A comparative study of Artificial Bee Colony algorithm

Artificial Bee Colony (ABC) algorithm is one of the most recently introduced swarm-based algorithms. ABC simulates the intelligent foraging behaviour of a honeybee swarm. In this work, ABC is used for optimizing a large set of numerical test functions and the results produced by ABC algorithm are compared with the results obtained by genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm and evolution strategies. Results show that the performance of the ABC is better than or similar to those of other population-based algorithms with the advantage of employing fewer control parameters.     

Gbest-guided artificial bee colony algorithm for numerical function optimization

Artificial bee colony (ABC) algorithm invented recently by Karaboga is a biological-inspired optimization algorithm, which has been shown to be competitive with some conventional biological-inspired algorithms, such as genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO). However, there is still an insufficiency in ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by PSO, we propose an improved ABC algorithm called gbest-guided ABC (GABC) algorithm by incorporating the information of global best (gbest) solution into the solution search equation to improve the exploitation. The experimental results tested on a set of numerical benchmark functions show that GABC algorithm can outperform ABC algorithm in most of the experiments.     

Improving artificial bee colony with one-position inheritance mechanism

Artificial bee colony (ABC) algorithm simulates the foraging behavior of honey bees. It shows good performance in many application problems and large scale optimization problems. However, variation of a solution in the ABC algorithm is only employed on one dimension of the solution. This would sometimes hamper the convergence speed of the ABC algorithm, especially for large scale optimization. This paper proposes a one-position inheritance (OPI) mechanism to overcome this drawback. The OPI mechanism aims to promote information exchange amongst employed bees of the ABC algorithm. For separable function, OPIABC has a higher probability resulting in function value improvement of the worst positions than ABC. Through one-position information exchange, the OPI mechanism can assist the ABC algorithm to find promising solutions. This mechanism has been tested on a set of 25 test functions with $D= 30$ and on CEC 2008 test suite with $D= 100$ and 1,000. Experimental results show that the OPI mechanism can speed up the convergence of the ABC algorithm. After the use of OPI, the performance of the ABC algorithm is significantly improved for both rotated problems and large scale problems. OPIABC is also competitive on both test suites comparing with other recently proposed swarm intelligence metaheuristics (e.g. SaDE and PSO2011). Furthermore, the OPI mechanism can greatly enhance the performance of other improved ABC algorithms.     

Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models

We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation–maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on sequential Monte Carlo methodology. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. Two simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation. Comparisons with iterated filtering for maximum likelihood inference, and Gibbs sampling and particle marginal methods for Bayesian inference are presented.     

The Alive Particle Filter and Its Use in Particle Markov Chain Monte Carlo

In the following article, we investigate a particle filter for approximating Feynman–Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require the use of advanced particle filter or MCMC algorithms to perform estimation. One of the drawbacks of existing particle filters is that they may “collapse,” in that the algorithm may terminate early, due to the indicator potentials. In this article, using a newly developed special case of the locally adaptive particle filter, we use an algorithm that can deal with this latter problem, while introducing a random cost per-time step. In particular, we show how this algorithm can be used within MCMC, using particle MCMC. It is established that, when not taking into account computational time, when the new MCMC algorithm is applied to a simplified model it has a lower asymptotic variance in comparison to a standard particle MCMC algorithm. Numerical examples are presented for ABC approximations of HMMs.     

A global best artificial bee colony algorithm for global optimization

The artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in the ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose a modified ABC algorithm (denoted as ABC/best), which is based on that each bee searches only around the best solution of the previous iteration in order to improve the exploitation. In addition, to enhance the global convergence, when producing the initial population and scout bees, both chaotic systems and opposition-based learning method are employed. Experiments are conducted on a set of 26 benchmark functions. The results demonstrate good performance of ABC/best in solving complex numerical optimization problems when compared with two ABC based algorithms.     

Opposition based lévy flight artificial bee colony

Artificial Bee Colony (ABC) is a well known optimization approach to solve nonlinear and complex problems. It is relatively a simple and recent population based probabilistic approach for global optimization. Similar to other population based algorithms, ABC is also computationally expensive due to its slow nature of search process. The solution search equation of ABC is significantly influenced by a random quantity which helps in exploration at the cost of exploitation of the search space. In the solution search equation of ABC due to the large step size the chance of skipping the true solution is high. Therefore, in this paper, to balance the diversity and convergence capability of the ABC, Lévy Flight random walk based local search strategy is proposed and incorporated with ABC along with opposition based learning strategy. The proposed algorithm is named as Opposition Based Lévy Flight ABC. The experiments over 14 un-biased test problems of different complexities and five well known engineering optimization problems show that the proposed algorithm outperforms the basic ABC and its recent variants namely Gbest guided ABC, Best-So-Far ABC, and Modified ABC in most of the experiments.     

