Multi-objective differential evolution with performance-metric-based self-adaptive mutation operator for chemical and biochemical dynamic optimization problems

Each mutation operator of differential evolution (DE) algorithm is generally suitable for certain specific types of multi-objective optimization problems (MOPs) or particular stages of the evolution. To automatically select an appropriate mutation operator for solving MOPs in different phases of the evolution, a multi-objective differential evolution with performance-metric-based self-adaptive mutation operator (MODE-PMSMO) is proposed in this study. In MODE-PMSMO, a modified inverted generational distance (IGD) is utilized to evaluate the performance of each mutation operator and guide the evolution of mutation operators. The proposed MODE-PMSMO is then compared with seven multi-objective evolutionary algorithms (MOEAs) on five bi-objective and five tri-objective optimization problems. Generally, MODE-PMSMO exhibits the best average performance among all compared algorithms on ten MOPs. Additionally, MODE-PMSMO is employed to solve four typical multi-objective dynamic optimization problems in chemical and biochemical processes. Experimental results indicate that MODE-PMSMO is suitable for solving these actual problems and can provide a set of nondominated solutions for references of decision makers.     

Global replacement-based differential evolution with neighbor-based memory for dynamic optimization

Dynamic optimization problems challenge the evolutionary algorithms, owing to the diversity loss or the low search efficiency of the algorithms, especially when the problems change frequently. This paper presents a novel differential evolution algorithm to address the dynamic optimization problems. Unlike the most used “DE/rand/1” mutation operator, in this paper, the “DE/best/1” mutation is employed to generate a mutant individual. In order to enhance the search efficiency of differential evolution, the classical differential evolution algorithm is modified by a novel replacement operator, in which the worst individual in the whole population is replaced by the newly generated trial vector as a “steady-state” manner. During optimizing, some newly generated solutions are stored into a memory set, in which these stored solutions are located around the current best solution. When the environmental change is detected, the stored solutions are expected to guide the reinitialized solutions to track the new location of global optimum as soon as possible. The performance of the proposed algorithm is compared with six state-of-the-art dynamic evolutionary algorithms over some benchmark problems. The experimental results show that the proposed algorithm clearly outperforms the competitors.     

Multiobjective evolutionary algorithm based on multimethod with dynamic resources allocation

In the last two decades, multiobjective optimization has become main stream and various multiobjective evolutionary algorithms (MOEAs) have been suggested in the field of evolutionary computing (EC) for solving hard combinatorial and continuous multiobjective optimization problems. Most MOEAs employ single evolutionary operators such as crossover, mutation and selection for population evolution. In this paper, we suggest a multiobjective evolutionary algorithm based on multimethods (MMTD) with dynamic resource allocation for coping with continuous multi-objective optimization problems (MOPs). The suggested algorithm employs two well known population based stochastic algorithms namely MOEA/D and NSGA-II as constituent algorithms for population evolution with a dynamic resource allocation scheme. We have examined the performance of the proposed MMTD on two different MOPs test suites: the widely used ZDT problems and the recently formulated test instances for the special session on MOEAs competition of the 2009 IEEE congress on evolutionary computation (CEC’09). Experimental results obtained by the suggested MMTD are more promising than those of some state-of-the-art MOEAs in terms of the inverted generational distance (IGD)-metric on most test problems.     

A gene-level hybrid search framework for multiobjective evolutionary optimization

This paper proposes a general framework of gene-level hybrid search (GLHS) for multiobjective evolutionary optimization. Regarding the existing hybrid search methods, most of them usually combine different search strategies and only select one search strategy to generate child solution. This kind of hybrid search is called as a chromosome-level approach in this paper. However, in GLHS, every gene bit of the child solution can be produced using different search strategies and such operation provides the enhanced exploration capability. As an example, two different DE mutation strategies are used in this paper as the variance candidate pool to implement the proposed GLHS framework, named GLHS-DE. To validate the effectiveness of GLHS-DE, it is embedded into one state-of-the-art algorithmic framework of MOEA/D, and is compared to a basic DE operator and two competitive hybrid search operators, i.e., FRRMAB and CDE, on 80 test problems with two to fifteen objectives. The experimental results show GLHS-DE obtains a superior performance over DE, FRRMAB and CDE on about 70 out of 80 test problems, indicating the promising application of our approach for multiobjective evolutionary optimization.

