A Probabilistic Analysis of a Simplified Biogeography-Based Optimization Algorithm

An analysis of the migration rates for biogeography-based optimization

Population size versus runtime of a simple evolutionary algorithm

Biogeography-based optimization (BBO) is a population-based evolutionary algorithm that is based on the mathematics of biogeography. Biogeography is the science and study of the geographical distribution of biological organisms. In BBO, problem solutions are analogous to islands, and the sharing of features between solutions is analogous to the migration of species. This paper derives Markov models for BBO with selection, migration, and mutation operators. Our models give the theoretically exact limiting probabilities for each possible population distribution for a given problem. We provide simulation results to confirm the Markov models.

Technology has enabled us to carry the world on our tips. Cloud computing has majorly contributed to this by providing infrastructure services on the go using pay per use model and with high quality of services. Cloud services provide resources through various distributed datacenters and client requests been fulfilled over these datacenters which act as resources. Therefore, resource allocation plays an important role in providing a high quality of service like utilization, network delay and finish time. Biogeography-based optimization (BBO) is an optimization algorithm that is an evolutionary algorithm used to find optimized solution. In this work BBO algorithm is been used for resource optimization problem in cloud environment at infrastructure as a service level. In past several task scheduling algorithms are being proposed to find a global best schedule to achieve least execution time and high performance like genetic algorithm, ACO and many more but as compared to GA, BBO has high probability to find global best solution. Existing solutions aim toward improving performance in term of power execution time, but they have not considered network performance and utilization of the systems performance parameters. Therefore, to improve the performance of cloud in network-aware environment we have proposed an efficient nature inspired BBO algorithm. Further, the proposed approach takes network overhead and utilization of the system into consideration to provide improved performance as compared to ACO, Genetic algorithm as well as with PSO.

Biogeography-based optimisation (BBO) is a relatively new bio-inspired and population-based optimisation algorithm. It is proved itself a worthy optimisation technique to solve various nonlinear optimisation problem. In this paper, the concept of predator-prey optimisation is incorporated in BBO to increase the diversity of the population. The proposed biogeography-based predator-prey optimisation (BPPO) technique is implemented on both single-input and dual-input power system stabilisers (PSSs). The effectiveness of the proposed algorithm is demonstrated on single machine infinite bus (SMIB) system using four different types of single and dual input PSS. From the simulation study, it is revealed that the transient performance of dual-input PSS is better than single-input PSS. The performance of the proposed algorithm is evaluated over a wide range of operating condition and the simulation results of the proposed method are compared with those obtained by BBO, seeker optimisation algorithm (SOA) and bacteria foraging optimisation (BFO). The results confirm the potential and effectiveness of the proposed BPPO algorithm over SOA, BFO and BBO.

Biogeography-based optimization (BBO) is an evolutionary algorithm that is based on the science of biogeography. Biogeography is the study of the geographical distribution of organisms. In BBO, problem solutions are represented as islands, and the sharing of features between solutions is represented as migration between islands. This paper develops a Markov analysis of BBO, including the option of elitism. Our analysis gives the probability of BBO convergence to each possible population distribution for a given problem. We compare our BBO Markov analysis with a similar genetic algorithm (GA) Markov analysis. Analytical comparisons on three simple problems show that with high mutation rates the performance of GAs and BBO is similar, but with low mutation rates BBO outperforms GAs. Our analysis also shows that elitism is not necessary for all problems, but for some problems it can significantly improve performance.

In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easy-to-apply approach designed particularly for population-based EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the so-called (N + N) EAs and we show that, on two well-known unimodal problems, leadingones and onemax , the EAs with the bitwise mutation and two commonly used selection schemes both need O(n ln n + n(2)/N) and O(n ln ln n + n ln n/N) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some population-based EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problem-specific knowledge to get the tight bounds. It is the first time a general idea for analyzing population-based EAs on unimodal problems is discussed theoretically.