Artificial Bee Colony training of neural networks: comparison with back-propagation

The Artificial Bee Colony (ABC) is a swarm intelligence algorithm for optimization that has previously been applied to the training of neural networks. This paper examines more carefully the performance of the ABC algorithm for optimizing the connection weights of feed-forward neural networks for classification tasks, and presents a more rigorous comparison with the traditional Back-Propagation (BP) training algorithm. The empirical results for benchmark problems demonstrate that using the standard “stopping early” approach with optimized learning parameters leads to improved BP performance over the previous comparative study, and that a simple variation of the ABC approach provides improved ABC performance too. With both improvements applied, the ABC approach does perform very well on small problems, but the generalization performances achieved are only significantly better than standard BP on one out of six datasets, and the training times increase rapidly as the size of the problem grows. If different, evolutionary optimized, BP learning rates are allowed for the two layers of the neural network, BP is significantly better than the ABC on two of the six datasets, and not significantly different on the other four.     

University course timetabling using hybridized artificial bee colony with hill climbing optimizer

University course timetabling is concerned with assigning a set of courses to a set of rooms and timeslots according to a set of constraints. This problem has been tackled using metaheuristics techniques. Artificial bee colony (ABC) algorithm has been successfully used for tackling uncapaciated examination and course timetabling problems. In this paper, a novel hybrid ABC algorithm based on the integrated technique is proposed for tackling the university course timetabling problem. First of all, initial feasible solutions are generated using the combination of saturation degree (SD) and backtracking algorithm (BA). Secondly, a hill climbing optimizer is embedded within the employed bee operator to enhance the local exploitation ability of the original ABC algorithm while tackling the problem. Hill climbing iteratively navigates the search space of each population member in order to reach a local optima. The proposed hybrid ABC technique is evaluated using the dataset established by Socha including five small, five medium and one large problem instances. Empirical results on these problem instances validate the effectiveness and efficiency of the proposed algorithm. Our work also shows that a well-designed hybrid technique is a competitive alternative for addressing the university course timetabling problem.     

云计算环境下人工蜂群作业调度算法设计

针对云计算环境下作业调度优化问题,提出了一种基于人工蜂群的调度算法.分析人工蜂群算法的求解组合优化问题过程,建立了收益度函数和蜜源位置更新公式,最后论述了利用该算法求解的具体步骤.并通过实验分析了该算法的性能.     

A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm

Swarm intelligence is a research branch that models the population of interacting agents or swarms that are able to self-organize. An ant colony, a flock of birds or an immune system is a typical example of a swarm system. Bees’ swarming around their hive is another example of swarm intelligence. Artificial Bee Colony (ABC) Algorithm is an optimization algorithm based on the intelligent behaviour of honey bee swarm. In this work, ABC algorithm is used for optimizing multivariable functions and the results produced by ABC, Genetic Algorithm (GA), Particle Swarm Algorithm (PSO) and Particle Swarm Inspired Evolutionary Algorithm (PS-EA) have been compared. The results showed that ABC outperforms the other algorithms.     

On the use of rational iterations and domain decomposition methods for the Helmholtz problem

An iterative algorithm for the numerical solution of the Helmholtz problem is considered. It is difficult to solve the problem numerically, in particular, when the imaginary part of the wave number is zero or small. We develop a parallel iterative algorithm based on a rational iteration and a nonoverlapping domain decomposition method for such a non-Hermitian, non-coercive problem. Algorithm parameters (artificial damping and relaxation) are introduced to accelerate the convergence speed of the iteration. Convergence analysis and effective strategies for finding efficient algorithm parameters are presented. Numerical results carried out on an nCUBE2 are given to show the efficiency of the algorithm. To reduce the boundary reflection, we employ a hybrid absorbing boundary condition (ABC) which combines the first-order ABC and the physical $Q$ ABC. Computational results comparing the hybrid ABC with non-hybrid ones are presented. Received May 19, 1994 / Revised version received March 25, 1997     

Performance evaluation of artificial bee colony optimization and new selection schemes

The artificial bee colony optimization (ABC) is a population-based algorithm for function optimization that is inspired by the foraging behavior of bees. The population consists of two types of artificial bees: employed bees (EBs) which scout for new, good solutions and onlooker bees (OBs) that search in the neighborhood of solutions found by the EBs. In this paper we study in detail the influence of ABC’s parameters on its optimization behavior. It is also investigated whether the use of OBs is always advantageous. Moreover, we propose two new variants of ABC which use new methods for the position update of the artificial bees. Extensive empirical tests were performed to compare the new variants with the standard ABC and several other metaheuristics on a set of benchmark functions. Our findings show that the ideal parameter values depend on the hardness of the optimization goal and that the standard values suggested in the literature should be applied with care. Moreover, it is shown that in some situations it is advantageous to use OBs but in others it is not. In addition, a potential problem of the ABC is identified, namely that it performs worse on many functions when the optimum is not located at the center of the search space. Finally it is shown that the new ABC variants improve the algorithm’s performance and achieve very good performance in comparison to other metaheuristics under standard as well as hard optimization goals.     

