An optimisation approach for uncertainty-based long-term production scheduling in open-pit mines using meta-heuristic algorithms

One of the surface mining methods is open-pit mining, by which a pit is dug to extract ore or waste downwards from the earth’s surface. In the mining industry, one of the most significant difficulties is long-term production scheduling (LTPS) of the open-pit mines. Deterministic and uncertainty-based approaches are identified as the main strategies, which have been widely used to cope with this problem. Within the last few years, many researchers have highly considered a new computational type, which is less costly, i.e., meta-heuristic methods, so as to solve the mine design and production scheduling problem. Although the optimality of the final solution cannot be guaranteed, they are able to produce sufficiently good solutions with relatively less computational costs. In the present paper, two hybrid models between augmented Lagrangian relaxation (ALR) and a particle swarm optimization (PSO) and ALR and bat algorithm (BA) are suggested so that the LTPS problem is solved under the condition of grade uncertainty. It is suggested to carry out the ALR method on the LTPS problem to improve its performance and accelerate the convergence. Moreover, the Lagrangian coefficients are updated by using PSO and BA. The presented models have been compared with the outcomes of the ALR-genetic algorithm, the ALR-traditional sub-gradient method, and the conventional method without using the Lagrangian approach. The results indicated that the ALR is considered a more efficient approach which can solve a large-scale problem and make a valid solution. Hence, it is more effectual than the conventional method. Furthermore, the time and cost of computation are diminished by the proposed hybrid strategies. The CPU time using the ALR-BA method is about 7.4% higher than the ALR-PSO approach.

In machine learning, feature selection is a crucial and important operation. The basic goal of the feature selection problem is to lower the size of the feature set while preserving performance accuracy. To classify the datasets, many approaches have been devised. Metaheuristic algorithms, on the other hand, have received a lot of interest for handling a variety of optimization problems. As a result, this paper gives a comprehensive assessment of the literature on employing metaheuristic algorithms to solve feature selection problems. Furthermore, based on their behavior, metaheuristic algorithms have been divided into four types. A classified list of over a hundred metaheuristic algorithms is also provided. Only binary variations of metaheuristic algorithms have been evaluated and categorized in order to address the feature selection problem, and a comprehensive explanation of each has been provided. The binary classification, name of the classifier used, datasets, and evaluation metrics for metaheuristic algorithms used to solve feature selection problems are all included. After analyzing the articles, problems and issues in getting the optimal feature subset using various metaheuristic methods are identified. Finally, several research needs are identified for researchers who want to continue their work on building or refining metaheuristic categorization algorithms. A case study is presented for an application in which UCI datasets are adopted and a number of metaheuristic algorithms are used to achieve the optimum functionality.KeywordsMachine learningMetaheuristic algorithmsFeature selectionClassificationBinary variations

ABSTRACTThe transient electromagnetic method (TEM) is a prominent geophysical technique, and the TEM inversion for resistivity models is a crucial aspect of physical exploration. However, TEM inversion faces challenges such as nonlinearity, multiple solutions and ill‐conditioning, which can lead to inaccurate results. In response to these challenges, metaheuristic algorithms have been extensively studied for their innovative approaches to solving inverse problems. Despite this, many existing metaheuristic inversion algorithms exhibit limitations, including premature convergence, slow convergence speed and inadequate computational accuracy. To address these issues, an improved bat algorithm (IBA) that incorporates logistic chaotic mapping and a spiral flight strategy (Logistic Chaotic Mapping and Spiral Flight Strategy‐Based Bat Algorithm, LSBA) has been proposed. The logistic chaotic mapping strategy is utilized to initialize the population of the bat algorithm to enhance the initial convergence rate. Moreover, the spiral flight strategy facilitates the bats’ escape from local optima, thereby improving the algorithm's local exploration capabilities and solution accuracy. Numerical simulations, synthetic models and field experiments have demonstrated that the LSBA significantly enhances solution precision (the degree of closeness between the algorithm's inverted parameters and the true values), convergence speed and anti‐noise performance. The LSBA effectively retrieves the stratigraphic parameters of the true model and accurately represents the geological information of actual mining areas, thereby validating the efficacy and feasibility of the proposed approach in TEM inversion.

