A cooperative coevolutionary algorithm for design of platform-based mass customized products

As a new business model, mass customization (MC) intends to enable enterprises to comply with customer requirements at mass production efficiencies. A widely advocated approach to implement MC is platform product customization (PPC). In this approach, a product variant is derived from a given product platform to satisfy customer requirements. Adaptive PPC is such a PPC mode in which the given product platform has a modular architecture where customization is achieved by swapping standard modules and/or scaling modular components to formulate multiple product variants according to market segments and customer requirements. Adaptive PPC optimization includes structural configuration and parametric optimization. This paper presents a new method, namely, a cooperative coevolutionary algorithm (CCEA), to solve the two interrelated problems of structural configuration and parametric optimization in adaptive PPC. The performance of the proposed algorithm is compared with other methods through a set of computational experiments. The results show that CCEA outperforms the existing hierarchical evolutionary approaches, especially for large-scale problems tested in the experiments. From the experiments, it is also noticed that CCEA is slow to converge at the beginning of evolutionary process. This initial slow convergence property of the method improves its searching capability and ensures a high quality solution.     

从动态适值空间补偿信息: 一种抗病态合作协同进化算法

针对合作协同进化算法(CCEA) 动态适值空间的特点, 研究信息补偿方法以消除由问题分解所导致的病态现象, 并提出基于动态多种群进化策略的抗病态CCEA. 每个协进化种群可动态分离出多个变化的子种群, 利用它们同时获取多个全局或局部最优解作为交互信息, 以实现信息补偿. 针对引发病态行为的标准测试函数, 与3 种典型CCEA 进行比较分析, 实验结果表明所提出算法能有效克服病态现象, 具有良好的全局优化能力.     

Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution

This article introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations or islands, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study how the performance of the cooperative coevolutionary multi-objective approaches can be drastically increased with respect to their corresponding original versions. This is specially interesting for solving complex problems involving a large number of variables, since the problem decomposition performed by the model at the island level allows for much faster executions (the number of variables to handle in every island is divided by the number of islands). We conduct a study on a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We propose a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine.     

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.     

The preservation of favored building blocks in the struggle for fitness: the puzzle algorithm

The shortest common superstring (SCS) problem, known to be NP-complete, seeks the shortest string that contains all strings from a given set. In this paper, we present a novel coevolutionary algorithm-the Puzzle Algorithm-where a population of building blocks coevolves alongside a population of solutions. We show experimentally that our novel algorithm outperforms a standard genetic algorithm (GA) and a benchmark greedy algorithm on instances of the SCS problem inspired by deoxyribonucleic acid (DNA) sequencing. We next compare our previously presented cooperative coevolutionary algorithm with the Co-Puzzle Algorithm-the puzzle algorithm coupled with cooperative coevolution-showing that the latter proves to be top gun. Finally, we discuss the benefits of using our puzzle approach in the general field of evolutionary algorithms.     

A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization

In addition to the need for satisfying several competing objectives, many real-world applications are also dynamic and require the optimization algorithm to track the changing optimum over time. This paper proposes a new coevolutionary paradigm that hybridizes competitive and cooperative mechanisms observed in nature to solve multiobjective optimization problems and to track the Pareto front in a dynamic environment. The main idea of competitive-cooperative coevolution is to allow the decomposition process of the optimization problem to adapt and emerge rather than being hand designed and fixed at the start of the evolutionary optimization process. In particular, each species subpopulation will compete to represent a particular subcomponent of the multiobjective problem, while the eventual winners will cooperate to evolve for better solutions. Through such an iterative process of competition and cooperation, the various subcomponents are optimized by different species subpopulations based on the optimization requirements of that particular time instant, enabling the coevolutionary algorithm to handle both the static and dynamic multiobjective problems. The effectiveness of the competitive-cooperation coevolutionary algorithm (COEA) in static environments is validated against various multiobjective evolutionary algorithms upon different benchmark problems characterized by various difficulties in local optimality, discontinuity, nonconvexity, and high-dimensionality. In addition, extensive studies are also conducted to examine the capability of dynamic COEA (dCOEA) in tracking the Pareto front as it changes with time in dynamic environments.      

