, and the second one is related to having no leading mechanism for direct search feature towards the promising regions. With that in mind, this study introduces an enhanced PDO variant, improved PDO (IPDO), addressing PDO's drawbacks through two key strategies: refraction-based learning (RBL) and spiral search learning (SSL). RBL enhances exploration by generating refraction solutions, while SSL conducts deep local searches around the best solution, strengthening exploitation. IPDO's performance is evaluated on benchmarks, IEEE CEC2017/CEC2020 test suites, and real-world constraint engineering optimization problems. Comparative analyses, including statistical measures, convergence analysis, and boxplot analysis, demonstrate IPDO's superiority. Besides, the IPDO is applied to estimate more promising parameters of power system stabilizer utilized in an interconnected multimachine power system using Western System Coordinating Council three-machine, nine-bus power system. Results illustrate that the IPDO harvests the better estimation among the other methods, making it to be an efficient and powerful tool for dealing with the efficient operation of an interconnected multimachine power system which is a challenging real-world engineering problem.

DMT-OMPA: Innovative applications of an efficient adversarial Marine Predators Algorithm based on dynamic matrix transformation in engineering design optimization

This paper introduces an innovative variant of the Marine Predators Algorithm (MPA), termed the Dynamic Matrix Transformation-based Oppositional Marine Predators Algorithm (DMT-OMPA), aimed at enhancing the efficiency of engineering optimization strategies. Traditional MPAs have several shortcomings, including insufficient solution diversity and coverage in the initialization phase, a tendency to become trapped in local optima, and inadequate search capabilities in the later stages of iteration, all of which negatively impact the algorithm’s efficiency and effectiveness. To address these issues, the DMT-OMPA incorporates oppositional learning mechanisms and dynamic matrix transformation strategies, significantly enhancing global search capabilities and accelerating convergence speed, particularly in handling complex multidimensional optimization problems.Experimental results on the CEC2013 and CEC2017 test suites demonstrate that DMT-OMPA outperforms other recent MPA variants, various classical algorithm variants, and newly proposed algorithms, verifying its advantages in precision and reliability. Furthermore, the application of this algorithm to various real-world engineering problems substantiates its broad applicability and high efficiency. The study’s findings not only deepen our understanding of swarm intelligence optimization algorithms but also provide a new efficient tool for solving complex engineering problems. The results indicate a promising potential for wider application in diverse fields, suggesting that the DMT-OMPA algorithm could become an effective tool for tackling complex optimization problems in the future.

Harmonic Mean Optimizer (HMO) for global problems solving

This study introduces the Harmonic Mean Optimizer (HMO), a novel meta-heuristic algorithm designed to address complex global optimization problems. The primary objective of this research is to develop an optimization technique that effectively balances exploration and exploitation without requiring extensive parameter tuning, thereby simplifying the optimization process and enhancing its robustness across various problem domains. The HMO employs a unique dual-fitness index that leverages the harmonic mean to assess both the quality and diversity of candidate solutions dynamically. This approach ensures a balanced search process that avoids premature convergence and improves the ability to find global optima. The methodology involves extensive benchmarking of the HMO against a comprehensive set of test functions, including 23 traditional functions from the Congress on Evolutionary Computation (CEC) 2017 test suite. The performance of the HMO is compared with that of established meta-heuristic algorithms, such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), to validate its efficacy in terms of convergence speed and solution accuracy. Additionally, the HMO is applied to several real-world engineering problems to demonstrate its practical utility. The results show that the HMO consistently outperforms the benchmark algorithms, achieving faster convergence and higher accuracy in finding optimal solutions across a diverse range of test problems. In practical applications, the HMO effectively optimized complex engineering tasks, achieving significant improvements in both solution quality and computational efficiency. These findings highlight the potential of the HMO as a versatile and powerful tool for global optimization tasks. the HMO offers a significant advancement in optimization methodologies by providing a robust, parameter-free approach that effectively balances exploration and exploitation. This study underscores the HMO’s applicability to a wide range of optimization challenges and sets the foundation for future research and development in enhancing and applying this innovative algorithm to more complex and diverse problem domains.

Optimization of Large-Scale Sparse Matrix-Vector Multiplication on Multi-GPU Systems

Sparse matrix-vector multiplication (SpMV) is one of the important kernels of many iterative algorithms for solving sparse linear systems. The limited storage and computational resources of individual GPUs restrict both the scale and speed of SpMV computing in problem-solving. As real-world engineering problems continue to increase in complexity, the imperative for collaborative execution of iterative solving algorithms across multiple GPUs is increasingly apparent. Although the multi-GPU-based SpMV takes less kernel execution time, it also introduces additional data transmission overhead, which diminishes the performance gains derived from parallelization across multi-GPUs. Based on the non-zero elements distribution characteristics of sparse matrices and the trade-off between redundant computations and data transfer overhead, this paper introduces a series of SpMV optimization techniques tailored for multi-GPU environments and effectively enhances the execution efficiency of iterative algorithms on multiple GPUs. Firstly, we propose a two-level non-zero elements-based matrix partitioning method to increase the overlap of kernel execution and data transmission. Then, considering the irregular non-zero elements distribution in sparse matrices, a long-row-aware matrix partitioning method is proposed to hide more data transmissions. Finally, an optimization using redundant and inexpensive short-row execution to exchange costly data transmission is proposed. Our experimental evaluation demonstrates that, compared with the SpMV on a single GPU, the proposed method achieves an average speedup of 2.00x and 1.85x on platforms equipped with two RTX 3090 and two Tesla V100-SXM2, respectively. The average speedup of 2.65x is achieved on a platform equipped with four Tesla V100-SXM2.

