An evolutionary strategy for decremental multiobjective optimization problems

In this article, an evolutionary algorithm for multiobjective optimization problems in a dynamic environment is studied. In particular, we focus on decremental multiobjective optimization problems, where some objectives may be deleted during evolution—for such a process we call it objective decrement. It is shown that the Pareto‐optimal set after objective decrement is actually a subset of the Pareto‐optimal set before objective decrement. Based on this observation, the inheritance strategy is suggested. When objective decrement takes place, this strategy selects good chromosomes according to the decremented objective set from the solutions found before objective decrement, and then continues to optimize them via evolution for the decremented objective set. The experimental results showed that this strategy can help MOGAs achieve better performance than MOGAs without using the strategy, where the evolution is restarted when objective decrement occurs. More solutions with better quality are found during the same time span. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 847–866, 2007.     

A multiobjective optimization solver using rank-niche evolution strategy

A rank-niche evolution strategy (RNES) algorithm has been developed in this paper to solve unconstrained multiobjective optimization problems. A required number of Pareto-optimal solutions can be generated by the algorithm in a single run. In addition to the operations of recombination, mutation and selection used in original evolution strategy (ES), an external elite set which contains a given number of non-dominated elites is updated and trimmed by a clustering technique to maintain a uniformly distributed Pareto front. The fitness function for each individual contains the information of rank and crowding status. The selection operation using this fitness function considers the superiority and distribution simultaneously. Eight test problems illustrated in other papers are used to test RNES. For some test problems the Pareto-optimal solutions obtained by RNES are better than those obtained by GA-based algorithms.     

多目标混沌差分进化算法

将差分进化算法用于多目标优化问题,提出了多目标混沌差分进化算法(CDEMO).该算法利用混沌序列初始化种群,并用混沌备用种群进行替换操作.该操作不仅起到了维持非劣最优解集均匀性的作用,而且增强了算法的搜索功能.对CDEMO的性能进行研究,数值实验结果表明了CDEMO的有效性.     

An elitist self-adaptive step-size search for structural design optimization

This paper presents a method for optimal sizing of truss structures based on a refined self-adaptive step-size search (SASS) algorithm. An elitist self-adaptive step-size search (ESASS) algorithm is proposed wherein two approaches are considered for improving (i) convergence accuracy, and (ii) computational efficiency. In the first approach an additional randomness is incorporated into the sampling step of the technique to preserve exploration capability of the algorithm during the optimization. Furthermore, an adaptive sampling scheme is introduced to enhance quality of the final solutions. In the second approach computational efficiency of the technique is accelerated through avoiding unnecessary analyses throughout the optimization process using the so-called upper bound strategy (UBS). The numerical results indicate the efficiency of the proposed ESASS algorithm.     

A novel adaptive control strategy for decomposition-based multiobjective algorithm

Recently, evolutionary algorithm based on decomposition (MOEA/D) has been found to be very effective and efficient for solving complicated multiobjective optimization problems (MOPs). However, the selected differential evolution (DE) strategies and their parameter settings impact a lot on the performance of MOEA/D when tackling various kinds of MOPs. Therefore, in this paper, a novel adaptive control strategy is designed for a recently proposed MOEA/D with stable matching model, in which multiple DE strategies coupled with the parameter settings are adaptively conducted at different evolutionary stages and thus their advantages can be combined to further enhance the performance. By exploiting the historically successful experience, an execution probability is learned for each DE strategy to perform adaptive adjustment on the candidate solutions. The proposed adaptive strategies on operator selection and parameter settings are aimed at improving both of the convergence speed and population diversity, which are validated by our numerous experiments. When compared with several variants of MOEA/D such as MOEA/D, MOEA/D-DE, MOEA/D-DE+PSO, ENS-MOEA/D, MOEA/D-FRRMAB and MOEA/D-STM, our algorithm performs better on most of test problems.     