There exists a direct need to automate the process of test suite generation to get the most optimal results as testing accounts for more than 40% of total cost. One method to solve this problem is the use of meta-heuristic algorithms which iteratively improve the test data to reach the most optimized test suites. This study focuses on the performance evaluation of six meta-heuristic algorithms namely: hill-climbing algorithm (HCA), particle swarm optimization (PSO), firefly algorithm (FA), cuckoo search algorithm (CS), bat algorithm (BA) and artificial bee colony algorithm (ABC) by using their standard implementation to optimize the path coverage and branch coverage produced by the test data. The goal of the study was to find the best-suited algorithm to narrow down the future research in the field of test automation for path coverage-based optimization approaches. Each algorithm was first implemented to automatically generate test suites based on the program under test. This was followed by the performance evaluation of each algorithm for five programs written in Java. The algorithms were compared using process metrics: average time, best time, worst time and product metrics: path coverage & objective function values of the generated test suites. Results indicated ABC as the best-suited algorithm as it gave the most optimal test suites in reasonable time. BA was found to be the fastest but produced less optimal results. FA was found to be the slowest algorithm, while CS, PSO and HCA performed in between. These results show the relative performance of the six algorithms for this scenario and may be used by the future researchers to narrow down and improve the best performing algorithms for path coverage-based optimization approaches.

The research and development of metaheuristic methods are critical issues in computer science. In the past decade, metaheuristic algorithms have been used in many engineering applications such as optimization of engineering problems, telecommunications, information security, and image processing. Many metaheuristic algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and genetic algorithm (GA) are recently becoming very popular.There are many studies conducted in the literature on the comparison of PSO with other metaheuristic algorithms. In this chapter, various studies carried out between the years of 2010 and 2020 about the comparison of PSO with the other metaheuristic algorithms will be examined. The metaheuristic algorithms to be considered are simulated annealing (SA), genetic algorithm (GA), differential evolution (DE), ant colony optimization (ACO), artificial bee colony (ABC) algorithm, particle swarm optimization (PSO), tabu search (TS), harmony search (HS), firefly algorithm (FF), cuckoo search (CS), bat-inspired algorithm (BA), water wave optimization (WWO), clonal selection algorithm (CLONALG), chemical reaction optimization (CRO), sine cosine algorithm (SCA), glowworm swarm optimization (GSO), and grey wolf optimizer (GWO). This study aims to evaluate and analyze the covered papers according to several criteria such as (a) rates of studies according to publishing years, (b) the metaheuristic algorithms that are compared to PSO, (c) performance evaluation of compared algorithms, (d) the metaheuristic algorithms with their inspirational approaches and their initial proposed studies and years, (e) the field of subjects where the algorithms are applied in the reviewed studies, and (f) used databases in the examined studies.This study is a comprehensive literature review of the comparison of PSO with the most popular metaheuristic algorithms. The intention of this review is to be useful for researchers who want to conduct a survey on this area of the subject as this chapter will cover the essential and helpful analysis of the related research.

Complex huge-scale scientific applications are simplified by workflow to execute in the cloud environment. The cloud is an emerging concept that effectively executes workflows, but it has a range of issues that must be addressed for it to progress. Workflow scheduling using a nature-inspired metaheuristic algorithm is a recent central theme in the cloud computing paradigm. It is an NP-complete problem that fascinates researchers to explore the optimum solution using swarm intelligence. This is a wide area where researchers work for a long time to find an optimum solution but due to the lack of actual research direction, their objectives become faint. Our systematic and extensive analysis of scheduling approaches involves recently high-cited metaheuristic algorithms like Genetic Algorithms (GA), Whale Search Algorithm (WSA), Ant Colony Optimization (ACO), Bat Algorithm, Artificial Bee Colony (ABC), Cuckoo Algorithm, Firefly Algorithm and Particle Swarm Optimization (PSO). Based on various parameters, we do not only classify them but also furnish a comprehensive striking comparison among them with the hope that our efforts will assist recent researchers to select an appropriate technique for further undiscovered issues. We also draw the attention of present researchers towards some open issues to dig out unexplored areas like energy consumption, reliability and security for considering them as future research work.

