Combinations of estimation of distribution algorithms and other techniques

This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems:a) guided mutation,an offspring generator in which the ideas from EDAs and genetic algorithms are combined together,we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem,b)evolutionary algorithms refining a heuristic,we advocate a strategy for solving a hard optimization problem with complicated data structure,and c) combination of two different local search techniques and EDA for numerical global optimization problems,its basic idea is that not all the new generated points are needed to be improved by an expensive local search.     

Evolutionary algorithms refining a heuristic: a hybrid method for shared-path protections in WDM networks under SRLG constraints.

An evolutionary algorithm (EA) can be used to tune the control parameters of a construction heuristic to an optimization problem and generate a nearly optimal solution. This approach is in the spirit of indirect encoding EAs. Its performance relies on both the heuristic and the EA. This paper proposes a three-phase parameterized construction heuristic for the shared-path protection problem in wavelength division multiplexing networks with shared-risk link group constraints and applies an EA for optimizing the control parameters of the proposed heuristics. The experimental results show that the proposed approach is effective on all the tested network instances. It was also demonstrated that an EA with guided mutation performs better than a conventional genetic algorithm for tuning the control parameters, which indicates that a combination of global statistical information extracted from the previous search and location information of the best solutions found so far could improve the performance of an algorithm.     

An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.

Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.     

多样性指导进化算法及其在机器人路径规划中的应用

通过分析及结合机器人路径规划的进化编程仿真实验发现，保存最优个体或淘汰最差个体都会引起进化算法早熟现象，而种群多样性无疑在进化算法中扮演着关键角色。虽然多样性已经用于分析算法中，但是很少用于指导搜索。多样性指导进化算法使用了众所周知的到平均点距离法使变异期与杂交期交替出现。多样性指导进化算法在机器人路径规划问题中展现出显著的结果，与用适应值比较的简单进化算法有着重大的区别。     

最大团问题的改进遗传算法求解

最大团问题是组合优化中经典的NP完全问题,该问题的枚举算法只适用于求解中小规模的图。提出了基于遗传算法的最大团问题求解算法,引入概率模型指导变异产生新的个体,并结合启发式局部算法搜索最大团。经算例测试,获得了较好的效果。     

A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.     

An improved model-based evolutionary algorithm for multi-objective optimization

The basic idea in the estimation of distribution algorithms is the replacement of heuristic operators with machine learning models such as regression models, clustering models, or classification models. So, recently, the model-based evolutionary algorithms (MBEAs) have been suggested in three groups: The estimation of distribution algorithms (EDAs), surrogate assisted evolutionary algorithms, and the inversed models to map from the objective space to the decision space. In this article, a new approach, based on an inversed model of Gaussian process and random forest framework, is proposed. The main idea is applying the process of random forest variable importance with a random grouping that determines some of the best assignment of decision variables to objective functions in order to form a Gaussian process in inverse models that maps to decision space the rich solutions which are discovered from objective space. Then these inverse models through sampling the objective space generate offspring. The proposed algorithm has been tested on the benchmark test suite for evolutionary algorithms (modified Deb K, Thiele L, Laumanns M, Zitzler E (DTLZ), and Walking Fish Group (WFG)) and indicates that the proposed method is a competitive and promising approach.     

进化迁移优化算法综述

进化算法是模拟自然界生物进化的启发式算法,具有良好的搜索能力和灵活性且广泛用于复杂优化问题的求解,但在求解过程中默认问题先验知识为零,然而由于问题很少孤立存在,解决单一任务积累的经验可迁移至其他相关任务。进化迁移优化算法利用相关领域的知识学习和迁移,实现了更好的优化效率和性能。介绍进化迁移优化算法的基本分类,从源任务选择、知识迁移、缩小搜索空间差异、进化算法搜索、进化资源分配等5个角度出发对主流进化迁移优化算法的核心策略和优劣势进行梳理和分析。通过中国知网和WOS平台对2014年至2021年的进化迁移优化相关文献进行检索,运用知识图谱进行数据挖掘、信息处理、知识计量和图形绘制,根据进化迁移优化的发展趋势和经验分析总结了其面临的主要挑战和未来研究方向。     

A hybridization of an evolutionary algorithm and a parallel branch and bound for solving the capacitated single allocation hub location problem

In this study, we propose a hybrid optimization method, consisting of an evolutionary algorithm (EA) and a branch-and-bound method (BnB) for solving the capacitated single allocation hub location problem (CSAHLP). The EA is designed to explore the solution space and to select promising configurations of hubs (the location part of the problem). Hub configurations produced by the EA are further passed to the BnB search, which works with fixed hubs and allocates the non-hub nodes to located hubs (the allocation part of the problem). The BnB method is implemented using parallelization techniques, which results in short running times. The proposed hybrid algorithm, named EA-BnB, has been tested on the standard Australia Post (AP) hub data sets with up to 300 nodes. The results demonstrate the superiority of our hybrid approach over existing heuristic approaches from the existing literature. The EA-BnB method has reached all the known optimal solutions for AP hub data set and found new, significantly better, solutions on three AP instances with 100 and 200 nodes. Furthermore, the extreme efficiency of the implementation of this hybrid algorithm resulted in short running times, even for the largest AP test instances.     