An improved adaptive differential evolution algorithm for continuous optimization

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集成协方差矩阵自适应进化策略与差分进化的优化算法

不同智能优化算法在求解优化问题时通常表现出显著的性能差异.差分进化(DE)算法具备较好的全局搜索能力,但存在收敛慢、效率低的不足,协方差矩阵自适应进化策略(CMA–ES)局部搜索能力强,具备旋转不变性,但容易陷入局部最优,因此, DE和CMA–ES之间具有潜在的协同互补能力.针对上述问题,提出了一种集成协方差矩阵自适应进化策略与差分进化的优化算法(CMADE).在CMADE框架中, DE算法负责全局搜索, CMA–ES算法进行局部搜索.通过周期性解交换机制实现CMA–ES和DE两个算法间协同交互和反馈控制.在解交换时,从DE种群中选择优秀个体,利用CMA–ES算法在优秀个体周围进行局部搜索.同时在DE和CMA–ES的混合种群中,综合考虑解的多样性和最优性,选取一定比例的解作为DE算法的新种群进行全局搜索,实现全局搜索与局部搜索的动态平衡.将CMADE算法与CMA–ES, DE, SaDE, jDE, EPSDE, ACODE和SHADE算法在CEC2014标准测试集上进行比较实验.结果表明, CMADE整体性能显著优于其它比较算法.     

一种基于相异因子的最优保存策略

提出一种基于相异因子的遗传算法最优保存策略,该策略首先产生与最优个体相异因子较大而目标值相近的个体,然后用该个体依次替换种群中与最劣个体相似因子较大且目标值相近的个体,既保证了种群的多样性,又加快了种群收敛速度,收敛效率明显提高。     

A fast and elitist multiobjective genetic algorithm: NSGA-II

Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN³) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN²) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed     

An adaptive knowledge evolution strategy for finding near-optimal solutions of specific problems

Most real-world problems cannot be mathematically defined and/or structured modularly for peer researchers in the same community to facilitate their work. This is partially because there are no concrete defined methods that can help researchers clearly describe their problems and partially because one method fits one problem but does not apply to others. In order to apply someone’s research results to new domains and for researchers to collaborate with each other more efficiently, a well-defined architecture with self-adaptive evolution strategies is proposed. It can automatically find the best solutions from existing knowledge and previous research experiences. The proposed architecture is based on object-oriented programming skills that in turn become foundations of the community interaction evolution strategy and knowledge sharing mechanism. They make up an autonomous evolution mechanism using a progressive learning strategy and a common knowledge packaging definition. The architecture defines fourteen highly modular classes that allow users to enhance collaboration with others in the same or similar research community. The presented evolution strategies also integrate the merits of users’ predefined algorithms, group interaction and learning theory to approach the best solutions of specific problems. Finally, resource limitation problems are tackled to verify both the re-usability and flexibility of the proposed work. Our results show that even without using any specific tuning of the problems, optimal or near-optimal solutions are feasible.     

An adaptive hybrid differential evolution algorithm for continuous optimization and classification problems

Neural Computing and Applications - Differential evolution (DE) is recognized as a simplistic yet robust evolutionary algorithm: it has been utilized to tackle different challenging optimization...     

An intelligent information sharing strategy within a swarm for unconstrained and constrained optimization problems

 In this paper we present a new multilevel information sharing strategy within a swarm to handle single objective, constrained and unconstrained optimization problems. A swarm is a collection of individuals having a common goal to reach the best value (minimum or maximum) of a function. Among the individuals in a swarm, there are some better performers (leaders) those that set the direction of search for the rest of the individuals. An individual that is not in the better performer list (BPL) improves its performance by deriving information from its closest neighbor in BPL. In an unconstrained problem, the objective values are the performance measures used to generate the BPL while a multilevel Pareto ranking scheme is implemented to generate the BPL for constrained problems. The information sharing strategy also ensures that all the individuals in the swarm are unique as in a real swarm, where at a given time instant two individuals cannot share the same location. The uniqueness among the individuals result in a set of near optimal individuals at the final stage that is useful for sensitivity analysis. The benefits of the information sharing strategy within a swarm are illustrated by solving two unconstrained problems with multiple equal and unequal optimum, a constrained optimization problem dealing with a test function and a well studied welded beam design problem.     