The optimisation of complex engineering design problems is highly challenging due to the consideration of various design variables. To obtain acceptable near-optimal solutions within reasonable computation time, metaheuristics can be employed for such problems. However, a plethora of novel metaheuristic algorithms are developed and constantly improved and hence it is important to evaluate the applicability of the novel optimisation strategies and compare their performance using real-world engineering design problems. Therefore, in this paper, eight recent population-based metaheuristic optimisation algorithms—African Vultures Optimisation Algorithm (AVOA), Crystal Structure Algorithm (CryStAl), Human-Behaviour Based Optimisation (HBBO), Gradient-Based Optimiser (GBO), Gorilla Troops Optimiser (GTO), Runge–Kutta optimiser (RUN), Social Network Search (SNS) and Sparrow Search Algorithm (SSA)—are applied to five different mechanical component design problems and their performance on such problems are compared. The results show that the SNS algorithm is consistent, robust and provides better quality solutions at a relatively fast computation time for the considered design problems. GTO and GBO also show comparable performance across the considered problems and AVOA is the most efficient in terms of computation time.

The parameters of the photovoltaic cells and panels are very important to forecast the power generated. There are a lot of methods to extract the parameters using analytical, metaheuristic, and hybrid algorithms. The comparison between the widely used analytical method and some of the best metaheuristic algorithms from the algorithm families is made for datasets from the specialized literature, using the following statistical tests: absolute error, root mean square error, and the coefficient of determination. The equivalent circuit and mathematical model considered is the single diode model. The result comparison shows that the metaheuristic algorithms have the best performance in almost all cases, and only for the genetic algorithm, there are poorer results for one chosen photovoltaic cell. The parameters of the photovoltaic cells and panels and also the current-voltage characteristic for real outdoor weather conditions are forecasted using the parameters calculated with the best method: one for analytical—the five-parameter analytical method—and one for the metaheuristic algorithms—hybrid successive discretization algorithm. Additionally, the genetic algorithm is used. The forecast current-voltage characteristic is compared with the one measured in real sunlight conditions, and the best results are obtained in the case of a hybrid successive discretization algorithm. The maximum power forecast using the calculated parameters with the five-parameter method is the best, and the error in comparison with the measured ones is 0.48%.

This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. In this paper, a general approach is suggested to solve a variety of linear and nonlinear ordinary differential equations (ODEs). With the aid of certain fundamental concepts of mathematics, Fourier series expansion and metaheuristic optimization methods, ODEs can be represented as an optimization problem. The aim is to minimize the weighted residual function (error function) of the ODEs. The boundary and initial values of ODEs are considered as constraints for the optimization model. Generational distance metric is used for evaluation and assessment of approximate solutions versus exact solutions. Two ODEs and one mechanical problem are approximately solved and compared with their exact solutions. The optimization task is carried out using different optimizers including the particle swarm optimization and the water cycle algorithm. The optimization results obtained show that the metaheuristic algorithms can be successfully applied for approximate solving of different types of ODEs.

The hyperparameters of a convolutional neural network always have been important, because the performance of the convolutional neural network depends largely on them. To find manually the optimal value requires a lot of work, experience, and time. Metaheuristic algorithms are approximate general-purpose search and optimization algorithms, they are used to find a good solution into search space. In the book chapter, the hyperparameters of a convolutional neural network are optimized. A metaheuristic algorithm is used to finds the best solution, that is, the best hyperparameter value for higher accuracy of the convolutional neural network (CNN). The results of four metaheuristic algorithms that have the same objective are compared, which are PSO (Particle Swarm Optimization), ABC (Artificial Bee Colony), ALO (Ant Lion Optimization), and BA (Bat Algorithm). Each algorithm uses the same convolutional neural network architecture as well as the same dataset (MNIST database) also each algorithm is run 30 times to perform the corresponding statistics. Finally, the results of the algorithms are shown.

