Intelligent Engineering Optimisation with the Bees Algorithm

This chapter discusses modifications to the basic Bees Algorithm to enhance its performance. The proposed changes involve adding an early neighbourhood scanning step to determine promising areas from which to start the local search operation and making the recruitment process dynamic by varying the number of bees recruited to exploit a patch according to how efficiently it has been exploited. The enhanced version of the Bees Algorithm was applied to well-known complex continuous benchmark functions with high dimensions to find their optima. The results obtained from this study show that the new Bees Algorithm performed better than the basic version. The results were also compared with those of other swarm-based optimisation methods.

The Bees Algorithm is a well-known metaheuristic optimisation method that has been applied in many disciplines with noticeable success. For example, it has been applied to machine scheduling, training artificial neural networks (ANNs) for pattern recognition, and the design of mechanical structures. There have been many attempts to improve the Bees Algorithm’s performance to tackle some of its weaknesses with more focus on the local search stage. This research attempts to improve the Bees Algorithm with more attention directed to stages other than the local search. The suggested method employs an adapted notion of the regional elimination method to achieve the abandonment and reduction of the search space within the Bees Algorithm. To assess the performance, the proposed method was tested on 24 benchmark functions, and it was applied to two engineering problems. The results obtained indicate a statistically significant improvement.

Inspired by the foraging behaviour of bees in nature, the bees algorithm (BA) is a biomimetic optimisation method designed according to how bees work together in choosing food sources and collecting high-quality honey. However, there are only a few mathematical studies on the convergence and optimisation problem of BA in the literature, and most of the BA implementations are dependent on trial-and-error. Thus, this study attempts to use Markov chain theory to enhance the understanding and analysis of BA convergence from the perspectives of the neighbourhood contraction strategy and site abandonment strategy. To improve the optimisation performance of the BA, this study established a combination model of the BA and a dynamic particle swarm optimisation algorithm on the local search process of the BA and the effect of the task allocation of scout bees for target location. Finally, the simulation experiment was conducted in MATLAB using the combination model. The simulation result shows that the probability of the combination model falling into the local optimum is much lower than that of the conventional BA based on the good convergence performance for the optimisation problem. It can enrich the theoretical base of the BA as a resource for convergence performance and further optimisation analysis.

This chapter presents a Bees Algorithm (BA) Optimisation Toolkit developed in LabVIEW. The BA is an effective optimisation algorithm that mimics the nectar-foraging behaviour of honey bees. LabVIEW is a powerful program for data acquisition and control applications that is very popular in industry. There are tools within the scope of optimisation within LabVIEW, but there is no toolkit for the BA. In this chapter, the preparation of the BA in LabVIEW is explained step by step. The toolkit has two parts. Optimisation can be performed on standard continuous test functions with the first part, and new functions and problems can be defined and solved. It has been observed that the minimum values of complex continuous functions can be reached quickly in experimental studies. With the second part, combinatorial optimisation can be conducted on travelling salesman problems (TSPs), and new TSPs can be defined and solved. It has been shown experimentally that minimum-cost solutions can be found in a small number of iterations using this toolkit.

The geometrical optimisation of smart sandwich plates on Pasternak-type elastic foundations is presented in this chapter. The basic equations are derived based on Reddy’s higher-order shear deformation plate theory and Hamilton’s principle, taking into account the effect of von Kármán kinematic nonlinearity. The forms of possible solutions and electric and magnetic potentials are chosen as double trigonometric functions based on boundary conditions. The expressions of the natural frequency and the critical buckling load are determined by using the Galerkin method. The Bees Algorithm is applied to obtain the maximum values of the natural frequency and the critical buckling load of the sandwich plate, which depends on geometrical and material parameters.

The bees algorithm (BA) is a novel swarm-based intelligent metaheuristic search algorithm that was proposed by Pham et al. in 2005. It has been applied to several complex optimisation problems successfully. One of the main mechanisms in BA is to direct search agents (bees) to the search sites that were discovered by the best-performing bees (elite bees). In the original BA, this mechanism is realised by generating random bees in the close neighbourhood of elite bees. In this chapter, a different approach borrowed from the weighted superposition attraction–repulsion algorithm (WSAR) is incorporated into BA for search direction determination. In this approach, attractive and repulsive superpositions are determined by considering “elite bees” and “nonselected site bees” (the worst performing bees), similar to WSAR. The performance of this new approach is tested on four different constrained engineering design optimisation problems. The obtained results are compared with the basic BA and some other metaheuristic algorithms from the literature. The performance of BA can be further improved by utilising such an approach.