Improved Dujiangyan Irrigation System Optimization (IDISO): A Novel Metaheuristic Algorithm for Hydrochar Characteristics

Hyperparameter tuning is crucial in the development of machine learning models. This study introduces the nonlinear shrinking factor and the Cauchy mutation mechanism to improve the Dujiangyan Irrigation System Optimization (DISO), proposing the improved Dujiangyan Irrigation System Optimization algorithm (IDISO) for hyperparameter tuning in machine learning. The optimization capabilities and convergence performance of IDISO were validated on 87 CEC2017 benchmark functions of varying dimensions and nine real-world engineering problems, demonstrating that it significantly outperforms DISO in terms of convergence speed and accuracy, and ranks first in overall performance among the seventeen advanced metaheuristic algorithms being compared. To construct a robust and generalizable prediction model for hydrochar element characteristics, this study utilized IDISO and DISO algorithms to fine-tune the parameters of the XGBoost model. The experimental results show that the IDISO-XGBoost model achieved an average prediction performance of 0.95, which represents a 4% improvement over the DISO-XGBoost model. These results indicate that the IDISO algorithm has significant potential and value in practical applications.

Arctic puffin optimization: A bio-inspired metaheuristic algorithm for solving engineering design optimization

In this paper, we innovatively propose the Arctic Puffin Optimization (APO), a metaheuristic optimization algorithm inspired by the survival and predation behaviors of the Arctic puffin. The APO consists of an aerial flight (exploration) and an underwater foraging (exploitation) phase. In the exploration phase, the Levy flight and velocity factor mechanisms are introduced to enhance the algorithm's ability to jump out of local optima and improve the convergence speed. In the exploitation phase, strategies such as the synergy and adaptive change factors are used to ensure that the algorithm can effectively utilize the current best solution and guide the search direction. In addition, the dynamic transition between the exploration and development phases is realized through the behavioral conversion factor, which effectively balances global search and local development. In order to verify the advancement and applicability of the APO algorithm, it is compared with nine advanced optimization algorithms. In the three test sets of CEC2017, CEC2019, and CEC2022, the APO algorithm outperforms the other compared algorithms in 72%, 70%, and 75% of the cases, respectively. Meanwhile, the Wilcoxon signed-rank test results and Friedman rank-mean statistically prove the superiority of the APO algorithm. Furthermore, on thirteen real-world engineering problems, APO outperforms the other compared algorithms in 85% of the test cases, demonstrating its potential in solving complex real-world optimization problems. In summary, APO proves its practical value and advantages in solving various complex optimization problems by its excellent performance.

A multi-strategy surrogate-assisted social learning particle swarm optimization for expensive optimization and applications

Evolutionary algorithms (EAs) require extensive fitness evaluations, which constitutes a barrier to solving computationally complex problems. In contrast, surrogate-assisted evolutionary algorithms (SAEAs) have the potential to solve complex expensive optimization problems. This paper proposes a surrogate-assisted social learning particle swarm optimization (SASLPSO) to handle expensive optimization problems. An adaptive local surrogate (ALS) strategy introduced in SASLPSO is introduced to accurately fit the landscape near the global optimum. ALS consists of two layers of surrogate, the part of the particles closest to the optimal particle and the closest to the optimal particle among the particles that have been eliminated historically. The proposed SASLPSO effectively combines global surrogate (GS) and adaptive local surrogate (ALS) to balance global exploration and local exploitation. Furthermore, a novel random group-based pre-screening (RGBPS) strategy is proposed to screen promising particles for real function evaluation. The proposed SASLPSO is compared with four other state-of-the-art SAEAs on 30D, 50D, and 100D benchmark functions. In addition, the significance of the SASLPSO algorithm was also verified using the Wilcoxon rank test. The test results on the benchmark function show that the SASLPSO algorithm performs better than other comparison algorithms, especially when dealing with high-dimensional benchmark functions. To further validate the effectiveness of the SASLPSO algorithm in solving expensive optimization problems, it was also applied to feature selection problems and real-world engineering problems. In addition, in the real application of node deployment in 3D wireless sensor networks, the highest coverage rate of the SASLPSO algorithm can reach 99.96%, confirming its performance advantages in solving real application problems. Finally, in the application of network intrusion detection, SASLPSO has shown more advantages in multiple metrics, proving its versatility.