In recent years, metaheuristic algorithms have gained prominence as powerful computational techniques for solving complex optimization problems across various domains, including healthcare. Their ability to effectively explore vast solution spaces enables them to identify optimal or near-optimal solutions to challenging problems. Despite their growing importance, metaheuristic algorithms, inspired by natural and human problem-solving strategies, are increasingly applied in healthcare to address complex optimization challenges such as diagnosis, treatment planning, and resource allocation. But traditional ML models often face problems like getting stuck in training, taking too much time to compute, and not balancing exploration and exploitation properly. These issues make them less effective for solving complex medical classification problems. To overcome these limitations, this study introduces new hybrid metaheuristic models such as Ropalidia Marginata (RM) hybrid with various metaheuristic algorithms such as Ant Colony Optimization (ACO), particle swarm optimization (PSO), Firefly, Artificial Bee Colony (ABC), Grey Wolf Optimizer (GWO), Differential Evolution (DE), and Bat Algorithm. Further all these hybrid metaheuristic algorithms are combined with a Feedforward Neural Network (FFNN) to train the network more efficiently. The proposed method uses the dominance-based behavior of RM wasp to improve the global search ability, is stable during learning, and improves classification accuracy. The performance of proposed frameworks is to check against several start of the art models on three critical medical datasets such as breast cancer, diabetes, and heart disease. The results showed that proposed models gave better results than the traditional algorithms in terms of accuracy, mean squared error (MSE), standard deviation (SD), and AUC-ROC.

The increasing adoption of solar energy as a clean and sustainable power source has intensified research efforts toward developing more efficient photovoltaic (PV) cells. These cells exhibit nonlinear characteristics that are significantly influenced by variations in irradiance and temperature. Accurate estimation of PV model parameters plays a crucial role in maximizing performance, particularly via precise maximum power point (MPP) tracking. This paper presents a new hybrid metaheuristic algorithm that combines the global exploration capability of the Bat Algorithm (BA) with local exploitation efficiency of the Crow Search Algorithm (CR) to optimize PV parameter estimation. The proposed approach is tested using Single-Diode (SDM), Double-Diode (DDM), and Triple-Diode (TDM) models based on the RTC France dataset. The hybrid model demonstrates better convergence behavior and robustness compared to conventional approaches. Qualitatively, it effectively manages parameter uncertainty; quantitatively, it achieves RMSE values of 0.00077299 (SDM), 0.0008215 (DDM), and 0.0008068 (TDM), outperforming traditional algorithms such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

Metaheuristic algorithms are used to solve many optimization problems. Firefly algorithm, particle swarm improvement, harmonic search, and bat algorithm are used as search algorithms to find the optimal solution to the problem field. In this paper, we have investigated and analyzed a new scaled conjugate gradient algorithm and its implementation, based on the exact Wolfe line search conditions and the restart Powell criterion. The new spectral conjugate gradient algorithm is a modification of the Birgin and Martínez method, a manner to overcome the lack of positive definiteness of the matrix defining the search direction. The preliminary computational results for a set of 30 unconstrained optimization test problems show that this new spectral conjugate gradient outperforms a standard conjugate gradient in this field and we have applied the newly proposed spectral conjugate gradient algorithm in bat algorithm to reach the lowest possible goal of bat algorithm. The newly proposed approach, namely, the directional bat algorithm (CG-BAT), has been then tested using several standard and nonstandard benchmarks from the CEC’2005 benchmark suite with five other algorithms and has been then tested using nonparametric statistical tests and the statistical test results show the superiority of the directional bat algorithm, and also we have adopted the performance profiles given by Dolan and More which show the superiority of the new algorithm (CG-BAT).

Due to the large size of open-pit mines’ long-term production scheduling (OPMPS) problem in large-scale deposits, it is challenging to solve that problem as the mixed integer linear programming (MILP) model. This study used an approach of the genetic algorithm (GA) to tackle this challenge. So, in a small hypothetical deposit, based on the blocks in the ultimate pit limit and scenarios with 2–6 phases, net present values (NPV) and computational times obtained from the GA and MILP model were compared to evaluate the GA. Also, the GA was applied to a large-scale deposit to determine the efficiency of the GA in real deposits. The maximum NPV was obtained for the four-phase scenario in the hypothetical deposit and the six-phase scenario in the large-scale deposit. Although the GA’s NPV decreased slightly compared to the global optimum solution from the MILP model, the computational time was significantly reduced.