The cooperative coevolutionary (1+1) EA

Coevolutionary algorithms are variants of traditional evolutionary algorithms and are often considered more suitable for certain kinds of complex tasks than noncoevolutionary methods. One example is a general cooperative coevolutionary framework for function optimization. This paper presents a thorough and rigorous introductory analysis of the optimization potential of cooperative coevolution. Using the cooperative coevolutionary framework as a starting point, the CC (1+1) EA is defined and investigated from the perspective of the expected optimization time. The research concentrates on separability, a key property of objective functions. We show that separability alone is not sufficient to yield any advantage of the CC (1+1) EA over its traditional, non-coevolutionary counterpart. Such an advantage is demonstrated to have its basis in the increased explorative possibilities of the cooperative coevolutionary algorithm. For inseparable functions, the cooperative coevolutionary set-up can be harmful. We prove that for some objective functions the CC (1+1) EA fails to locate a global optimum with overwhelming probability, even in infinite time; however, inseparability alone is not sufficient for an objective function to cause difficulties. It is demonstrated that the CC (1+1) EA may perform equal to its traditional counterpart, and may even outperform it on certain inseparable functions.     

LeCMPSO算法求解异构无人机协同多任务重分配问题

无人机系统在军事领域有着广泛应用, 由于战场环境复杂多变, 无人机遭遇突发状况后需进行任务重分配.异构无人机是指多种类型的无人机, 可完成单一无人机无法完成的多类型复杂任务, 异构无人机协同多任务重分配问题约束条件复杂且包含混合变量, 现有多目标优化算法不能有效处理此类问题. 为高效求解上述问题, 本文构建多约束异构无人机协同多任务重分配问题模型, 提出一种学习引导的协同多目标粒子群优化算法(LeCMPSO), 该算法引入基于先验知识的初始化策略和基于历史信息学习的粒子更新策略, 能有效避免不可行解的产生并提升算法的搜索效率. 通过在4组实例上的仿真实验表明, 与其他典型的协同进化多目标优化算法相比, 所提算法在解集的多样性、收敛性及搜索时间方面均具有较好的性能.     

Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization

The existing algorithms to solve dynamic multiobjective optimization (DMO) problems generally have difficulties in non-uniformity, local optimality and non-convergence. Based on artificial immune system, quantum evolutionary computing and the strategy of co-evolution, a quantum immune clonal coevolutionary algorithm (QICCA) is proposed to solve DMO problems. The algorithm adopts entire cloning and evolves the theory of quantum to design a quantum updating operation, which improves the searching ability of the algorithm. Moreover, coevolutionary strategy is incorporated in global operation and coevolutionary competitive operation and coevolutionary cooperative operation are designed to improve the uniformity, the diversity and the convergence performance of the solutions. The results on test problems and performance metrics compared with ICADMO and DBM suggest that QICCA has obvious effectiveness and advantages which shows great capability of evolving convergent, diverse and uniformly distributed Pareto fronts.     

A Tournament-Based Competitive Coevolutionary Algorithm

For an efficient competitive coevolutionary algorithm, it is important that competing populations be capable of maintaining a coevolutionary balance and hence, continuing evolutionary arms race to increase the levels of complexity. We propose a competitive coevolutionary algorithm that combines the strategies of neighborhood-based evolution, entry fee exchange tournament competition (EFE-TC) and localized elitism. An emphasis is placed on analyzing the effects of these strategies on the performance of competitive coevolutionary algorithms. We have tested the proposed algorithm with two adversarial problems: sorting network and Nim game problems that have different characteristics. The experimental results show that the interacting effects of the strategies appear to promote a balanced evolution between host and parasite populations, which naturally leads them to keep on evolutionary arms race. Consequently, the proposed algorithm provides good quality solutions with a little computation time.     

