Localized biogeography-based optimization

Biogeography-based optimization (BBO) is a relatively new heuristic method, where a population of habitats (solutions) are continuously evolved and improved mainly by migrating features from high-quality solutions to low-quality ones. In this paper we equip BBO with local topologies, which limit that the migration can only occur within the neighborhood zone of each habitat. We develop three versions of localized BBO algorithms, which use three different local topologies namely the ring topology, the square topology, and the random topology respectively. Our approach is quite easy to implement, but it can effectively improve the search capability and prevent the algorithm from being trapped in local optima. We demonstrate the effectiveness of our approach on a set of well-known benchmark problems. We also introduce the local topologies to a hybrid DE/BBO method, resulting in three localized DE/BBO algorithms, and show that our approach can improve the performance of the state-of-the-art algorithm as well.     

基于人工萤火虫局部决策域的改进生物地理学优化算法

针对生物地理学优化（BBO）算法搜索能力不足的缺点,提出基于萤火虫算法局部决策域策略的改进迁移操作来提算法的全局寻优能力。改进的迁移操作能够在考虑不同栖息地各自的迁入率与迁出率的基础上,进一步利用栖息地之间的相互影响关系。将改进算法应用于12个典型的函数优化问题来测试改进生物地理学优化算法的性能,验证了改进算法的有效性。与BBO、改进BBO（IBBO）、基于差分进化的BBO（DE/BBO）算法的实验结果表明,改进算法提高了算法的全局搜索能力、收敛速度和解的精度。     

Accelerated biogeography-based optimization with neighborhood search for optimization

Biogeography-based optimization (BBO) inherently lacks exploration capability that leads to slow convergence. To address this limitation, authors present a memetic algorithm (MA) named as aBBOmDE, which is a new variant of BBO. In aBBOmDE, the performance of BBO is accelerated with the help of a modified mutation and clear duplicate operators. Then modified DE (mDE) is embedded as a neighborhood search operator to improve the fitness from a predefined threshold. mDE is used with mutation operator DE/best/1/bin to explore the search near the best solution. The length of local search is a choice that balances between the search capability and the computational cost. In aBBOmDE, migration mechanism is kept same as that of BBO in order to maintain its exploitation ability. Modified operators are utilized to enhance the exploration ability while a neighborhood search operator further enhances the search capability of the algorithm. This combination significantly improves the convergence characteristics of the original algorithm. Extensive experiments have been carried out on forty benchmark functions to show the effectiveness of the proposed algorithm. The results have been compared with original BBO, DE, CMAES, other MA and DE/BBO, a hybrid version of DE and BBO. aBBOmDE is also applied to compute patch dimensions of rectangular microstrip patch antennas (MSAs) with various substrate thicknesses so as to be used a CAD formula for antenna design.     

Two-stage update biogeography-based optimization using differential evolution algorithm (DBBO)

The present paper proposes a new stochastic optimization algorithm as a hybridization of a relatively recent stochastic optimization algorithm, called biogeography-based optimization (BBO) with the differential evolution (DE) algorithm. This combination incorporates DE algorithm into the optimization procedure of BBO with an attempt to incorporate diversity to overcome stagnation at local optima. We also propose to implement an additional selection procedure for BBO, which preserves fitter habitats for subsequent generations. The proposed variation of BBO, named DBBO, is tested for several benchmark function optimization problems. The results show that DBBO can significantly outperform the basic BBO algorithm and can mostly emerge as the best solution providing algorithm among competing BBO and DE algorithms.     

Hybrid differential evolution with biogeography-based optimization algorithm for solution of economic emission load dispatch problems

This paper presents combination of differential evolution (DE) and biogeography-based optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO_X, SO_X, CO_X, Power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3-generator system with NO_X and SO_X emission, in a 6-generators system considering NO_X emission, in a 6-generator system addressing both valve-point loading and NO_X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained.     

A hybrid biogeography-based optimization algorithm for job shop scheduling problem

In this paper, a hybrid biogeography-based optimization (HBBO) algorithm has been proposed for the job-shop scheduling problem (JSP). Biogeography-based optimization (BBO) is a new bio-inpired computation method that is based on the science of biogeography. The BBO algorithm searches for the global optimum mainly through two main steps: migration and mutation. As JSP is one of the most difficult combinational optimization problems, the original BBO algorithm cannot handle it very well, especially for instances with larger size. The proposed HBBO algorithm combines the chaos theory and “searching around the optimum” strategy with the basic BBO, which makes it converge to global optimum solution faster and more stably. Series of comparative experiments with particle swarm optimization (PSO), basic BBO, the CPLEX and 14 other competitive algorithms are conducted, and the results show that our proposed HBBO algorithm outperforms the other state-of-the-art algorithms, such as genetic algorithm (GA), simulated annealing (SA), the PSO and the basic BBO.     

DE/EDA: A new evolutionary algorithm for global optimization

Differential evolution (DE) was very successful in solving the global continuous optimization problem. It mainly uses the distance and direction information from the current population to guide its further search. Estimation of distribution algorithm (EDA) samples new solutions from a probability model which characterizes the distribution of promising solutions. This paper proposes a combination of DE and EDA (DE/EDA) for the global continuous optimization problem. DE/EDA combines global information extracted by EDA with differential information obtained by DE to create promising solutions. DE/EDA has been compared with the best version of the DE algorithm and an EDA on several commonly utilized test problems. Experimental results demonstrate that DE/EDA outperforms the DE algorithm and the EDA. The effect of the parameters of DE/EDA to its performance is investigated experimentally.     

Blended biogeography-based optimization for constrained optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems.     

Incorporating mutation scheme into krill herd algorithm for global numerical optimization

Recently, Gandomi and Alavi proposed a robust meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization. To improve the performance of the KH algorithm, harmony search (HS) is applied to mutate between krill during the process of krill updating instead of physical diffusion used in KH. A novel hybrid meta-heuristic optimization approach HS/KH is proposed to solve global numerical optimization problem. HS/KH combines the exploration of harmony search (HS) with the exploitation of KH effectively, and hence, it can generate the promising candidate solutions. The detailed implementation procedure for this improved meta-heuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most cases, the performance of this hybrid meta-heuristic method (HS/KH) is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, HS, KH, PSO, and SGA. The effect of the HS/FA parameters is also analyzed.     

On the equivalences and differences of evolutionary algorithms

Evolutionary algorithms (EAs) are fast and robust computation methods for global optimization, and have been widely used in many real-world applications. We first conceptually discuss the equivalences of various popular EAs including genetic algorithm (GA), biogeography-based optimization (BBO), differential evolution (DE), evolution strategy (ES) and particle swarm optimization (PSO). We find that the basic versions of BBO, DE, ES and PSO are equal to the GA with global uniform recombination (GA/GUR) under certain conditions. Then we discuss their differences based on biological motivations and implementation details, and point out that their distinctions enhance the diversity of EA research and applications. To further study the characteristics of various EAs, we compare the basic versions and advanced versions of GA, BBO, DE, ES and PSO to explore their optimization ability on a set of real-world continuous optimization problems. Empirical results show that among the basic versions of the algorithms, BBO performs best on the benchmarks that we studied. Among the advanced versions of the algorithms, DE and ES perform best on the benchmarks that we studied. However, our main conclusion is that the conceptual equivalence of the algorithms is supported by the fact that algorithmic modifications result in very different performance levels.     

An analysis of the equilibrium of migration models for biogeography-based optimization

Motivated by the migration mechanisms of ecosystems, various extensions to biogeography-based optimization (BBO) are proposed here. As a global optimization method, BBO is an original algorithm based on the mathematical model of organism distribution in biological systems. BBO is an evolutionary process that achieves information sharing by biogeography-based migration operators. In BBO, habitats represent candidate problem solutions, and species migration represents the sharing of features between candidate solutions according to the fitness of the habitats. This paper generalizes equilibrium species count results in biogeography theory, explores the behavior of six different migration models in BBO, and investigates performance through 23 benchmark functions with a wide range of dimensions and diverse complexities. The performance study shows that sinusoidal migration curves provide the best performance among the six different models that we explored. In addition, comparison with other biology-based optimization algorithms is investigated, and the influence of the population size, problem dimension, mutation rate, and maximum migration rate of BBO are also studied.     

一种改进的生物地理学优化算法

生物地理学优化算法（BBO）作为一种新型的智能算法,在其提出不到十年的时间内受到学界的广泛关注和研究,并显示出了广阔的应用前景。为了提高算法的优化性能,对BBO算法提出一种改进,该算法在将差分优化算法（DE）中的局部搜索策略同BBO算法中的迁移策略相结合的基础上,针对迁移算子和变异算子分别进行改进,提出了二重迁移算子和二重变异算子,使得栖息地个体在进化过程中得到更高的进化概率,从而使得算法的寻优能力得到进一步提升。通过6个高维函数的测试,结果表明该算法在优化高维优化问题时,较其他几种生物地理学优化算法具有更好的收敛性和稳定性。     

Handling multiple objectives with biogeography-based optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization (BBMO) is introduced, which uses the cluster attribute of islands to naturally decompose the problem. The proposed algorithm makes use of nondominated sorting approach to improve the convergence ability effciently. It also combines the crowding distance to guarantee the diversity of Pareto optimal solutions. We compare the BBMO with two representative state-of-the-art evolutionary multi-objective optimization methods, non-dominated sorting genetic algorithm-II (NSGA-II) and archive-based micro genetic algorithm (AMGA) in terms of three metrics. Simulation results indicate that in most cases, the proposed BBMO is able to find much better spread of solutions and converge faster to true Pareto optimal fronts than NSGA-II and AMGA do.     

改进迁移算子的BBO算法及其在PID参数中的优化

针对生物地理学优化（BBO）算法寻优过程中易陷入搜索动力不足、收敛精度不高等问题,提出一种基于改进迁移算子的生物地理学优化算法（IMO-BBO）。在BBO算法基础上,结合“优胜劣汰”的进化思想,将迁移距离作为影响因素对迁移算子进行改进,并用差分策略将不适宜迁移的个体进行替换,以增加算法的局部探索能力。同时为丰富物种的多样性,引入多种群概念。利用IMO-BBO算法分别对13个基准测试函数进行测试,与基于协方差迁移算子和混合差分策略的BBO （CMM-DE/BBO）算法和BBO算法相比,改进算法提高了对全局最优解的搜索能力,在收敛速度和精确度上也都有显著提高;将IMO-BBO算法应用到PID参数整定中,仿真结果表明,所提算法优化后的控制器具有更快的响应速度和更稳定的精度。     

Analytical and numerical comparisons of biogeography-based optimization and genetic algorithms

We show that biogeography-based optimization (BBO) is a generalization of a genetic algorithm with global uniform recombination (GA/GUR). Based on the common features of BBO and GA/GUR, we use a previously-derived BBO Markov model to obtain a GA/GUR Markov model. One BBO characteristic which makes it distinctive from GA/GUR is its migration mechanism, which affects selection pressure (i.e., the probability of retaining certain features in the population from one generation to the next). We compare the BBO and GA/GUR algorithms using results from analytical Markov models and continuous optimization benchmark problems. We show that the unique selection pressure provided by BBO generally results in better optimization results for a set of standard benchmark problems. We also present comparisons between BBO and GA/GUR for combinatorial optimization problems, include the traveling salesman, the graph coloring, and the bin packing problems.     