The biogeography-based optimisation (BBO) algorithm is a novel evolutionary algorithm inspired by biogeography. Similarly, to other evolutionary algorithms, entrapment in local optima and slow convergence speed are two probable problems it encounters in solving challenging real problems. Due to the novelty of this algorithm, however, there is little in the literature regarding alleviating these two problems. Chaotic maps are one of the best methods to improve the performance of evolutionary algorithms in terms of both local optima avoidance and convergence speed. In this study, we utilise ten chaotic maps to enhance the performance of the BBO algorithm. The chaotic maps are employed to define selection, emigration, and mutation probabilities. The proposed chaotic BBO algorithms are benchmarked on ten test functions. The results demonstrate that the chaotic maps (especially Gauss/mouse map) are able to significantly boost the performance of BBO. In addition, the results show that the combination of chaotic selection and emigration operators results in the highest performance.

Biogeography-based optimization (BBO) is an evolutionary algorithm which is inspired by the migration of species between habitats. Almost 10 years have passed since the first BBO paper was published in 2008. BBO has successfully solved optimization problems in many different domains and has reached a relatively mature state. Considering the significant and expanding research on BBO and its applications, we find that the time is right to provide a 10-year anniversary review of the published literature, and also to point out some important avenues of future research. The purpose of this paper is to summarize and organize the literature related to the past 10 years of BBO research. Beginning with a foundation of basic BBO, we review the family of BBO algorithms and discuss BBO modifications, hybridizations, applications in science and engineering, and mathematical theory. Finally, the paper presents some interesting open problems and future research directions for BBO.

Population initialization techniques for evolutionary algorithms for single-objective constrained optimization problems: Deterministic vs. stochastic techniques

VariableZ0, a new concept in antenna design and optimization, is applied to two optimization problems: a multi-stub matching network (MSMN) using biogeography-based optimization (BBO), and an ultra wideband meander monopole antenna (MMA) using central force optimization (CFO). BBO is a newly-proposed stochastic global search and optimization evolutionary algorithm (EA) used to determine MSMN stub lengths and locations for optimum (minimum) reflection coefficient. CFO is a deterministic EA used to optimize the MMA's impedance bandwidth (IBW) while maintaining good average gain without considering the radiation pattern in detail. Two cases are investigated for both problems: (a) fixed characteristic impedanceZ0, and (b) variable characteristic impedance. In the first case,Z0is a fixed user-specified parameter (the traditional methodology), whereas in the second, it is a true variable quantity whose value is determined by the optimization methodology, which is a new technology. VariableZ0is a fundamentally different design approach in optimization problems. BBO's fixedZ0results for MSMN are compared to published data computed using Nelder–Mead optimization with BBO exhibiting better performance. BBO's results are improved even more using VariableZ0technology. A similar performance improvement is seen for VariableZ0applied to the CFO-optimized MMA.

Biogeography-based Optimization (BBO) Algorithm for Single Machine Total Weighted Tardiness Problem (SMTWTP)

A robust approach for optimal design of plate fin heat exchangers using biogeography based optimization (BBO) algorithm

We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current mutation rate and the other half with half the current rate. The mutation rate is then updated to the rate used in that subpopulation which contains the best offspring. We analyze how the $$(1+\lambda )$$ evolutionary algorithm with this self-adjusting mutation rate optimizes the OneMax test function. We prove that this dynamic version of the $$(1+\lambda )$$ EA finds the optimum in an expected optimization time (number of fitness evaluations) of $$O(n\lambda /\log \lambda +n\log n)$$ . This time is asymptotically smaller than the optimization time of the classic $$(1+\lambda )$$ EA. Previous work shows that this performance is best-possible among all $$\lambda $$ -parallel mutation-based unbiased black-box algorithms. This result shows that the new way of adjusting the mutation rate can find optimal dynamic parameter values on the fly. Since our adjustment mechanism is simpler than the ones previously used for adjusting the mutation rate and does not have parameters itself, we are optimistic that it will find other applications.

An implementation of differential evolution algorithm for inversion of geoelectrical data