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

Enhancing the Bees algorithm for global optimisation using search space manipulation

The aim of this research is to improve the ability of the Bees Algorithm to tackle global optimisation problems. The Bees Algorithm was formulated and inspired by the foraging behaviour of honeybees. The proposed enhancements target the initialisation and global search stages of the algorithm. The reason for this is that the initialisation stage could save efforts by directing the search earlier towards the more promising areas of the search space, leading to a better optimised result. Targeting during the global search is due to the researcher’s belief that the neighbourhood search depends on it and any improvement will positively affect the neighbourhood search. In this research, three enhancements were formulated based on the manipulation of the search space. The first enhancement (BAwSSR) involves continuous and gradual reduction of the search space with different scenarios that vary according to the starting point of reduction. The second enhancement (BADS) deals with the segmentation of search space into independent segments while using two sampling approaches to tackle a wide variety of problems. The third enhancement (BAOSS) also involves the segmentation of search space but divides it into independent segments to increase flexibility in handling a wider range of problems. These proposed algorithms were tested on 24 benchmark functions with a broad range of characteristics. This test involves performance comparisons with the Quick Artificial Bee Colony (qABC) and the Standard Particle Swarm Optimisation 2011 (SPSO2011) algorithms. The obtained test data indicated noticeable improvements with an adequate level of stability over the original Bees Algorithm. The results were supported by the Mann–Whitney significance test, showing the improvements are statically significant for both accuracy and speed. Additionally, the proposed algorithms were tested on two engineering problems that included a comparison with a group of competitor algorithms. However, only the first proposed algorithm (BAwSSR) showed an obvious improvement. The other two algorithms (BADS) and (BAOSS) did not reveal any improvement

Improvements on the bees algorithm for continuous optimisation problems

This work focuses on the improvements of the Bees Algorithm in order to enhance the algorithm’s performance especially in terms of convergence rate. For the first enhancement, a pseudo-gradient Bees Algorithm (PG-BA) compares the fitness as well as the position of previous and current bees so that the best bees in each patch are appropriately guided towards a better search direction after each consecutive cycle. This method eliminates the need to differentiate the objective function which is unlike the typical gradient search method. The improved algorithm is subjected to several numerical benchmark test functions as well as the training of neural network. The results from the experiments are then compared to the standard variant of the Bees Algorithm and other swarm intelligence procedures. The data analysis generally confirmed that the PG-BA is effective at speeding up the convergence time to optimum. Next, an approach to avoid the formation of overlapping patches is proposed. The Patch Overlap Avoidance Bees Algorithm (POA-BA) is designed to avoid redundancy in search area especially if the site is deemed unprofitable. This method is quite similar to Tabu Search (TS) with the POA-BA forbids the exact exploitation of previously visited solutions along with their corresponding neighbourhood. Patches are not allowed to intersect not just in the next generation but also in the current cycle. This reduces the number of patches materialise in the same peak (maximisation) or valley (minimisation) which ensures a thorough search of the problem landscape as bees are distributed around the scaled down area. The same benchmark problems as PG-BA were applied against this modified strategy to a reasonable success. Finally, the Bees Algorithm is revised to have the capability of locating all of the global optimum as well as the substantial local peaks in a single run. These multi-solutions of comparable fitness offers some alternatives for the decision makers to choose from. The patches are formed only if the bees are the fittest from different peaks by using a hill-valley mechanism in this so called Extended Bees Algorithm (EBA). This permits the maintenance of diversified solutions throughout the search process in addition to minimising the chances of getting trap. This version is proven beneficial when tested with numerous multimodal optimisation problems