Quantum inspired evolutionary algorithm for ordering problems

This paper proposes a new quantum-inspired evolutionary algorithm for solving ordering problems. Quantum-inspired evolutionary algorithms based on binary and real representations have been previously developed to solve combinatorial and numerical optimization problems, providing better results than classical genetic algorithms with less computational effort. However, for ordering problems, order-based genetic algorithms are more suitable than those with binary and real representations. This is because specialized crossover and mutation processes are employed to always generate feasible solutions. Therefore, this work proposes a new quantum-inspired evolutionary algorithm especially devised for ordering problems (QIEA-O). Two versions of the algorithm have been proposed. The so-called pure version generates solutions by using the proposed procedure alone. The hybrid approach, on the other hand, combines the pure version with a traditional order-based genetic algorithm. The proposed quantum-inspired order-based evolutionary algorithms have been evaluated for two well-known benchmark applications – the traveling salesman problem (TSP) and the vehicle routing problem (VRP) – as well as in a real problem of line scheduling. Numerical results were obtained for ten cases (7 VRP and 3 TSP) with sizes ranging from 33 to 101 stops and 1 to 10 vehicles, where the proposed quantum-inspired order-based genetic algorithm has outperformed a traditional order-based genetic algorithm in most experiments.     

Quantum cooperative search algorithm for 3-SAT

Grover's search algorithm, one of the most popular quantum algorithms, provides a good solution to solve NP complexity problems, but requires a large number of quantum bits (qubits) for its functionality. In this paper, a novel algorithm called quantum cooperative search is proposed to make Grover's search algorithm work on 3-SAT problems with a small number of qubits. The proposed algorithm replaces some qubits with classical bits and finds assignments to these classical bits using the traditional 3-SAT algorithms including evolutionary algorithms and heuristic local search algorithms. In addition, the optimal configuration of the proposed algorithm is suggested by mathematical analysis. The experimental results show that the quantum cooperative search algorithm composed by Grover's search and heuristic local search performs better than other pure traditional 3-SAT algorithms in most cases. The mathematical analysis of the appropriate number of qubits is also verified by the experiments.     

一种求解多目标优化问题的进化算法混合框架

为了提高多目标优化算法的求解性能,提出一种启发式的基于种群的全局搜索与局部搜索相结合的多目标进化算法混合框架.该框架采用模块化、系统化的设计思想,不同模块可以采用不同策略构成不同的算法.采用经典的改进非支配排序遗传算法(NSGA-II)和基于分解的多目标进化算法(MOEA/D)作为进化算法的模块算法来验证所提混合框架的有效性.数值实验表明,所提混合框架具有良好性能,可以兼顾算法求解的多样性和收敛性,有效提升现有多目标进化算法的求解性能.     

基于交流的求解数值优化问题的混合演化算法

演化算法中有很多不同的演化算子,每一种算子对于不同的优化问题都有自己的优点和缺点。提出了一种基于交流模型的多算子混合演化算法。在该算法中,有两个种群,使用两种算子:多父体杂交算子和Cauchy变异算子。种群间的信息交换通过个体交流实现。对23个标准测试函数的数值仿真表明,该算法具有良好的全局收敛性和鲁棒性。     

An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation

The ability of an Evolutionary Algorithm (EA) to find a global optimal solution depends on its capacity to find a good rate between exploitation of found-so-far elements and exploration of the search space. Inspired by natural phenomena, researchers have developed many successful evolutionary algorithms which, at original versions, define operators that mimic the way nature solves complex problems, with no actual consideration of the exploration-exploitation balance. In this paper, a novel nature-inspired algorithm called the States of Matter Search (SMS) is introduced. The SMS algorithm is based on the simulation of the states of matter phenomenon. In SMS, individuals emulate molecules which interact to each other by using evolutionary operations which are based on the physical principles of the thermal-energy motion mechanism. The algorithm is devised by considering each state of matter at one different exploration–exploitation ratio. The evolutionary process is divided into three phases which emulate the three states of matter: gas, liquid and solid. In each state, molecules (individuals) exhibit different movement capacities. Beginning from the gas state (pure exploration), the algorithm modifies the intensities of exploration and exploitation until the solid state (pure exploitation) is reached. As a result, the approach can substantially improve the balance between exploration–exploitation, yet preserving the good search capabilities of an evolutionary approach. To illustrate the proficiency and robustness of the proposed algorithm, it is compared to other well-known evolutionary methods including novel variants that incorporate diversity preservation schemes. The comparison examines several standard benchmark functions which are commonly considered within the EA field. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration–exploitation balance.     