     

Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II

Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also proposes a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes.     

Multiobjective differential evolution using homeostasis based mutation for application in software cost estimation

The problem in software cost estimation revolves around accuracy. To improve the accuracy, heuristic/meta-heuristic algorithms have been known to yield better results when it is applied in the domain of software cost estimation. For the sake of accuracy in results, we are still modifying these algorithms. Here we have proposed a new meta-heuristic algorithm based on Differential Evolution (DE) by Homeostasis mutation operator. Software development requires high prediction and low Root Mean Squared Error (RMSE) and mean magnitude relative error(MMRE). The problem in software cost estimation relates to accurate prediction and minimization of RMSE and MMRE, which are used to solve multiobjective optimization. Many versions of DE were proposed, however multi-objective versions where the concept of Pareto optimality is used, are most popular. Pareto-Based Differential Evolution (PBDE) is one of them. Although the performance of this algorithm is very good, its convergence rate can be further improved by minimizing the time complexity of nondominated sorting, and by improving the diversity of solutions. This has been implemented by using efficient nondominated algorithm whose time complexity is better than the previous one and a new mutation scheme is implemented in DE which can provide more diversity among solutions. The proposed variant multiplies the Homeostasis value with one more vector, named the Homeostasis mutation vector, in the existing mutation vector to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escape the situation of stagnation. The performance of the proposed algorithm is evaluated on twelve benchmark test functions (bi-objective and tri-objective) on the Pareto-optimal front. The performance of the proposed algorithm is compared with other state-of-the-art algorithms on five multi-objective evolutionary algorithms (MOEAs). The result verifies that our proposed Homeostasis mutation strategy performs better than other state-of-the-art algorithms. Finally, application of MODE-HBM is applied to solve in terms of Pareto front, representing the trade-off between development RMSE, MMRE, and prediction for COCOMO model.     

改进差分进化策略在多峰值函数优化中的应用

针对差分演化算法与进化策略算法中所存在的不足,将模拟退火算子引入到差分演化算法的变异操作中,这样有助于在进化前期进行全局搜索,后期进行局部搜索;在标准进化策略的基础上,加入差分变异操作,提出了一种新的差分进化策略双重变异算法。通过测试算例可看出,该方法在多峰值函数优化问题中,具有求解精度较高,收敛速度较快等特点。     

一种基于云模型的多目标进化算法

在多目标进化算法的基础上,提出了一种基于云模型的多目标进化算法(CMOEA).算法设计了一种新的变异算子来自适应地调整变异概率,使得算法具有良好的局部搜索能力.算法采用小生境技术,其半径按X条件云发生器非线性动态地调整以便于保持解的多样性,同时动态计算个体的拥挤距离并采用云模型参数来估计个体的拥挤度,逐个删除种群中超出的非劣解以保持解的分布性.将该算法用于多目标0/1背包问题来测试CMOEA的性能,并与目前最流行且有效的多目标进化算法NSGA-II及SPEA2进行了比较.结果表明,CMOEA具有良好的搜索性能,并能很好地维持种群的多样性,快速收敛到Pareto前沿,所获得的Pareto最优解集具有更好的收敛性与分布性.     