A framework for learning in search-based systems

We provide an overall framework for learning in search based systems that are used to find optimum solutions to problems. This framework assumes that prior knowledge is available in the form of one or more heuristic functions (or features) of the problem domain. An appropriate clustering strategy is used to partition the state space into a number of classes based on the available features. The number of classes formed will depend on the resource constraints of the system. In the training phase, example problems are run using a standard admissible search algorithm. In this phase, heuristic information corresponding to each class is learned. This new information can be used in the problem solving phase by appropriate search algorithms so that subsequent problem instances can be solved more efficiently. In this framework, we also show that heuristic information of forms other than the conventional single valued underestimate value can be used, since we maintain the heuristic of each class explicitly. We show some novel search algorithms that can work with some such forms. Experimental results have been provided for some domains     

带准备时间的单机调度问题的混合进化算法研究

提出了一种混合进化算法（HEA）用于求解具有序列相关依赖且带准备时间的单机调度问题, 其优化目标为最小化总延迟。该混合进化算法由局部搜索和进化算法框架混合而成。HEA具有一些新的特点, 例如在局部搜索中采用了一种新提出的基于块移动的邻域结构, 这种邻域结构合理地限制了搜索空间, 提高了算法的搜索效率; 在HEA中采用了一种新的组合算子——块顺序交叉算符（BOX）来产生新的子代工作序列。用本算法对当前国际文献中公开的两组共64个算例进行了测试, HEA改进了9个算例在当前文献中的最优解, 表明了所提出的HEA算法的优越性。与之前的国际文献中最好的四个启发式算法进行了详细比较, 表明了HEA算法的优势。     

A differential memetic algorithm

Memetic algorithms have been devised to rectify the absence of a local search mechanism in evolutionary algorithms. This paper proposes a differential memetic algorithm (DMA). To this end, first we propose a differential bidirectional random search as a local search algorithm. Then, a randomized blending crossover (RBleX) is proposed which aimed to scatter the new born offspring more diversely in the whole search space. We devise our proposed DMA, by using the RBleX crossover in the GA, and including the DBRS local search algorithm. A comparison of the performance of the DMA and those of seven other evolutionary/memetic or hybrid algorithms reported in two different papers on numerous bechmark functions demonstrates better performance of proposed DMA algorithm in most of the cases.     

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.     

Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems.

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations.     

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.     

Chain-reaction solution update in MOEA/D and its effects on multi- and many-objective optimization

MOEA/D is one of the promising evolutionary algorithms for multi- and many-objective optimization. To improve the search performance of MOEA/D, this work focuses on the solution update method in the conventional MOEA/D and proposes its alternative, the chain-reaction solution update. The proposed method is designed to maintain and improve the variable (genetic) diversity in the population by avoiding duplication of solutions in the population. In addition, the proposed method determines the order of existing solutions to be updated depending on the location of each offspring in the objective space. Furthermore, when an existing solution in the population is replaced by a new offspring, the proposed method tries to reutilize the existing solution for other search directions by recursively performing the proposed chain-reaction update procedure. This work uses discrete knapsack and continuous WFG4 problems with 2–8 objectives. Experimental results using knapsack problems show the proposed chain-reaction update contributes to improving the search performance of MOEA/D by enhancing the diversity of solutions in the objective space. In addition, experimental results using WFG4 problems show that the search performance of MOEA/D can be further improved using the proposed method.     

构建在最大熵原理上的分布估计算法及其应用研究

分布估计算法是进化计算领域的一个新方向.它主要用概率模型来建造进化计算中的遗传算法,它不再依赖于交叉与变异,而是估计较好个体的概率分布,用概率分布来引导对搜寻空间的探索.本文提出一类基于最大熵的分布估计算法.实验结果表明,在解决某些较复杂问题时,本文算法比遗传算法更具优势.     

有导向变异算子的无线Mesh网负载均衡算法研究*

为了提高无线Mesh网络(WMN)的传输性能,提出基于有导向变异算子的进化算法GM-EA(guidedmutation EA)来优化WMN网关负载均衡问题。在已有的WMN负载均衡算法基础上,GM-EA算法通过结合粒子群优化的方法,更好地利用种群中的全局信息,在较少迭代次数下可以达到网关数量和负载均衡两方面的优化。仿真实验表明,GM-EA算法以增加执行时间为代价下得到的网关数量与比其他算法得到的结果更优;在网关负载均衡方面,该算法也取得较好的结果。     

Combined Petri net modelling and AI-based heuristic hybrid search for flexible manufacturing systems—part II. Heuristic hybrid search

This two-part paper presents modelling and scheduling approaches of flexible manufacturing systems using Petri nets (PNs) and artificial intelligence (AI)-based heuristic search methods. In Part I, PN-based modelling approaches and basic AI-based heuristic search algorithms were presented. In Part II, a new heuristic function that exploits PN information is proposed. Heuristic information obtained from the PN model is used to dramatically reduce the search space. This heuristic is derived from a new concept, the resource cost reachability matrix, which builds on the properties of B-nets proposed in Part I. Two hybrid search algorithms, (1) an approach to model dispatching rules using analysis information provided by the PN simulation and (2) an approach of the modified stage-search algorithm, are proposed to reduce the complexity of large systems. A random problem generator is developed to test the proposed methods. The experimental results show promising results.     

Dynamic and heuristic fuzzy connectives-based crossover operators for controlling the diversity and convergence of real-coded genetic algorithms

Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profitable way, the heuristic fuzzy connectives-based crossover operators. We combine both crossover operators for designing dynamic heuristic fuzzy connectives-based crossover operators that show a robust behavior. © 1996 John Wiley & Sons, Inc.