Nature-inspired optimisation: Improvements to the Particle Swarm Optimisation Algorithm and the Bees Algorithm

This research focuses on nature-inspired optimisation algorithms, in particular, the Particle Swarm Optimisation (PSO) Algorithm and the Bees Algorithm. The PSO Algorithm is a population-based stochastic optimisation technique first invented in 1995. It was inspired by the social behaviour of birds flocking or a school of fish. The Bees Algorithm is a population-based search algorithm initially proposed in 2005. It mimics the food foraging behaviour of swarms of honey bees. The thesis presents three algorithms. The first algorithm called the PSO-Bees Algorithm is a cross between the PSO Algorithm and the Bees Algorithm. The PSO-Bees Algorithm enhanced the PSO Algorithm with techniques derived from the Bees Algorithm. The second algorithm called the improved Bees Algorithm is a version of the Bees Algorithm that incorporates techniques derived from the PSO Algorithm. The third algorithm called the SNTO-Bees Algorithm enhanced the Bees Algorithm using techniques derived from the Sequential Number-Theoretic Optimisation (SNTO) Algorithm. To demonstrate the capability of the proposed algorithms, they were applied to different optimisation problems. The PSO-Bees Algorithm is used to train neural networks for two problems, Control Chart Pattern Recognition and Wood Defect Classification. The results obtained and those from tests on well known benchmark functions provide an indication of the performance of the algorithm relative to that of other swarm-based stochastic optimisation algorithms. The improved Bees Algorithm was applied to mechanical design optimisation problems (design of welded beams and coil springs) and the mathematical benchmark problems used previously to test the PSO-Bees Algorithm. The algorithm incorporates cooperation and communication between different neighbourhoods. The results obtained show that the proposed cooperation and communication strategies adopted enhanced the performance and convergence of the algorithm. The SNTO-Bees Algorithm was applied to a set of mechanical design optimisation problems (design of welded beams, coil springs and pressure vessel) and mathematical benchmark functions used previously to test the PSO-Bees Algorithm and the improved Bees Algorithm. In addition, the algorithm was tested with a number of deceptive multi modal benchmark functions. The results obtained help to validate the SNTO-Bees Algorithm as an effective global optimiser capable of handling problems that are deceptive in nature with high dimensions

the Bees Algorithm: a novel optimisation tool

This work introduces the Bees Algorithm, a new optimisation algorithm inspired by the foraging behaviour of honey-bees. In its basic version, the Bees Algorithm performs a kind of neighbourhood search combined with global random search and can be used for both continuous and discrete optimisation problems. An improved version of the Bees Algorithm including replacing global random search with interpolation and extrapolation, shrinking neighbourhood size, and abandoning sites with no new information was developed. The improved version could solve benchmark function optimisation problems with less sampling of the search space. The Bees Algorithm has been applied to mechanical design optimisation. Two standard mechanical design problems, the design of a welded beam structure and the design of coil springs, were used to benchmark the Bees Algorithm against other optimisation techniques. Computer-aided preliminary design can be regarded as a special case of optimisation, where the goal is to generate as many solutions as possible above a predefined performance threshold. The higher the number of solutions satisfying the preliminary selection criteria, the greater is the chance to produce a good final solution. An adapted version of the Bees Algorithm for discrete function optimisation was developed and tested on a simple machine design task, preliminary gearbox design. The test consists of finding alternative gearbox configurations that approximately produce the required output speeds using one of the available input speeds. Experimental results show that the Bees Algorithm outperforms random search and a genetic optimisation algorithm. A modified version of the Bees Algorithm was used to search for multiple Pareto optimal solutions in a multi-objective optimisation design problem. Compared to two non-dominated genetic algorithms, the Bees Algorithm was able to find more trade-off solutions. Finally, the Bees Algorithm was employed to train Radial Basis Function (RBF) neural networks for two different problems. Despite the high dimensionality of the problems - each bee represented 2345 parameters in the control chart pattern recognition case and 1581 parameters in the wood defect classification case - the algorithm successfully trained very accurate classifiers. Although the accuracies achieved were marginally lower than those obtained with conventional RBF training methods, the total output errors were less than those for conventionally RBF-trained networks with same number of hidden neurons

Improved versions of the bees algorithm for global optimisation

This research focuses on swarm-based optimisation algorithms, specifically the Bees Algorithm. The Bees Algorithm was inspired by the foraging behaviour of honey bees in nature. It employs a combination of exploration and exploitation to find the solutions of optimisation problems. This thesis presents three improved versions of the Bees Algorithm aimed at speeding up its operation and facilitating the location of the global optimum. For the first improvement, an algorithm referred to as the Nelder and Mead Bees Algorithm (NMBA) was developed to provide a guiding direction during the neighbourhood search stage. The second improved algorithm, named the recombination-based Bees Algorithm (rBA), is a variant of the Bees Algorithm that utilises a recombination operator between the exploited and abandoned sites to produce new candidates closer to optimal solutions. The third improved Bees Algorithm, called the guided global best Bees Algorithm (gBA), introduces a new neighbourhood shrinking strategy based on the best solution so far for a more effective exploitation search and develops a new bee recruitment mechanism to reduce the number of parameters. The proposed algorithms were tested on a set of unconstrained numerical functions and constrained mechanical engineering design problems. The performance of the algorithms was compared with the standard Bees Algorithm and other swarm based algorithms. The results showed that the improved Bees Algorithms performed better than the standard Bees Algorithm and other algorithms on most of the problems tested. Furthermore, the algorithms also involve no additional parameters and a reduction on the number of parameters as well

An enhancement to the Bees Algorithm with slope angle computation and Hill Climbing Algorithm and its applications on scheduling and continuous-type optimisation problem

This paper focuses on improvements to the Bees Algorithm (BA) with slope angle computation and Hill Climbing Algorithm (SACHCA) during the local search process. First, the SAC was employed to determine the inclination of the current sites. Second, according to the slope angle, the HCA was utilised to guide the algorithm to converge to the local optima. This enabled the global optimum of the given problem to be found faster and more precisely by focusing on finding the available local optima first before turning the attention on the global optimum. The proposed enhancements to the BA have been tested on continuous-type benchmark functions and compared with other optimisation techniques. The results show that the proposed algorithm performed better than other algorithms on most of the benchmark functions. The enhanced BA performs better than the basic BA, in particular on higher dimensional and complex optimisation problems. Finally, the proposed algorithm has been used to solve the single machine scheduling problem and the results show that the proposed SAC and HCA-BA outperformed the basic BA in almost all the considered instances, in particular when the complexity of the problem increases

Creep modelling of polypropylenes using artificial neural networks trained with Bee algorithms

Polymeric materials, being capable of high mouldability, usability of long lifetime up to 50 years and availability at low cost properties compared to metallic materials, are in demand but finite element-based design engineers have limited means in terms of the limited material data and mathematical models. In particular, in the analysis of products with complex geometry, the stresses and strains of various amounts formed in the product should be known and evaluated in terms of a precise design of the product to fulfil life expectancy. Due to time and cost constraints, experimental data cannot be available for all cases required in analysis, therefore, finite element method-based simulations are commonly used by design engineers. This is also computationally expensive and requires a simpler and more precise way to complete the design more realistically. In this study, the whole creep behaviour of polypropylene for all stresses were obtained with 10% accuracy errors by artificial neural networks trained using existing experimental test results of the materials for a particular working range. The artificial neural network model was trained with traditional as well as heuristic based methods. It is demonstrated that heuristically trained ANN models have provided much accurate and precise results, which are in line with 10% accuracy of experimental data