动态环境中的进化算法

目前关于进化算法（EA）的研究主要局限于静态优化问题,然而很多现实世界中的问题是动态的,对于这类时变的优化问题通常并不是要求EA发现极值点,而是需要EA能够尽可能紧密地跟踪极值点在搜索空间内的运行轨迹.为此,综述了使EA适用于动态优化问题的各种方法,如增加种群多样性、保持种群多样性、引入某种记忆策略和采用多种群策略等.     

Multi-population Based Univariate Marginal Distribution Algorithm for Dynamic Optimization Problems

Many real-world problems are dynamic optimization problems in which the optimal solutions need to be continuously tracked over time. In this paper a multi-population based univariate marginal distribution algorithm (MUMDA) is proposed to solve dynamic optimization problems. The main idea of the algorithm is to construct several probability models by dividing the population into several parts. The objective is to divide the search space into several regions to maintain the diversity. Concretely, MUMDA uses one probability vector to do the search in the promising areas identified previously, and uses other probability vectors to search for new promising optimal solutions. Moreover the convergence of univariate marginal distribution algorithm (UMDA) is proved, which can be used to analyze the validity of the proposed algorithm. Finally, the experimental study was carried out to compare the performance of several UMDA, and the results show that the MUMDA is effective and can be well adaptive to the dynamic environments rapidly.     

A Fast Clustering Based Evolutionary Algorithm for Super-Large-Scale Sparse Multi-Objective Optimization

During the last three decades, evolutionary algorithms (EAs) have shown superiority in solving complex optimization problems, especially those with multiple objectives and non-differentiable landscapes. However, due to the stochastic search strategies, the performance of most EAs deteriorates drastically when handling a large number of decision variables. To tackle the curse of dimensionality, this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions. The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution, and provides a fast clustering method to highly reduce the dimensionality of the search space. More importantly, all the operations related to the decision variables only contain several matrix calculations, which can be directly accelerated by GPUs. While existing EAs are capable of handling fewer than 10 000 real variables, the proposed algorithm is verified to be effective in handling 1 000 000 real variables. Furthermore, since the proposed algorithm handles the large number of variables via accelerated matrix calculations, its runtime can be reduced to less than 10% of the runtime of existing EAs.      

用演化算法求解抛物型方程扩散系数的识别问题

基于演化算法给出了一类求解参数识别反问题的一般方法,该方法表明只要找到好的、求解相应的正问题的数值方法,演化算法就可以用于求解此类反问题。设计有效的求解反问题的演化算法的关键是寻找一种适合反问题的解空间的编码表示形式、适当的适应值函数形式以及有效的计算正问题的数值方法。该文结合算法、传统的求解反问题的工方法和正则化技术,设计了一类求解参数识别反问题的方法。为验证此类方法,将其用于求解一维扩散方程的     

CDEPSO: a bi-population hybrid approach for dynamic optimization problems

Many real-world optimization problems are dynamic, in which the environment, i.e. the objective function and restrictions, can change over time. In this case, the optimal solution(s) to the problem may change as well. These problems require optimization algorithms to continuously and accurately track the trajectory of the optima (optimum) through the search space. In this paper, we propose a bi-population hybrid collaborative model of Crowding-based Differential Evolution (CDE) and Particle Swarm Optimization (PSO) for Dynamic Optimization Problems (DOPs). In our approach, called CDEPSO, a population of genomes is responsible for locating several promising areas of the search space and keeping diversity throughout the run using CDE. Another population is used to exploit the area around the best found position using the PSO. Several mechanisms are used to increase the efficiency of CDEPSO when finding and tracking peaks in the solution space. A set of experiments was carried out to evaluate the performance of the proposed algorithm on dynamic test instances generated using the Moving Peaks Benchmark (MPB). Experimental results show that the proposed approach is effective in dealing with DOPs.     

An Evolutionary Algorithm for Global Optimization Based on Level-Set Evolution and Latin Squares

In this paper, the level-set evolution is exploited in the design of a novel evolutionary algorithm (EA) for global optimization. An application of Latin squares leads to a new and effective crossover operator. This crossover operator can generate a set of uniformly scattered offspring around their parents, has the ability to search locally, and can explore the search space efficiently. To compute a globally optimal solution, the level set of the objective function is successively evolved by crossover and mutation operators so that it gradually approaches the globally optimal solution set. As a result, the level set can be efficiently improved. Based on these skills, a new EA is developed to solve a global optimization problem by successively evolving the level set of the objective function such that it becomes smaller and smaller until all of its points are optimal solutions. Furthermore, we can prove that the proposed algorithm converges to a global optimizer with probability one. Numerical simulations are conducted for 20 standard test functions. The performance of the proposed algorithm is compared with that of eight EAs that have been published recently and the Monte Carlo implementation of the mean-value-level-set method. The results indicate that the proposed algorithm is effective and efficient.     