Learning cooking algorithm for solving global optimization problems

In recent years, many researchers have made a continuous effort to develop new and efficient meta-heuristic algorithms to address complex problems. Hence, in this study, a novel human-based meta-heuristic algorithm, namely, the learning cooking algorithm (LCA), is proposed that mimics the cooking learning activity of humans in order to solve challenging problems. The LCA strategy is primarily motivated by observing how mothers and children prepare food. The fundamental idea of the LCA strategy is mathematically designed in two phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef. The performance of the proposed LCA algorithm is evaluated on 51 different benchmark functions (which includes the first 23 functions of the CEC 2005 benchmark functions) and the CEC 2019 benchmark functions compared with state-of-the-art meta-heuristic algorithms. The simulation results and statistical analysis such as the t-test, Wilcoxon rank-sum test, and Friedman test reveal that LCA may effectively address optimization problems by maintaining a proper balance between exploitation and exploration. Furthermore, the LCA algorithm has been employed to solve seven real-world engineering problems, such as the tension/compression spring design, pressure vessel design problem, welded beam design problem, speed reducer design problem, gear train design problem, three-bar truss design, and cantilever beam problem. The results demonstrate the LCA’s superiority and capability over other algorithms in solving complex optimization problems.

A novel community development algorithm and its application to optimize main steam temperature of supercritical units

This paper summarizes the community where people live development laws and proposes a novel meta-heuristic called community development algorithm (CDA). To enhance the optimization process, CDA innovatively designed two unique attraction effects based on the degree of people’s direct contribution to society and abstracted four novel inter-particle learning ways based on people’s four social activities: Marriage, Entrepreneurship, Working, and University. Theoretically, it is demonstrated that CDA can satisfactorily balance the exploration and the exploitation stages, and necessary and sufficient conditions for CDA convergence are derived. The 59 functions of Congress on Evolutionary Computation 2014 and 2017 are introduced as the benchmark. Under the pressure of other 32 well-known meta-heuristics, statistical results, including averages, standard deviations, rank-sum tests, and sign-rank tests, as well as graphical results, including convergence curves and box plots, confirm that CDA is competent for solving numerical optimization problems with efficiency and reliability. Significantly, the quantitative analysis demonstrated that CDA’s average ranking is ahead of the emperor penguin optimizer by 73.5% while ahead of the fully informed search algorithm by 62.1%, respectively. Additionally, the scalability and fastness of CDA are validated by scalability and wall clock time analysis, and the classical application of Congress on Evolutionary Computation 2011 demonstrates the outstanding accuracy and stability of CDA. Finally, CDA is utilized to optimize the controller parameter in the main steam temperature control system of the supercritical unit. The control response curves show that CDA generally provides better parameters than compared algorithms, demonstrating the merits and potential to solve complex real-world engineering problems.

A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems

We consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker’s preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations.

A novel giant pacific octopus optimizer for real-world engineering problem

A novel giant pacific octopus optimizer for real-world engineering problem

Multi-Strategy Improved Dung Beetle Optimization Algorithm and Its Applications.

The dung beetle optimization (DBO) algorithm, a swarm intelligence-based metaheuristic, is renowned for its robust optimization capability and fast convergence speed. However, it also suffers from low population diversity, susceptibility to local optima solutions, and unsatisfactory convergence speed when facing complex optimization problems. In response, this paper proposes the multi-strategy improved dung beetle optimization algorithm (MDBO). The core improvements include using Latin hypercube sampling for better population initialization and the introduction of a novel differential variation strategy, termed "Mean Differential Variation", to enhance the algorithm's ability to evade local optima. Moreover, a strategy combining lens imaging reverse learning and dimension-by-dimension optimization was proposed and applied to the current optimal solution. Through comprehensive performance testing on standard benchmark functions from CEC2017 and CEC2020, MDBO demonstrates superior performance in terms of optimization accuracy, stability, and convergence speed compared with other classical metaheuristic optimization algorithms. Additionally, the efficacy of MDBO in addressing complex real-world engineering problems is validated through three representative engineering application scenarios namely extension/compression spring design problems, reducer design problems, and welded beam design problems.

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.

Multi-objective generalized normal distribution optimization: a novel algorithm for multi-objective problems

This study introduces the Multi-objective Generalized Normal Distribution Optimization (MOGNDO) algorithm, an advancement of the Generalized Normal Distribution Optimization (GNDO) algorithm, now adapted for multi-objective optimization tasks. The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism, designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field. The algorithm's effectiveness is rigorously tested across 35 varied case studies, encompassing both mathematical and engineering challenges, and benchmarked against prominent algorithms like MOPSO, MOGWO, MOHHO, MSSA, MOALO, MOMVO, and MOAOS. Utilizing metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the study underscores MOGNDO's ability to produce Pareto fronts of high quality, marked by exceptional precision and diversity. The results affirm MOGNDO's superior performance and versatility, not only in theoretical tests but also in addressing complex real-world engineering problems, showcasing its high convergence and coverage capabilities. The source codes of the MOGNDO algorithm are publicly available at https://nimakhodadadi.com/algorithms-%2B-codes.