基于年龄动力学模型的自适应种群演化算法

本文针对演化算法中的自适应动态种群问题,探讨了年龄动力学模型,给出了简化的模型框架,提出了基于该模型的自适应种群演化算法,实现了对进化种群规模的动态控制 。实验表明,该算法比固定种群规模的经典算法具有更好的性能。     

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。     

The partial solutions consideration based self-adaptive evolutionary algorithm: A learning structure of neuro-fuzzy networks

Evolutionary computation has become a popular research field due to its global searching ability. Therefore, it raises a challenge to develop an efficient and robustness evolutionary algorithm to not only reduce the evolution process but also increase the chances to meet the global solution. To this end, this study aims to provide a novel evolutionary algorithm named the partial solutions consideration based self-adaptive evolutionary algorithm (PSC-SEA) to address this issue; the proposed algorithm is applied to adjust the parameters of the neuro-fuzzy networks. More specifically, different from the existing evolution algorithms, the partial solutions consideration (PSC) tends to consider both the specializations and complementary relationships of the partial solutions from the complete solution to prevent converging to suboptimal solution. Moreover, a self-adaptive evolutionary algorithm (SEA) is proposed to dynamically adjust the searching space according to the performance. By doing so, the proposed evolutionary algorithm can consider the influence of partial solutions and provide a suitable searching space to increase the chances to meet the global solution. As shown in the results, the proposed evolutionary algorithm obtains better performance and smoother learning curves than other existing evolutionary algorithms. In other words, the proposed evolutionary algorithm can efficient tune the parameters of the neuro-fuzzy networks to meet the global solution. Base on the results, a framework is proposed to build a benchmark for developing the evolutionary algorithms that can not only consider the influence of partial solutions but also provide a suitable searching space.     

Evolving Evolutionary Algorithms with Patterns

A new model for evolving evolutionary algorithms (EAs) is proposed in this paper. The model is based on the multi expression programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern which is repeatedly used for generating the individuals of a new generation. The evolved pattern is embedded into a standard evolutionary scheme which is used for solving a particular problem. Several evolutionary algorithms for function optimization are evolved by using the considered model. The evolved evolutionary algorithms are compared with a human-designed genetic algorithm. Numerical experiments show that the evolved evolutionary algorithms can compete with standard approaches for several well-known benchmarking problems.     

自适应偏好半径划分区域的多目标进化方法

偏好多目标进化算法是一类帮助决策者找到感兴趣的Pareto最优解的算法.目前,在以参考点位置作为偏好信息载体的偏好多目标进化算法中,不合适的参考点位置往往会严重影响算法的收敛性能,偏好区域的大小难以控制,在高维问题上效果较差.针对以上问题,通过计算基于种群的自适应偏好半径,利用自适应偏好半径构造一种新的偏好关系模型,通过对偏好区域进行划分,提出基于偏好区域划分的偏好多目标进化算法.将所提算法与4种常用的以参考点为偏好信息载体的多目标进化算法g-NSGA-II、r-NSGA-II、角度偏好算法、MOEA/D-PRE进行对比实验,结果表明,所提算法具有较好的收敛性能和分布性能,决策者可以控制偏好区域大小,在高维问题上也具有较好的收敛效果.     