Modified differential evolution approach for optimization of planar parallel manipulators force capabilities

The global optimization problem is not easy to solve and is still an open challenge for researchers since an analytical optimal solution is difficult to obtain even for relatively simple application problems. Conventional deterministic numerical algorithms tend to stop the search in local minimum nearest to the input starting point, mainly when the optimization problem presents nonlinear, non-convex and non-differential functions, multimodal and nonlinear. Nowadays, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. The primary advantage of EAs over other numerical methods is that they just require the objective function values, while properties such as differentiability and continuity are not necessary. In this context, the differential evolution (DE), a paradigm of the evolutionary computation, has been widely used for solving numerical global optimization problems in continuous search space. DE is a powerful population-based stochastic direct search method. DE simulates natural evolution combined with a mechanism to generate multiple search directions based on the distribution of solutions in the current population. Among DE advantages are its simple structure, ease of use, speed, and robustness, which allows its application on several continuous nonlinear optimization problems. However, the performance of DE greatly depends on its control parameters, such as crossover rate, mutation factor, and population size and it often suffers from being trapped in local optima. Conventionally, users have to determine the parameters for problem at hand empirically. Recently, several adaptive variants of DE have been proposed. In this paper, a modified differential evolution (MDE) approach using generation-varying control parameters (mutation factor and crossover rate) is proposed and evaluated. The proposed MDE presents an efficient strategy to improve the search performance in preventing of premature convergence to local minima. The efficiency and feasibility of the proposed MDE approach is demonstrated on a force optimization problem in Robotics, where the force capabilities of a planar 3-RRR parallel manipulator are evaluated considering actuation limits and different assembly modes. Furthermore, some comparison results of MDE approach with classical DE to the mentioned force optimization problem are presented and discussed.     

A spy search mechanism for memetic algorithm in dynamic environments

Searching within the sample space for optimal solutions is an important part in solving optimization problems. The motivation of this work is that today’s problem environments have increasingly become dynamic with non-stationary optima and in order to improve optima search, memetic algorithm has become a preferred search method because it combines global and local search methods to obtain good solutions. The challenge is that existing search methods perform the search during the iterations without being guided by solid information about the nature of the search environment which affects the quality of a search outcome. In this paper, a spy search mechanism is proposed for memetic algorithm in dynamic environments. The method uses a spy individual to scope out the search environment and collect information for guiding the search. The method combines hyper-mutation, random immigrants, hill climbing local search, crowding and fitness, and steepest mutation with greedy crossover hill climbing to enhance the efficiency of the search. The proposed method is tested on dynamic problems and comparisons with other methods indicate a better performance by the proposed method.     

多目标协调进化算法研究

进化算法适合解决多目标优化问题,但难以产生高维优化问题的最优解,文中针对此问题提出了一种求解高维目标优化问题的新进化方法,即多目标协调进化算法,主要特点是进化群体按协调模型使用偏好信息进行偏好排序,而不是基于Pareto优于关系进行了个体排序,实验结果表明,所提出的算法是可行而有效的,且能在有限进化代数内收敛。     

A nature-inspired multi-objective optimisation strategy based on a new reduced space searching algorithm for the design of alloy steels

In this paper, a salient search and optimisation algorithm based on a new reduced space searching strategy, is presented. This algorithm originates from an idea which relates to a simple experience when humans search for an optimal solution to a ‘real-life’ problem, i.e. when humans search for a candidate solution given a certain objective, a large area tends to be scanned first; should one succeed in finding clues in relation to the predefined objective, then the search space is greatly reduced for a more detailed search. Furthermore, this new algorithm is extended to the multi-objective optimisation case. Simulation results of optimising some challenging benchmark problems suggest that both the proposed single-objective and multi-objective optimisation algorithms outperform some of the other well-known Evolutionary Algorithms (EAs). The proposed algorithms are further applied successfully to the optimal design problem of alloy steels, which aims at determining the optimal heat treatment regime and the required weight percentages for chemical composites to obtain the desired mechanical properties of steel hence minimising production costs and achieving the overarching aim of ‘right-first-time production’ of metals.     

一种新的求解多维背包问题的分散算法

为了避免蚁群算法在优化搜索过程中易陷入局部最优和早熟收敛,提出一种求解多维背包问题的新型分散搜索算法。该算法是把蚁群算法的构解方法引入到分散搜索算法中,在搜索过程中,既考虑解的质量,又考虑解的分散性。同时,该分散算法还采用了动态更新参考集与阈值接收算法的阈值参数,以控制搜索空间来加快收敛速度。通过选取国际通用MDKP实例库中的多个实例进行测试表明,该算法可以避免陷入局部最优解,能提高全局寻优能力,其结果优于其他现有的方法,并获得了较好的结果。     

Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Multimodal optimization aims at finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs) due to their population-based approach are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.     

求解动态优化问题的多群体UMDA

提出一种求解动态优化问题的多群体单变量边缘分布算法(MUMDA).首先,利用多个概率模型(对应多个群体)将搜索空间分成几个部分,通过对不同区域的搜索或探索将好解进行迁移,扩大搜索空间,增加种群多样性,跟踪最优解的变化;然后,利用对UMDA收敛性的证明分析了所提出算法的有效性;最后,对两个动态优化问题进行仿真计算,并与传统UMDA和基于随机迁移的UMDA(iUMDA)进行了比较.结果表明,MUMDA能快速适应环境的变化,跟踪最优解.     