The welding sequence has a significant influence on the magnitude and distribution of the final welding distortion, which often contributes negatively to the dimensional accuracy, structural instability, fabrication cost, and in-service performance of the welded assembly. Hence, it is of great significance to automatically plan optimal welding robot paths for minimum residual deformations in real-world engineering. In this study, an integrated optimisation approach combining an artificial neural network (ANN) model and intelligent optimisation algorithm was proposed to optimise welding sequences for minimising residual distortions in the assembly of thin-walled aluminium tubes. During the optimisation process, an ANN model was successfully established and implanted into this optimisation method to rapidly predict welding distortion within good computational precision. Subsequently, the Bees Algorithm (BA) was developed to systematically search for the optimal welding sequence. This algorithm takes advantage of performing a multi-neighbourhood search combined with a randomised global search to improve computational efficiency and solve premature convergence problems. Finally, a series of experiments were conducted to confirm the accuracy of the proposed BA. Verification experiments demonstrate that the acquired optimum welding sequence was in good agreement with the experimental results.

The Bees Algorithm (BA) has proven its effectiveness in performing optimisation in many problems in recent years with many applications, but the global search of the BA is not its strength. This chapter summarised reports on a hybrid model called the Genetic Bees Algorithm (GBA) to enhance the BA for both continuous and combinatorial optimisation problems. For continuous problems, GBA in training a multilayer perceptron (MLP) is reported for the first time to solve real-world problems. Experimental results show that GBA provides significantly better performance than Particle Swarm Optimisation (PSO) in training MLP with higher accuracy. For combinatorial problems, in the two-stage flow shop scheduling problem (TFSSP), three methods, such as Particle Swam Optimiser (PSO), Genetic Algorithm (GA) and GBA, are compared. GBA is competitive and better than PSO and GA in a majority of instances in terms of results, proving that GBA is a realistic and efficient solution to the TFSSP. Finally, GBA proves its strength in solving the Just-in-Time Job Shop Scheduling Problem (JITJSSP) by solving a set of 36 benchmark instances ranging from 20 to 200 operations, the outcomes obtained from that are then compared to an exact method, two recent studies, and best-known solutions. The results show that the GBA has its strengths and weaknesses in solving the JITJSSP, and it performs well in some instances but does not perform well in others.

Additive manufacturing (AM) is renowned for its capability to produce parts that are low-cost and have less manufacturing time. One of the main challenges in this additive manufacturing technology is selecting proper input process parameters to achieve good quality of the 3D printed model. The focus of this study is to determine the optimum input parameter of the 3D printer using the Bees Algorithm (BA). This study uses the Bees Algorithm to predict the best combination parameters to optimise the surface roughness of parts printed by a fused deposition modelling (FDM) machine. The predicted results are compared with the experimental 3D model sample and previous findings of other optimisation methods. Comparative analysis between predicted and actual surface roughness measurements showed good agreement with differences of less than 2%, indicating a significant prediction method. The result also shows that the Bees Algorithm found a better combination of parameters compared to other algorithms. This research provides another alternative optimisation approach for industries that utilise 3D printing.

Robotics-enabled collaborative manufacturing is vital to improving the efficiency and flexibility of industrial manufacturing processes and realising the digitalisation and intelligentisation of industry. In recent years, enabled by intelligent optimisation algorithms, robotics-enabled collaborative manufacturing approaches have been steadily developed as promising solutions to support industries. However, each robotics-enabled collaborative manufacturing approach has some optimisation problems, limiting its applicability in practice. To address this issue, in this chapter, the Bees Algorithm and robotics-enabled collaborative manufacturing are integrated as an effective approach. In this approach, the efficiency and flexibility of robotics-enabled collaborative manufacturing are significantly improved. Robotics-enabled collaborative manufacturing is composed of robotic collaborative manufacturing and human–robot collaborative manufacturing. In terms of robotic collaborative manufacturing, the improved multiobjective discrete Bees Algorithm and the improved discrete Bees Pareto algorithm are utilised to solve the robotic disassembly line balancing optimisation problem and multiobjective robotic collaborative manufacturing service aggregation optimal selection problem. In terms of human–robot collaborative manufacturing, the Pareto-based modified discrete Bees Algorithm is used to solve the task sequence planning optimisation problem. Afterwards, two case studies are presented to show the performance of the Bees Algorithm in robotics-enabled collaborative manufacturing. The results demonstrate that the Bees Algorithm is superior to some other comparative approaches.