A hybrid classification algorithm based on coevolutionary EBFNN and domain covering method

A new hybrid scheme of the elliptical basis function neural network (EBFNN) model combined with the cooperative coevolutionary algorithm (Co-CEA) and domain covering method is presented for multiclass classification tasks. This combination of the Co-CEA EBFNN (CC-EBFNN) and the domain covering method is proposed to enhance the predictive capability of the estimated model. The whole training process is divided into two stages: the evolutionary process, and the heuristic structure refining process. First, the initial hidden nodes of the EBFNN model are selected randomly in the training samples, which are further partitioned into modules of hidden nodes with respect to their class labels. Subpopulations are initialized on modules, and the Co-CEA evolves all subpopulations to find the optimal EBFNN structural parameters. Then the heuristic structure refining process is performed on the individual in the elite pool with the special designed constructing and pruning operators. Finally, the CC-EBFNN model is tested on six real-world classification problems from the UCI machine learning repository, and experimental results illustrate that the EBFNN model can be estimated in fewer evolutionary trials, and is able to produce higher prediction accuracies with much simpler network structures when compared with conventional learning algorithms.     

Immune clonal coevolutionary algorithm for dynamic multiobjective optimization

In this paper, a new evolutionary algorithm, called immune clonal coevolutionary algorithm (ICCoA) for dynamic multiobjective optimization (DMO) is proposed. On the basis of the basic principles of artificial immune system, the proposed algorithm adopts the immune clonal selection to solve DMO problems. In addition, the theory of coevolution is incorporated in ICCoA in global operation to preserve the diversity of Pareto-fronts. Moreover, coevolutionary competitive and cooperative operation is designed to enhance the uniformity and the diversity of the solutions. In comparison with NSGA-II, immune clonal algorithm for DMO and direction-based method, the simulation results obtained on 5 difficult test problems and on related performance metrics suggest that ICCoA can achieve better distributed solutions and be very effective in maintaining the uniformity of Pareto-fronts.     

协同演化算法研究进展

协同演化算法(coevolutionary algorithms,CEA)是当前国际上计算智能研究的一个热点,它运用生物协同演化的思想,是针对演化算法的不足而兴起的,通过构造两个或多个种群,建立它们之间的竞争或合作关系,多个种群通过相互作用来提高各自性能,适应复杂系统的动态演化环境,以达到种群优化的目的.介绍了协同演化算法的研究状况以及目前的研究进展,概述了它的基本算法、主要特点、理论与技术,同时介绍了一些主要的应用领域,指出了协同演化算法的研究方向.     

Solving the balance problem of massively multiplayer online role-playing games using coevolutionary programming

In massively multiplayer online role-playing games (MMORPGs), each race holds some attributes and skills. Each skill contains several abilities such as physical damage and hit rate. All those attributes and abilities are functions of the character's level, which are called Ability-Increasing Functions (AIFs). A well-balanced MMORPG is characterized by having a set of well-balanced AIFs. In this paper, we propose a coevolutionary design method, including integration with the modified probabilistic incremental program evolution (PIPE) and the cooperative coevolutionary algorithm (CCEA), to solve the balance problem of MMORPGs. Moreover, we construct a simplest turn-based game model and perform a series of experiments based on it. The results indicate that the proposed method is able to obtain a set of well-balanced AIFs more efficiently, compared with the simple genetic algorithm (SGA), the simulated annealing algorithm (SAA) and the hybrid discrete particle swarm optimization (HDPSO) algorithm. The results also show that the performance of PIPE has been significantly improved through the modification works.     

多策略协同进化粒子群优化算法

为了提高粒子群优化(PSO)算法的优化性能, 提出了一种多策略协同进化PSO(MSCPSO)算法。该方法引入了多策略进化模式和多子群协同进化机制, 将整个种群划分为多个子群, 每个子群中的粒子按照不同的进化策略产生新的粒子。子群周期性地更新共享信息, 以加快算法的收敛速度。通过六个基准函数实验, 仿真结果表明, 新算法在计算精度和收敛速度方面均优于其他七种PSO算法。     