Efficient algorithms based on the k-means and Chaotic League Championship Algorithm for numeric,categorical, and mixed-type data clustering

The success rates of the expert or intelligent systems depend on the selection of the correct data clusters. The k-means algorithm is a well-known method in solving data clustering problems. It suffers not only from a high dependency on the algorithm's initial solution but also from the used distance function. A number of algorithms have been proposed to address the centroid initialization problem, but the produced solution does not produce optimum clusters. This paper proposes three algorithms (i) the search algorithm C-LCA that is an improved League Championship Algorithm (LCA), (ii) a search clustering using C-LCA (SC-LCA), and (iii) a hybrid-clustering algorithm called the hybrid of k-means and Chaotic League Championship Algorithm (KSC-LCA) and this algorithm has of two computation stages. The C-LCA employs chaotic adaptation for the retreat and approach parameters, rather than constants, which can enhance the search capability. Furthermore, to overcome the limitation of the original k-means algorithm using the Euclidean distance that cannot handle the categorical attribute type properly, we adopt the Gower distance and the mechanism for handling a discrete value requirement of the categorical value attribute. The proposed algorithms can handle not only the pure numeric data but also the mixed-type data and can find the best centroids containing categorical values. Experiments were conducted on 14 datasets from the UCI repository. The SC-LCA and KSC-LCA competed with 16 established algorithms including the k-means, k-means++, global k-means algorithms, four search clustering algorithms and nine hybrids of k-means algorithm with several state-of-the-art evolutionary algorithms. The experimental results show that the SC-LCA produces the cluster with the highest F-Measure on the pure categorical dataset and the KSC-LCA produces the cluster with the highest F-Measure for the pure numeric and mixed-type tested datasets. Out of 14 datasets, there were 13 centroids produced by the SC-LCA that had better F-Measures than that of the k-means algorithm. On the Tic-Tac-Toe dataset containing only categorical attributes, the SC-LCA can achieve an F-Measure of 66.61 that is 21.74 points over that of the k-means algorithm (44.87). The KSC-LCA produced better centroids than k-means algorithm in all 14 datasets; the maximum F-Measure improvement was 11.59 points. However, in terms of the computational time, the SC-LCA and KSC-LCA took more NFEs than the k-means and its variants but the KSC-LCA ranks first and SC-LCA ranks fourth among the hybrid clustering and the search clustering algorithms that we tested. Therefore, the SC-LCA and KSC-LCA are general and effective clustering algorithms that could be used when an expert or intelligent system requires an accurate high-speed cluster selection.     

Scaling Up Inductive Logic Programming: An Evolutionary Wrapper Approach

Inductive logic programming (ILP) algorithms are classification algorithms that construct classifiers represented as logic programs. ILP algorithms have a number of attractive features, notably the ability to make use of declarative background (user-supplied) knowledge. However, ILP algorithms deal poorly with large data sets (>10⁴ examples) and their widespread use of the greedy set-covering algorithm renders them susceptible to local maxima in the space of logic programs.This paper presents a novel approach to address these problems based on combining the local search properties of an inductive logic programming algorithm with the global search properties of an evolutionary algorithm. The proposed algorithm may be viewed as an evolutionary wrapper around a population of ILP algorithms.The evolutionary wrapper approach is evaluated on two domains. The chess-endgame (KRK) problem is an artificial domain that is a widely used benchmark in inductive logic programming, and Part-of-Speech Tagging is a real-world problem from the field of Natural Language Processing. In the latter domain, data originates from excerpts of the Wall Street Journal. Results indicate that significant improvements in predictive accuracy can be achieved over a conventional ILP approach when data is plentiful and noisy.     