Hyperparameter searching is one of the significant challenges in training deep learning models. To solve this challenge, the Bees Algorithm (BA), which simulates the foraging behaviour of honey bees, is used for hyperparameter searching and finding the best set of hyperparameters for a given deep learning model. This study applies a two-parameter version of the Bees Algorithm (BA₂) to search for the best set of hyperparameters for a Convolutional Neural Network (CNN) combined with a Long Short-Term Memory (LSTM) model. Then, the model is used to predict the remaining useful life (RUL) of ball bearings. BA₂ uses the traplining foraging technique of bees to integrate explorative and exploitative search mechanisms, reduce the number of parameters to only two and improve the remaining useful life (RUL) prediction. The algorithm can find a set of hyperparameters that makes the deep learning model perform better than the IEEE PHM 2012 Prognostic challenge winner by 38.97%.

Feature selection can be defined as an optimisation problem and solved by bioinspired algorithms. The Bees Algorithm (BA) returns great performance in the feature selection optimisation task. On the other hand, local phase quantisation (LPQ) is a frequency domain feature that has excellent performance on depth images. Here, after extracting LPQ features from RGB (colour) and depth images from the Iranian Kinect Face Database (IKFDB), the Bees feature selection algorithm is applied to select the desired number of features for final classification tasks. IKFDB is recorded with Kinect sensor V.2 and contains colour and depth images for facial and facial microexpression recognition purposes. Here, five facial expressions, Anger, Joy, Surprise, Disgust and Fear, are used for final validation. The proposed Bees LPQ method is compared with Particle Swarm Optimisation (PSO) LPQ, PCA LPQ, Lasso LPQ, and just LPQ features for classification tasks with Support Vector Machines (SVM), K-Nearest Neighbourhood (KNN), Shallow Neural Network and Ensemble Subspace KNN. The returned results show a promising performance of the proposed algorithm (99% accuracy) in comparison with others.

The convolutional neural network (CNN) is one of the most popular deep learning algorithms that deals mainly with image data. In this study, the application of the Bees Algorithm (BA), which behaves like honeybees, was used along with the Bayesian Optimisation (BO) approach to improve CNN performance (BA-BO-CNN). Applying the hybrid algorithm on Cifar10DataDir images increased the accuracy on the validation set from 80.72% for the existing BO-CNN to 82.22% for the hybrid algorithm. Applying BA-BO-CNN on digit datasets showed the same accuracy as the existing hybrid BO-CNN, but with a computational time shortened by 3 min and 12 s. Finally, concrete crack benchmark image data yielded almost similar results to existing algorithms. Similarly, a new hybrid Bees Convolutional Neural Network (BA-CNN) algorithm was proposed that uses BA to design better CNN topology by optimising its hyperparameters, which increases the network accuracy. Applying the hybrid algorithm to the Cifar10DataDir dataset yielded the same accuracy as existing CNNs and BO-CNNs. Applying it to the digits dataset produced the lowest computational time with 4 min and 14 s reductions compared to BO-CNN, so it is the best algorithm in terms of cost-effectiveness. Finally, applying it to concrete crack images produced similar results to the existing algorithms.

This study proposes a methodology for integrating the use of the Bees Algorithm (BA) and simulation to reduce the workload for workers on production and assembly lines. Simulation is first employed for retrieving ergonomics data for different workers. Then, the BA is used as a tool for optimising the job rotations of the workers among the workstations, considering as objective the minimisation of the 2 indices, the Ovako Working Posture Analysing System (OWAS) and Energy Expenditure (EE). A case study related to a car assembly line is then proposed to test the methodology. Six workstations (WSs) are considered in this study, and the BA is validated by comparing its results with the exact solution evaluated by analysing all the possible combinations. The results show the good accuracy of the BA in finding solutions for this type of problem and the capacity to reduce the computational times compared with those of the exact solution.

How to build a team of experts plays an important role in the smooth development of a new project. The Internet company was investigated to determine how to form a team that can communicate effectively. This problem is known as the problem of expert team formation in Internet companies (TFPICs). We construct a mathematical optimisation model based on an undirected graph and propose a bees algorithm using knowledge transfer, named KT-BA. KT-BA uses the best information obtained through cooperative search of multiple subpopulations and transfers the dominant subpopulations to other subpopulations. A reproduction mechanism is also used in the algorithm to generate new individuals to enhance population diversity. The experimental results verify the solution performance of KT-BA, and the obtained expert team formation scheme outperforms the traditional bees algorithm and neighbourhood search algorithm. Thus, KT-BA is suitable for application in large Internet companies to provide scientific decisions for project development.