An improved artificial bee colony algorithm for directing orbits of chaotic systems

Artificial bee colony algorithm (ABC) is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. To address this concerning issue, we propose an improved ABC (IABC) by using a modified search strategy to generate a new food source in order that the exploration and exploitation can be well balanced and satisfactory optimization performances can be achieved. In addition, to enhance the global convergence, when producing the initial population, both opposition-based learning method and chaotic maps are employed. In this paper, the proposed algorithm is applied to control and synchronization of discrete chaotic systems which can be formulated as both multimodal numerical optimization problems with high dimension. Numerical simulation and comparisons with some typical existing algorithms demonstrate the effectiveness and robustness of the proposed approach.     

ABC methods for model choice in Gibbs random fields

We consider the problem of model selection within the class of Gibbs random fields. In a Bayesian framework, this choice relies on the evaluation of the posterior probabilities of all models. We define an extended parameter setting, including the model index and show the existence of a corresponding sufficient statistic made of the conjunction of the sufficient statistics of all models. We use this statistic to derive an ABC algorithm. To cite this article: A. Grelaud et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Inference for SDE Models via Approximate Bayesian Computation

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model, for example, financial, neuronal, and population growth dynamics. However, inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allows to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus here is on the case where the SDE describes latent dynamics in state-space models; however, the methodology is not limited to the state-space framework. We consider simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions and we provide a Matlab package that implements our ABC-MCMC algorithm.     

ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations

Approximate Bayesian computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some applications. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC–CDE, help address three nontrivial challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC–CDE procedures that directly estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate. Supplemental materials for this article are available online.     

LLL & ABC

This note is an observation that the LLL algorithm applied to prime powers can be used to find “good” examples for the ABC and Szpiro conjectures.     

Chain ladder method: Bayesian bootstrap versus classical bootstrap

The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilizing a Markov chain Monte Carlo (MCMC) technique, ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. The ABC methodology arises because we work in a distribution-free setting in which we make no parametric assumptions, meaning we cannot evaluate the likelihood point-wise or in this case simulate directly from the likelihood model. The use of a bootstrap procedure allows us to generate samples from the intractable likelihood without the requirement of distributional assumptions; this is crucial to the ABC framework. The developed methodology is used to obtain the empirical distribution of the DFCL model parameters and the predictive distribution of the outstanding loss liabilities conditional on the observed claims. We then estimate predictive Bayesian capital estimates, the value at risk (VaR) and the mean square error of prediction (MSEP). The latter is compared with the classical bootstrap and credibility methods.     

Synchronous and asynchronous Pareto-based multi-objective Artificial Bee Colony algorithms

Pareto-based multi-objective optimization algorithms prefer non-dominated solutions over dominated solutions and maintain as much as possible diversity in the Pareto optimal set to represent the whole Pareto-front. This paper proposes three multi-objective Artificial Bee Colony (ABC) algorithms based on synchronous and asynchronous models using Pareto-dominance and non-dominated sorting: asynchronous multi-objective ABC using only Pareto-dominance rule (A-MOABC/PD), asynchronous multi-objective ABC using non-dominated sorting procedure (A-MOABC/NS) and synchronous multi-objective ABC using non-dominated sorting procedure (S-MOABC/NS). These algorithms were investigated in terms of the inverted generational distance, hypervolume and spread performance metrics, running time, approximation to whole Pareto-front and Pareto-solutions spaces. It was shown that S-MOABC/NS is more scalable and efficient compared to its asynchronous counterpart and more efficient and robust than A-MOABC/PD. An investigation on parameter sensitivity of S-MOABC/NS was presented to relate the behavior of the algorithm to the values of the control parameters. The results of S-MOABC/NS were compared to some state-of-the art algorithms. Results show that S-MOABC/NS can provide good approximations to well distributed and high quality non-dominated fronts and can be used as a promising alternative tool to solve multi-objective problems with the advantage of being simple and employing a few control parameters.