Solution of multiobjective optimization problems: coevolutionary algorithm based on evolutionary game theory

When attempting to solve multiobjective optimization problems (MOPs) using evolutionary algorithms, the Pareto genetic algorithm (GA) has now become a standard of sorts. After its introduction, this approach was further developed and led to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to keep diversity. On the other hand, the scheme for solving MOPs presented by Nash introduced the notion of Nash equilibrium and aimed at solving MOPs that originated from evolutionary game theory and economics. Since the concept of Nash Equilibrium was introduced, game theorists have attempted to formalize aspects of the evolutionary equilibrium. Nash genetic algorithm (Nash GA) is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash equilibrium through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an evolutionary stable strategy (ESS). In this article, we find the ESS as a solution of MOPs using a coevolutionary algorithm based on evolutionary game theory. By applying newly designed coevolutionary algorithms to several MOPs, we can confirm that evolutionary game theory can be embodied by the coevolutionary algorithm and this coevolutionary algorithm can find optimal equilibrium points as solutions for an MOP. We also show the optimization performance of the co-evolutionary algorithm based on evolutionary game theory by applying this model to several MOPs and comparing the solutions with those of previous evolutionary optimization models. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003.     

MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.     

Solving bus terminal location problems using evolutionary algorithms

Bus terminal assignment with the objective of maximizing public transportation service is known as bus terminal location problem (BTLP). We formulate the BTLP, a problem of concern in transportation industry, as a p-uncapacitated facility location problem (p-UFLP) with distance constraint. The p-UFLP being NP-hard (Krarup and Pruzan, 1990), we propose evolutionary algorithms for its solution. According to the No Free Lunch theorem and the good efficiency of the distinctive preserve recombination (DPX) operator, we design a new recombination operator for solving a BTLP by new evolutionary and memetic algorithms namely, genetic local search algorithms (GLS). We also define the potential objective function (POF) for the nodes and design a new mutation operator based on POF. To make the memetic algorithm faster, we estimate the variation of the objective function based on POF in the local search as part of an operator in memetic algorithms. Finally, we explore numerically the performance of nine proposed algorithms on over a thousand randomly generated problems and select the best two algorithms for further testing. The comparative studies show that our new hybrid algorithm composing the evolutionary algorithm with the GLS outperforms the multistart simulated annealing algorithm.     

A statistical study of a class of cellular evolutionary algorithms.

Parallel evolutionary algorithms, over the past few years, have proven empirically worthwhile, but there seems to be a lack of understanding of their workings. In this paper we concentrate on cellular (fine-grained) models, our objectives being: (1) to introduce a suite of statistical measures, both at the genotypic and phenotypic levels, which are useful for analyzing the workings of cellular evolutionary algorithms; and (2) to demonstrate the application and utility of these measures on a specific example-the cellular programming evolutionary algorithm. The latter is used to evolve solutions to three distinct (hard) problems in the cellular-automata domain: density, synchronization, and random number generation. Applying our statistical measures, we are able to identify a number of trends common to all three problems (which may represent intrinsic properties of the algorithm itself), as well as a host of problem-specific features. We find that the evolutionary algorithm tends to undergo a number of phases which we are able to quantitatively delimit. The results obtained lead us to believe that the measures presented herein may prove useful in the general case of analyzing fine-grained evolutionary algorithms.     

进化算法在job-shop调度问题中的应用研究

研究了应用进化算法(遗传算法(GA)和进化规 划(EP))以及混合模拟退火进化算法(SAGA和SAEP)求解job-shop调度问题．仿真实验结果表 明这四种算法是可行的．文中最后对它们的优劣作了比较．     

BP网络进化及其在雷达目标识别中的应用

针对常规ＢＰ神经网络的ＢＰ算法只能训练固定结构的神经网络,存在诸如易落入局部极值、没有引入提高泛化能力的训练机制等固有不足之处,以及一些神经网络进化算法的进化机制中存在的缺陷,本文提出一种ＢＰ神经网络进化算法,并用于高分辨雷达目标一维距离像的识别问题。实验结果表明,经所述方法优化后的神经网络结构简单、泛化能力优于ＢＰ算法和一些进化算法训练的网络。     

Biogeography-based optimisation with chaos

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.     

Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.