一种基于引导策略的自适应粒子群算法

为解决粒子群算法前期搜索“盲目”,后期搜索速度慢且易陷入局部极值的问题,对算法中粒子更新方式和惯性权重进行了改进,提出了一种基于引导策略的自适应粒子群算法。该算法在种群中引入4种粒子,即主体粒子、双中心粒子、协同粒子和混沌粒子对粒子位置更新进行引导,克服算法的随机性,从而提高搜索效率;为进一步克服粒子群优化算法进化后期易陷入早熟收敛的缺点,引入聚焦距离变化率的概念,通过聚焦距离变化率的大小动态调整惯性权重,以提高算法的收敛速度和精度,两者结合极大地提高了搜索到全局最优解的有效性。对4个标准测试函数进行仿真,实验结果表明IPSO算法在收敛速度、收敛精度以及成功率上都明显优于LDWPSO和WPSO算法。     

Game-theoretic differential evolution for multiobjective optimization of green sand mould system

Many large-scale engineering problems often take a multiobjective form. Thus, several solution options to the MO problem are usually ascertained by the engineer. Then the most desirable options with respect to the industrial circumstances and online operating conditions are selected. In this work, the trade-off solutions are obtained using the weighted-sum approach. In addition the standard metaheuristic, differential evolution is improved using concepts from evolutionary game theory. These techniques are then applied to solve the industrial green sand mould development problem. The solutions are then examined and discussed from various standpoints.     

A new hybrid mutation operator for multiobjective optimization with differential evolution

Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance compared with the previous state of the art.     

Constrained differential evolution with multiobjective sorting mutation operators for constrained optimization

Differential evolution (DE) is a simple and powerful evolutionary algorithm for global optimization. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems (COPs). In existing CDEs, the parents are randomly selected from the current population to produce trial vectors. However, individuals with fitness and diversity information should have more chances to be selected. This study proposes a new CDE framework that uses nondominated sorting mutation operator based on fitness and diversity information, named MS-CDE. In MS-CDE, firstly, the fitness of each individual in the population is calculated according to the current population situation. Secondly, individuals in the current population are ranked according to their fitness and diversity contribution. Lastly, parents in the mutation operators are selected in proportion to their rankings based on fitness and diversity. Thus, promising individuals with better fitness and diversity are more likely to be selected as parents. The MS-CDE framework can be applied to most CDE variants. In this study, the framework is applied to two popular representative CDE variants, (μ + λ)-CDE and ECHT-DE. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms.     

An efficient multiobjective differential evolution algorithm for engineering design

Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints, a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions with good coverage and convergence to true Pareto-optimal fronts.     

一种求解旅行商问题的进化多目标优化方法

为了克服传统小生境(Niching)策略中的参数设置难题,提出一种求解旅行商问题的进化多目标优化方法:建立以路径长度和平均离群距离为目标的双目标优化模型,利用改进非支配排序遗传算法(NSGAII)进行求解.为了在全局探索能力与局部开发能力之间保持平衡,算法中采用一种使路径长度相同的可行解互不占优的评价策略,并通过一种新的离散差分进化算子和简化的2-Opt策略生成候选解.与已有算法的数值试验结果比较表明,求解旅行商问题(TSP)的改进非支配排序遗传算法(NSGAII-TSP)能够更好地保持种群多样性,从而克服局部最优解的吸引并具有更鲁棒的全局探索能力.通过借助特殊的个体评价策略,所提出的算法可以更好地进行全局优化,甚至同时得到多个全局最优解.