Autonomous Bee Colony Optimization for Multi-objective Function

An Autonomous Bee Colony Optimization (A-BCO) algorithm for solving multi-objective numerical problems is proposed. In contrast with previous Bee Colony algorithms, A-BCO utilizes a diversity-based performance metric to dynamically assess the archive set. This assessment is employed to adapt the bee colony structures and flying patterns. This self-adaptation feature is introduced to optimize the balance between exploration and exploitation during the search process. Moreover, the total number of search iterations is also determined/optimized by A-BCO, according to user pre-specified conditions, during the search process. We evaluate A-BCO upon numerical benchmark problems and the experimental results demonstrate the effectiveness and robustness of the proposed algorithm when compared with the Non-dominated Sorting Genetic Algorithm II and the latest Multi-objective Bee Colony Algorithm proposed to date

A study of search neighbourhood in the bees algorithm

The Bees Algorithm, a heuristic optimisation procedure that mimics bees foraging behaviour, is becoming more popular among swarm intelligence researchers. The algorithm involves neighbourhood and global search and is able to find promising solutions to complex multimodal optimisation problems. The purpose of neighbourhood search is to intensify the search effort around promising solutions, while global search is to enable avoidance of local optima. Despite numerous studies aimed at enhancing the Bees Algorithm, there have not been many attempts at studying neighbourhood search. This research investigated different kinds of neighbourhoods and their effects on neighbourhood search. First, the adaptive enlargement of the search neighbourhood was proposed. This idea was implemented in the Bees Algorithm and tested on a set of mathematical benchmarks. The modified algorithm was also tested on single objective engineering design problems. The experimental results obtained confirmed that the adaptive enlargement of the search neighbourhood improved the performance of the proposed algorithm. Normally, a symmetrical search neighbourhood is employed in the Bees Algorithm. As opposed to this practice, an asymmetrical search neighbourhood was tried in this work to determine the significance of neighbourhood symmetry. In addition to the mathematical benchmarks, the algorithm with an asymmetrical search neighbourhood was also tested on an engineering design problem. The analysis verified that under certain measurements of asymmetry, the proposed ii algorithm produced a similar performance as that of the Bees Algorithm. For this reason, it was concluded that users were free to employ either a symmetrical or an asymmetrical search neighbourhood in the Bees Algorithm. Finally, the combination of adaptive enlargement and reduction of the search neighbourhood was presented. In addition to the above mathematical benchmarks and engineering design problems, a multi-objective design optimisation exercise with constraints was selected to demonstrate the performance of the modified algorithm. The experimental results obtained showed that this combination was beneficial to the proposed algorithm.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A study of search neighbourhood in the bees algorithm

The Bees Algorithm, a heuristic optimisation procedure that mimics bees foraging behaviour, is becoming more popular among swarm intelligence researchers. The algorithm involves neighbourhood and global search and is able to find promising solutions to complex multimodal optimisation problems. The purpose of neighbourhood search is to intensify the search effort around promising solutions, while global search is to enable avoidance of local optima. Despite numerous studies aimed at enhancing the Bees Algorithm, there have not been many attempts at studying neighbourhood search. This research investigated different kinds of neighbourhoods and their effects on neighbourhood search. First, the adaptive enlargement of the search neighbourhood was proposed. This idea was implemented in the Bees Algorithm and tested on a set of mathematical benchmarks. The modified algorithm was also tested on single objective engineering design problems. The experimental results obtained confirmed that the adaptive enlargement of the search neighbourhood improved the performance of the proposed algorithm. Normally, a symmetrical search neighbourhood is employed in the Bees Algorithm. As opposed to this practice, an asymmetrical search neighbourhood was tried in this work to determine the significance of neighbourhood symmetry. In addition to the mathematical benchmarks, the algorithm with an asymmetrical search neighbourhood was also tested on an engineering design problem. The analysis verified that under certain measurements of asymmetry, the proposed ii algorithm produced a similar performance as that of the Bees Algorithm. For this reason, it was concluded that users were free to employ either a symmetrical or an asymmetrical search neighbourhood in the Bees Algorithm. Finally, the combination of adaptive enlargement and reduction of the search neighbourhood was presented. In addition to the above mathematical benchmarks and engineering design problems, a multi-objective design optimisation exercise with constraints was selected to demonstrate the performance of the modified algorithm. The experimental results obtained showed that this combination was beneficial to the proposed algorithm

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