The green vehicle routing problem (GVRP) aims to find a set of vehicle tours that minimise the total distance travelled to service a subset of customers while incorporating stops at alternative fuel stations because of the vehicle's limited fuel capacity. This is the first study to investigate using the Bees Algorithm to find a solution to the GVRP. The aim is to apply the Bees Algorithm to the GVRP and compare the results of six optimisation algorithms. A grid search was used to find the best parameters of the algorithms. For a fair comparison, the same number function of evaluation was used as the stopping criterion for all algorithms in this study. Statistical analysis is used to evaluate the performance of the algorithms. The results demonstrate that the Bees Algorithm outperforms other algorithms and can find near-optimal solutions.

Due to the significant interest in Unmanned Aerial Vehicles (UAVs), numerous metaheuristic or nature-inspired algorithms have been proposed for path-planning problems, allowing units to navigate through diverse threats effectively. By strategically avoiding threats identified by radar, these algorithms aim to determine the most optimal route. This chapter explores the application of two variants of the Bees Algorithm (BA) to address this issue and evaluates their performance against other metaheuristic algorithms. The comparison encompasses various configurations of waypoints and threats, with statistical analyses conducted to assess performance differences. The findings indicate that the Bees Algorithm with two parameters (BA2) surpasses the performance of the Basic BA and other metaheuristic algorithms. Statistical estimates derived from the data are utilised for comparisons, ensuring that optimisation parameters for all algorithms are selected unbiased and meaningfully.

Unmanned aerial vehicles (UAVs) play a vital role in maritime search and rescue (SAR). The ability to find people overboard quickly is closely related to the flight path setting. We construct a mathematical programming model considering the task size of each SAR center and the overall search time as the objective function for the maritime search and rescue path planning (SARPP) problem. Then, a Tabu-based bees algorithm (TBBA) is proposed considering the complex problem space and constraints. The TBBA adopts the idea of the Tabu strategy to guide bees’ search and records the improvement of the individual structure of scout bees’ search to reduce the possibility of invalid search occurrence. An individual replacement strategy is also used in the algorithm to randomly generate a new site to replace the worst site when the search is unsatisfactory. The effectiveness of the proposed algorithm is verified by various experiments. TBBA can obtain a more ideal SAR solution than the genetic algorithm and neighbourhood search algorithm.

Electrified propulsion systems are a promising way of reducing traffic-related pollution. Because of the characteristics of the exhaust systems of engine-assisted vehicles, it is possible that pedestrians in close proximity to vehicles may encounter situations with high enough concentrations of emissions to cause specific health effects. To decrease the impact of vehicle emissions and pollutants on surrounding pedestrians, this chapter presents a cyber-physical optimisation technique for the pedestrian-aware supervisory control strategy of hybrid propulsion systems. The technique is a combination of the Bees Algorithm and a fuzzy adaptive cost map to optimise the rule-based power-split parameters. It is capable of self-adjusting the intertarget weights of exhaust emissions and fuel with real-time pedestrian density information during the optimisations. To examine the robustness of the hybrid propulsion system optimised by the introduced technique, the effects of communication quality and bootstrap sampling techniques are studied. The results show that applying the developed fuzzy adaptive cost map can reduce emissions to nearby pedestrians by 14.42%.

Microwave filter optimisation is an important example of black-box optimisation, where the objective function is unknown and requires full-wave electromagnetic (EM) simulations. This problem is challenging and even computationally intractable for commonly used global optimisation techniques due to the multimodal and computationally expensive nature of its objective function. This chapter proposes the surrogate-model-assisted Bees Algorithm. Gaussian process regression is used to model the unknown objective function and prescreen promising candidates for expensive EM simulations. In this scheme, the Bees algorithm is used to perform a global search and intelligent sampling for surrogate modelling. This method was evaluated on 7 benchmark functions and compared with the standard Bees Algorithm. Mann‒Whitney U tests indicated the statistical significance of the results. A case study involving a microwave dielectric filter demonstrated the significant advantages of using the proposed method in terms of high-quality design and a reduced number of EM simulation-based evaluations.