基于模拟退火的混合差分进化算法及其在联合补货-配送集成优化中的应用

针对差分进化 (Differential evolution, DE)算法搜索效率较低和容易陷入局部最优的缺点,设计了基于SA的混合差分进化算法(SA-based Hybrid DE, SAHDE),以提高DE算法的全局寻优能力。该算法采用自适应变异算子和交叉算子,并结合模拟退火(Simulated Annealing, SA)算法的Metropolis 准则。首先通过标准测试函数对改进的SAHDE进行性能测试,证明了该算法比DE、自适应混合DE (Adaptive Hybrid DE, AHDE)和遗传算法(Genetic Algorithm, GA)更有效。进而将该算法运用到联合补货-配送集成优化(典型NP-hard)问题的求解中,通过大规模的算例分析,证实SAHDE在解决联合补货-配送优化问题比DE、AHDE和GA更有效。     

Adaptive direction information in differential evolution for numerical optimization

Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. It has been successfully used in various scientific and engineering fields. In most of the DE algorithms, the neighborhood and direction information are not fully and simultaneously exploited to guide the search. Most recently, to make full use of these information, a DE framework with neighborhood and direction information (NDi-DE) was proposed. It was experimentally demonstrated that NDi-DE was effective for most of the DE algorithms. However, the performance of NDi-DE heavily depends on the selection of direction information. To alleviate this drawback and improve the performance of NDi-DE, the adaptive operator selection (AOS) mechanism is introduced into NDi-DE to adaptively select the direction information for the specific DE mutation strategy. Therefore, a new DE framework, adaptive direction information based NDi-DE (aNDi-DE), is proposed in this study. With AOS, the good balance between exploration and exploitation of aNDi-DE can be dynamically achieved. In order to evaluate the effectiveness of aNDi-DE, the proposed framework is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results show that aNDi-DE is able to adaptively select the most suitable type of direction information for the specific DE mutation strategy during the evolutionary process. The efficiency and robustness of aNDi-DE are also confirmed by comparing with NDi-DE.     

改进的PSO混合算法

为了提高粒子群算法的寻优速度和寻优精度,提出一种改进的PSO混合算法。在差分进化(DE)算法中引入了动态比例因子,在PSO算法中引入DE算法的变异、交叉操作,重新构造PSO算法的粒子位置更新公式。选取了4个基准函数进行测试,并与其他PSO混合算法作了比较。仿真结果表明该方法是有效的。     

Two hybrid differential evolution algorithms for engineering design optimization

This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb's parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters.     

基于分解和多策略变异的多目标差分进化算法*

差分进化是一种有效的优化技术,已成功用于多目标优化问题。但也存在Pareto最优集合的收敛慢和多样性差等问题。针对上述不足,本文提出了一种基于分解和多策略变异的多目标差分进化算法(MODE/DMSM)。该算法利用基于分解的方法将多目标优化问题分解为多个单目标优化问题;通过高效的非支配排序方法选择具有良好收敛性和多样性的解来指导差分进化过程;采用了多策略变异方法来平衡进化过程中收敛性和多样性。在ZDT和DTLZ的10个测试函数上的仿真结果表明,本文算法在Parato最优集合的收敛性和多样性优于其他六种代表性多目标优化算法。     

混合整数非线性规划问题的改进差分进化算法*

提出一种改进差分进化算法求解混合整数非线性规划问题。该算法利用同态映射方法,解决差分进化算法无法直接处理整数决策变量问题;提出改进的自适应交替变异算子,提高算法的搜索性能;提出一种自适应保留不可行解的方法处理约束条件,并对差分进化算法的选择算子进行改进,提出一种直接处理约束条件的新选择算子。六个常用的混合整数非线性规划问题的实验结果表明了该方法的有效性和适用性。     

基于二维可变邻域编码方式的混合遗传算法

针对现有混合遗传算法无法兼顾有效性及高效性的问题,提出一种基于二维可变邻域编码方式的新型混合遗传算法(VNHGA)。首先提出了一种将个体“基因型”与“邻域型”分开编码、同步遗传的新型编码方式,以替换传统二进制编码方式;然后设计了一种稳定变异算子,以替换传统变异算子来提高效率。通过多维函数最小值问题对VNHGA进行测试:首先验证采用所提二维可变邻域编码方式后,使用“鲍德温(Baldwin)效应”作为将局部搜索嵌入传统遗传算法策略时,相对于基于“拉马克(Lamarckian)进化”的嵌入策略,仍然具有采用传统二进制编码方式时的特性,即具有良好有效性但高效性不足;其次验证引入稳定变异算子后,算法在保持其有效性的同时提升了效率,运行时间缩短到之前的50%左右;最后,与两种改进混合遗传算法进行比较,验证所提算法优势。结果表明VNHGA兼具有效性与高效性特点,可用于解决最优化问题。     