Modeling and convergence analysis of distributed coevolutionary algorithms

A theoretical foundation is presented for modeling and convergence analysis of a class of distributed coevolutionary algorithms applied to optimization problems in which the variables are partitioned among p nodes. An evolutionary algorithm at each of the p nodes performs a local evolutionary search based on its own set of primary variables, and the secondary variable set at each node is clamped during this phase. An infrequent intercommunication between the nodes updates the secondary variables at each node. The local search and intercommunication phases alternate, resulting in a cooperative search by the p nodes. First, we specify a theoretical basis for a class of centralized evolutionary algorithms in terms of construction and evolution of sampling distributions over the feasible space. Next, this foundation is extended to develop a model for a class of distributed coevolutionary algorithms. Convergence and convergence rate analyzes are pursued for basic classes of objective functions. Our theoretical investigation reveals that for certain unimodal and multimodal objectives, we can expect these algorithms to converge at a geometrical rate. The distributed coevolutionary algorithms are of most interest from the perspective of their performance advantage compared to centralized algorithms, when they execute in a network environment with significant local access and internode communication delays. The relative performance of these algorithms is therefore evaluated in a distributed environment with realistic parameters of network behavior.     

多群多策略差分大规模多目标优化算法

针对差分进化算法在解决大规模多目标优化问题时,出现优化后期多样性不足、收敛速度慢等问题,提出一种多群多策略差分大规模多目标优化算法.根据个体特性不同,将种群分为3个等级不同的子群,利用多群策略的优势维持种群多样性.为减少种群陷入局部最优的概率,在不同等级的子群中引入多个变异策略以较好地平衡子群个体的多样性和收敛性.为保证不同子群间信息得到有效交换,根据3个子群的进化状态确定重新分群时机,既保证个体在本群内得到充分进化,又保证个体在一定的条件下进行信息交换.为利用更多的信息生成优秀的子代,将更新后的子群与其父代子群合并,选出下一代子群.为验证所提出算法的有效性,在一组大规模基准测试问题上评估算法的性能,实验结果表明,所提出算法在两个常用测试指标IGD和HV上明显优于其他对比算法.     

教与学信息交互粒子群优化算法

针对单一种群在解决高维问题中收敛速度较慢和多样性缺失的问题,提出了一种教与学信息交互粒子群优化(PSO)算法.根据进化过程将种群动态地划分为两个子种群,分别采用粒子群优化算法和教与学优化算法,同时粒子利用学习者阶段进行子种群之间信息交互,并通过评价收敛性和多样性指标让粒子的收敛能力和多样性在进化过程中得到平衡.与粒子群...     

Coevolutionary learning of neural network ensemble for complex classification tasks

Ensemble approaches to classification have attracted a great deal of interest recently. This paper presents a novel method for designing the neural network ensemble using coevolutionary algorithm. The bootstrap resampling procedure is employed to obtain different training subsets that are used to estimate different component networks of the ensemble. Then the cooperative coevolutionary algorithm is developed to optimize the ensemble model via the divide-and-cooperative mechanism. All component networks are coevolved in parallel in the scheme of interacting co-adapted subpopulations. The fitness of an individual from a particular subpopulation is assessed by associating it with the representatives from other subpopulations. In order to promote the cooperation of all component networks, the proposed method considers both the accuracy and the diversity among the component networks that are evaluated using the multi-objective Pareto optimality measure. A hybrid output-combination method is designed to determine the final ensemble output. Experimental results illustrate that the proposed method is able to obtain neural network ensemble models with better classification accuracy in comparison with currently popular ensemble algorithms.     

An Endosymbiotic Evolutionary Algorithm for Optimization

This paper proposes a new symbiotic evolutionary algorithm to solve complex optimization problems. This algorithm imitates the natural evolution process of endosymbionts, which is called endosymbiotic evolutionary algorithm. Existing symbiotic algorithms take the strategy that the evolution of symbionts is separated from the host. In the natural world, prokaryotic cells that are originally independent organisms are combined into an eukaryotic cell. The basic idea of the proposed algorithm is the incorporation of the evolution of the eukaryotic cells into the existing symbiotic algorithms. In the proposed algorithm, the formation and evolution of the endosymbionts is based on fitness, as it can increase the adaptability of the individuals and the search efficiency. In addition, a localized coevolutionary strategy is employed to maintain the population diversity. Experimental results demonstrate that the proposed algorithm is a promising approach to solving complex problems that are composed of multiple sub- problems interrelated with each other.