求解动态优化问题的多种群热力学遗传算法

多种群方法已被证明是提高演化算法动态优化性能的重要方法之一。提出了多种群热力学遗传算法（multi-population based thermodynamic genetic algorithm,MPTDGA）。该算法使用一个概率向量在热力学遗传算法迭代过程中不断演化优化与竞争学习,环境变化时分化成三个概率向量,并分别抽样产生原对偶和随机迁入三个子种群,依据这三个种群和记忆种群最好解的情况,选择新的工作概率向量进入新环境进行学习。在动态背包问题上的实验结果表明,MPTDGA比原对偶遗传算法跟踪最优解的能力更强,有很好的多样性,非常适合求解0-1动态优化问题。     

目标空间映射策略的高维多目标粒子群优化算法

为了平衡优化算法在高维多目标优化问题中收敛性和多样性之间的关系,增加算法的选择压力,本文提出了一种基于目标空间映射策略的高维多目标粒子群优化算法(many-objective particle swarm optimization algorithm based on objective space mapping strategy,MOPSO-OSM)。在求解高维多目标优化问题时,Pareto准则难以从众多的非支配解中确定最优“折中”解,因此将高维多目标空间映射为以收敛性和多样性评价指标的2维空间,再将上述2维空间根据性能指标的优劣划分为4个不同区域。同时,使用反向学习策略提高算法跳出局部最优的能力。实验表明,MOPSO-OSM算法可以有效平衡收敛性和多样性之间的关系,达到求解复杂多目标优化问题的目的。     

Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints

The optimal design of a truss structure with dynamic frequency constraints is a highly nonlinear optimization problem with several local optimums in its search space. In this type of structural optimization problems, the optimization methods should have a high capability to escape from the traps of the local optimums in the search space. This paper presents hybrid electromagnetism-like mechanism algorithm and migration strategy (EM–MS) for layout and size optimization of truss structures with multiple frequency constraints. The electromagnetism-like mechanism (EM) algorithm simulates the attraction and repulsion mechanism between the charged particles in the field of the electromagnetism to find optimal solutions, in which each particle is a solution candidate for the optimization problem. In the proposed EM–MS algorithm, two mechanisms are utilized to update the position of particles: modified EM algorithm and a new migration strategy. The modified EM algorithm is proposed to effectively guide the particles toward the region of the global optimum in the search space, and a new migration strategy is used to provide efficient exploitation between the particles. In order to test the performance of the proposed algorithm, this study utilizes five benchmark truss design examples with frequency constraints. The numerical results show that the EM–MS algorithm is an alternative and competitive optimizer for size and layout optimization of truss structures with frequency constraints.     

Negative selection based immune optimization

An immune optimization algorithm is proposed in this paper based on the immune negative selection. The algorithm NSIOA is motivated by the negative selection mechanism in biological immune recognition. Different from the existing immune optimization methods, NSIOA constantly removes the worst solutions to get the optimal solution. Considering that removal of poor members of a population might lead to the loss of design information that may actually help identify better solutions in the search space, the proposed NSIOA is designed to keep the diversity of antibodies while removing poor members, therefore the algorithm will converge to global optimal solution with high probability. The convergence property and the complexity of the algorithm have also been analyzed. To illustrate the efficiency of the algorithm is used in solving the travel salesman problem. The theoretical analysis and experimental results show that the algorithm is of a strong potential in solving practical problems.     

Multimodal optimization using a bi-objective evolutionary algorithm

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.     

A space search optimization algorithm with accelerated convergence strategies

Evolutionary algorithms (EAs), which have been widely used to solve various scientific and engineering optimization problems, are essentially stochastic search algorithms operating in the overall solution space. However, such random search mechanism may lead to some disadvantages such as a long computing time and premature convergence. In this study, we propose a space search optimization algorithm (SSOA) with accelerated convergence strategies to alleviate the drawbacks of the purely random search mechanism. The overall framework of the SSOA involves three main search mechanisms: local space search, global space search, and opposition-based search. The local space search that aims to form new solutions approaching the local optimum is realized based on the concept of augmented simplex method, which exhibits significant search abilities realized in some local space. The global space search is completed by Cauchy searching, where the approach itself is based on the Cauchy mutation. This operation can help the method avoid of being trapped in local optima and in this way alleviate premature convergence. An opposition-based search is exploited to accelerate the convergence of space search. This operator can effectively reduce a substantial computational overhead encountered in evolutionary algorithms (EAs). With the use of them SSOA realizes an effective search process. To evaluate the performance of the method, the proposed SSOA is contrasted with a method of differential evolution (DE), which is a well-known space concept-based evolutionary algorithm. When tested against benchmark functions, the SSOA exhibits a competitive performance vis-a-vis performance of some other competitive schemes of differential evolution in terms of accuracy and speed of convergence, especially in case of high-dimensional continuous optimization problems.     

A particle swarm optimization based memetic algorithm for dynamic optimization problems

Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic optimization problems. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments.