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.     

生物地理学优化算法理论及其应用研究综述

生物地理学优化算法（Biogeography-Based Optimization,BBO）是Simon提出的一种基于生物地理学理论的新型智能优化算法,具有良好的收敛性和稳定性。从BBO算法提出的背景出发,介绍了算法的基本理论、算法特点以及算法流程。总结了BBO算法的研究进展,包括BBO算法的理论分析、算法的改进、算法与其他优化算法的混合算法以及BBO算法在函数优化、电力系统、图像处理、机器人路径规划以及调度优化等领域的典型应用。对BBO算法有待解决的问题和未来研究方向进行了总结。     

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.     

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.     

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.     

Enhancing the performance of biogeography-based optimization using polyphyletic migration operator and orthogonal learning

Biogeography-based optimization (BBO) is a powerful population-based algorithm inspired by biogeography and has been extensively applied to many science and engineering problems. However, its direct-copying-based migration and random mutation operators make BBO possess local exploitation ability but lack global exploration ability. To remedy the defect and enhance the performance of BBO, an enhanced BBO variant, called POLBBO, is developed in this paper. In POLBBO, a proposed efficient operator named polyphyletic migration operator can formally utilize as many as four individuals’ features to construct a new solution vector. This operator cannot only generate new features from more promising areas in the search space, but also effectively increase the population diversity. On the other hand, an orthogonal learning (OL) strategy based on orthogonal experimental design is employed. The OL strategy can quickly discover more useful information from the search experiences and efficiently utilize the information to construct a more promising solution, and thereby provide a systematic and elaborate reasoning method to guide the search directions of POLBBO. The proposed POLBBO is verified on a set of 24 benchmark functions with diverse complexities, and is compared with the basic BBO, five state-of-the-art BBO variants, five existing OL-based algorithms, and nine other evolutionary algorithms. The experimental results and comparisons demonstrate that the polyphyletic migration operator and the OL strategy can work together well and enhance the performance of BBO significantly in terms of the quality of the final solutions and the convergence rate.     

Water wave optimization: A new nature-inspired metaheuristic

Nature-inspired computing has been a hot topic in scientific and engineering fields in recent years. Inspired by the shallow water wave theory, the paper presents a novel metaheuristic method, named water wave optimization (WWO), for global optimization problems. We show how the beautiful phenomena of water waves, such as propagation, refraction, and breaking, can be used to derive effective mechanisms for searching in a high-dimensional solution space. In general, the algorithmic framework of WWO is simple, and easy to implement with a small-size population and only a few control parameters. We have tested WWO on a diverse set of benchmark problems, and applied WWO to a real-world high-speed train scheduling problem in China. The computational results demonstrate that WWO is very competitive with state-of-the-art evolutionary algorithms including invasive weed optimization (IWO), biogeography-based optimization (BBO), bat algorithm (BA), etc. The new metaheuristic is expected to have wide applications in real-world engineering optimization problems.     

Ecogeography-based optimization: Enhancing biogeography-based optimization with ecogeographic barriers and differentiations

Biogeography-based optimization (BBO) is a bio-inspired metaheuristic based on the mathematics of island biogeography. The paper proposes a new variation of BBO, named ecogeography-based optimization (EBO), which regards the population of islands (solutions) as an ecological system with a local topology. Two novel migration operators are designed to perform effective exploration and exploitation in the solution space, mimicking the species dispersal under ecogeographic barriers and differentiations. Experimental results show that the EBO outperforms the basic BBO and several other popular evolutionary algorithms (EAs) on a set of well-known benchmark problems. We also present a real-world application of the proposed EBO to an emergency airlift problem in the 2013 Ya׳an–Lushan Earthquake, China.     

Analysis of migration models of biogeography-based optimization using Markov theory

Biogeography-based optimization (BBO) is a new evolutionary algorithm inspired by biogeography, which involves the study of the migration of biological species between habitats. Previous work has shown that various migration models of BBO result in significant changes in performance. Sinusoidal migration models have been shown to provide the best performance so far. Motivated by biogeography theory and previous results, in this paper a generalized sinusoidal migration model curve is proposed. A previously derived BBO Markov model is used to analyze the effect of migration models on optimization performance, and new theoretical results which are confirmed with simulation results are obtained. The results show that the generalized sinusoidal migration model is significantly better than other models for simple but representative problems, including a unimodal one-max problem, a multimodal problem, and a deceptive problem. In addition, performance comparison is further investigated through 23 benchmark functions with a wide range of dimensions and diverse complexities, to verify the superiority of the generalized sinusoidal migration model.     

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。     

生物地理学优化算法综述

生物地理学(Biogeography)是一门研究自然界种群迁移机制的科学,Dan Simon用生物地理学的方法和机制来解决工程优化问题,提出了生物地理学优化算法(BBO,Biogeography-Based Optimization).生物地理学优化算法以其独特的搜索机制和较好的性能在智能优化算法领域得到了广泛的关注.对生物地理学优化算法的设计原理、迁徙模型、算法流程及相应迁移和突变操作进行了综述.通过BBO算法在14个基准函数下与传统算法,如遗传算法、蚁群算法和粒子群等优化算法的性能比较,表明生物地理学优化算法是有效的.论述了算法与传统优化算法之间的差异以及BBO算法有待解决的问题.     