A novel memetic algorithm based on invasive weed optimization and differential evolution for constrained optimization

This paper presents a novel memetic algorithm, named as IWO_DE, to tackle constrained numerical and engineering optimization problems. In the proposed method, invasive weed optimization (IWO), which possesses the characteristics of adaptation required in memetic algorithm, is firstly considered as a local refinement procedure to adaptively exploit local regions around solutions with high fitness. On the other hand, differential evolution (DE) is introduced as the global search model to explore more promising global area. To accommodate the hybrid method with the task of constrained optimization, an adaptive weighted sum fitness assignment and polynomial distribution are adopted for the reproduction and the local dispersal process of IWO, respectively. The efficiency and effectiveness of the proposed approach are tested on 13 well-known benchmark test functions. Besides, our proposed IWO_DE is applied to four well-known engineering optimization problems. Experimental results suggest that IWO_DE can successfully achieve optimal results and is very competitive compared with other state-of-art algorithms.     

Biogeography-based optimization with covariance matrix based migration

Biogeography-based optimization (BBO) is a new evolutionary algorithm. The major problem of basic BBO is that its migration operator is rotationally variant, which leaves BBO performing poorly in non-separable problems. To overcome this drawback of BBO, in this paper, we propose the covariance matrix based migration (CMM) to relieve BBO’s dependence upon the coordinate system so that BBO’s rotational invariance is enhanced. By embedding the CMM into BBO, we put forward a new BBO approach, namely biogeography-based optimization with covariance matrix based migration, called CMM-BBO. Specifically, CMM-BBO algorithms are developed by the CMM operator being randomly combined with the original migration in various existing BBO variants. Numeric simulations on 37 benchmark functions show that our CMM-BBO approach effectively improves the performance of the existing BBO algorithms.     

Control and synchronization of chaotic systems by an improved biogeography-based optimization algorithm

Biogeography-based optimization algorithm (BBO) is a relatively new optimization technique which has been shown to be competitive to other biology-based algorithms. However, there is still an insufficiency in BBO regarding its migration operator, which is good at exploitation but poor at exploration. To address this concerning issue, we propose an improved BBO (IBBO) by using a modified search strategy to generate a new mutation operator so that the exploration and exploitation can be well balanced and then satisfactory optimization performances can be achieved. In addition, to enhance the global convergence, both opposition-based learning methods and chaotic maps are employed, when producing the initial population. In this paper, the proposed algorithm is applied to control and synchronization of discrete chaotic systems which can be formulated as high-dimension numerical optimization problems with multiple local optima. Numerical simulations and comparisons with some typical existing algorithms demonstrate the effectiveness and efficiency of the proposed approach.     

基于差分进化的生物地理学优化算法

针对生物地理学优化算法在实数编码时搜索能力较弱的缺点,提出一种基于差分进化的混合优化算法(BBO/DEs)。通过将差分进化的搜索性与生物地理优化算法的利用性有机结合,以解决原算法在局部搜索时容易出现早熟的问题;并构造一种基于Levy分布的变异方式,确保种群在进化过程中保持多样性;最后通过实验比较,选取了合适的试验策略。利用高维标准测试函数对相关算法进行实验,结果表明该算法能够克服搜索能力不足的缺点,并继承了原算法的快速收敛性能,可以有效兼顾精度与速度的要求。     

A 2-Opt based differential evolution for global optimization

Differential evolution (DE) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problems. However, DE has shown some weaknesses, especially the long computational times because of its stochastic nature. This drawback sometimes limits its application to optimization problems. Therefore we propose the 2-Opt based DE (2-Opt DE) which is inspired by 2-Opt algorithms to accelerate DE. The novel mutation schemes of 2-Opt DE, DE/2-Opt/1 and DE/2-Opt/2 are substituted for mutation schemes of the original DE namely DE/rand/1 and DE/rand/2. We also provide a comparison of 2-Opt DE to DE. A comprehensive set of 19 benchmark functions is employed for experimental verification. The experimental results confirm that 2-Opt DE outperforms the original DE in terms of solution accuracy and convergence speed.