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.     

Virtual machine consolidated placement based on multi-objective biogeography-based optimization

Virtual machine placement (VMP) is an important issue in selecting most suitable set of physical machines (PMs) for a set of virtual machines (VMs) in cloud computing environment. VMP problem consists of two sub problems: incremental placement (VMiP) problem and consolidated placement (VMcP) problem. The goal of VMcP is to consolidate the VMs to more suitable PMs. The challenge in VMcP problem is how to find optimal solution effectively and efficiently especially when VMcP is a kind of NP-hard problem. In this paper, we present a novel solution to the VMcP problem called VMPMBBO. The proposed VMPMBBO treats VMcP problem as a complex system and utilizes the biogeography-based optimization (BBO) technique to optimize the virtual machine placement that minimizes both the resource wastage and the power consumption at the same time. Extensive experiments have been conducted using synthetic data from related literature and data from two real datasets. First of all, the necessity of VMcP has been proved by experimental results obtained by applying VMPMBBO. Then, the proposed method is compared with two existing multi-objective VMcP optimization algorithms and it is shown that VMPMBBO has better convergence characteristics and is more computationally efficient as well as robust. And then, the issue of parameter setting of the proposed method has been discussed. Finally, adaptability and extensibility of VMPMBBO have also been proved through experimental results. To the best of our knowledge, this work is the first approach that applies biogeography-based optimization (BBO) to virtual machine placement.     

引入物种演化的改进生物地理学优化算法

针对生物地理学优化算法(biogeography-based optimization, BBO)易早熟收敛、陷入局部最优的问题,引入物种演化理论提出了改进生物地理学优化算法。该算法将所有栖息地按照物种数量划分为三种地区,并建立协同进化关系,合理地采用区间入侵、区内合作/竞争策略,满足多样性的同时避免了早熟收敛。定义了物种更迭和物种进化两种变异策略,提出的双策略协同变异算子旨在解决变异算子对较优解的破坏。通过CEC2017中的八个基准测试函数与标准BBO及相关改进算法相比,该算法在算法性能、稳定性等方面优于BBO及其他改进算法,且该算法不易被局部最优值所限制。将该算法应用于以最大完工时间为目标的柔性作业车间调度问题(flexible Job-Shop scheduling problem, FJSP)以检验其实际应用价值,实验表明,该算法在解决FJSP上具有一定的有效性。     

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.     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.     

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。     

一种生物地理学移动机器人路径规划算法

目前,虽然有多种智能计算方法用于移动机器人路径规划问题,但在复杂环境下,多数智能计算方法表现出效率低下,结果较差的问题。提出一种结合基于有效顶点的栅格编码法和改进的生物地理学优化算法的移动机器人路径规划方法,以解决该类问题。结合已知的环境信息,从精英策略、降维机制和基于惯性算子的迁移操作3方面改进了生物地理学优化算法。改进算法用于机器人移动路径,与人工蜂群算法、粒子群算法和人工鱼群算法等智能算法进行比较,实验的结果证实改进算法能够更有效地解决复杂环境下机器人路径规划问题。     

Fruit classification by biogeography‐based optimization and feedforward neural network

Accurate fruit classification is difficult to accomplish because of the similarities among the various categories. In this paper, we proposed a novel fruit‐classification system, with the goal of recognizing fruits in a more efficient way. Our methodology included the following steps. First, a four‐step pre‐processing was employed. Second, the features (colour, shape, and texture) were extracted. Third, we utilized principal component analysis to remove excessive features. Fourth, a novel fruit‐classification system based on biogeography‐based optimization (BBO) and feedforward neural network (FNN) was proposed, with the short name of BBO‐FNN. The experiment employed over 1653 chromatic fruit images (18 categories) by fivefold stratified cross‐validation. The results showed that the proposed BBO‐FNN yielded an overall accuracy of 89.11%, which was higher than the five state‐of‐the‐art methods: genetic algorithm‐FNN, artificial bee colony‐FNN, particle swarm optimization‐FNN, kernel support vector machine, and ant colony optimization‐FNN. Also, the BBO‐FNN achieved the same accuracy as fitness‐scaling chaotic artificial bee colony‐FNN, but it performed much faster than the latter. The proposed BBO‐FNN was effective in fruit‐classification in terms of classification accuracy and computation time. This indicated that it can be applied in credible use.     

Multi-objective ordinal optimization for simulation optimization problems

Ordinal optimization (OO) has been successfully applied to accelerate the simulation optimization process with single objective by quickly narrowing down the search space. In this paper, we extend the OO techniques to address multi-objective simulation optimization problems by using the concept of Pareto optimality. We call this technique the multi-objective OO (MOO). To define the good enough set and the selected set, we introduce two performance indices based on the non-dominance relationship among the designs. Then we derive several lower bounds for the alignment probability under various scenarios by using a Bayesian approach. Numerical experiments show that the lower bounds of the alignment probability are valid when they are used to estimate the size of the selected set as well as the expected alignment level. Though the lower bounds are conservative, they have great practical value in terms of narrowing down the search space.