求解多目标问题的Memetic免疫优化算法

将基于Pareto支配关系的局部下山算子和差分算子引入免疫多目标优化算法之中,提出了一种求解多目标问题的Memetic免疫优化算法(Memetic immune algorithm for multiobjective optimization,简称MIAMO).该算法利用种群中抗体在决策空间上的位置关系设计了两种有效的启发式局部搜索策略,提高了免疫多目标优化算法的求解效率.仿真实验结果表明,MIAMO与其他4种有效的多目标优化算法相比,不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且算法的收敛速度与免疫多目标优化算法相比明显加快.     

A directional mutation operator for differential evolution algorithms

Differential evolution (DE) is widely studied in the past decade. In its mutation operator, the random variations are derived from the difference of two randomly selected different individuals. Difference vector plays an important role in evolution. It is observed that the best fitness found so far by DE cannot be improved in every generation. In this article, a directional mutation operator is proposed. It attempts to recognize good variation directions and increase the number of generations having fitness improvement. The idea is to construct a pool of difference vectors calculated when fitness is improved at a generation. The difference vector pool will guide the mutation search in the next generation once only. The directional mutation operator can be applied into any DE mutation strategy. The purpose is to speed up the convergence of DE and improve its performance. The proposed method is evaluated experimentally on CEC 2005 test set with dimension 30 and on CEC 2008 test set with dimensions 100 and 1000. It is demonstrated that the proposed method can result in a larger number of generations having fitness improvement than classic DE. It is combined with eleven DE algorithms as examples of how to combine with other algorithms. After its incorporation, the performance of most of these DE algorithms is significantly improved. Moreover, simulation results show that the directional mutation operator is helpful for balancing the exploration and exploitation capacity of the tested DE algorithms. Furthermore, the directional mutation operator modifications can save computational time compared to the original algorithms. The proposed approach is compared with the proximity based mutation operator as both are claimed to be applicable to any DE mutation strategy. The directional mutation operator is shown to be better than the proximity based mutation operator on the five variants in the DE family. Finally, the applications of two real world engineering optimization problems verify the usefulness of the proposed method.     

A hybrid evolutionary multiobjective optimization strategy for the dynamic power supply problem in magnesia grain manufacturing

The supply trajectory of electric power for submerged arc magnesia furnace determines the yields and grade of magnesia grain during the manufacture process. As the two production targets (i.e., the yields and the grade of magnesia grain) are conflicting and the process is subject to changing conditions, the supply of electric power needs to be dynamically optimized to track the moving Pareto optimal set with time. A hybrid evolutionary multiobjective optimization strategy is proposed to address the dynamic multiobjective optimization problem. The hybrid strategy is based on two techniques. The first one uses case-based reasoning to immediately generate good solutions to adjust the power supply once the environment changes, and then apply a multiobjective evolutionary algorithm to accurately solve the problem. The second one is to learn the case solutions to guide and promote the search of the evolutionary algorithm, and the best solutions found by the evolutionary algorithm can be used to update the case library to improve the accuracy of case-based reasoning in the following process. Due to the effectiveness of mutual promotion, the hybrid strategy can continuously adapt and search in dynamic environments. Two prominent multiobjective evolutionary algorithms are integrated into the hybrid strategy to solve the dynamic multiobjective power supply optimization problem. The results from a series of experiments show that the proposed hybrid algorithms perform better than their component multiobjective evolutionary algorithms for the tested problems.     

Biogeography-based optimization with improved migration operator and self-adaptive clear duplicate operator

Biogeography-based optimization (BBO) is a new emerging population-based algorithm that has been shown to be competitive with other evolutionary algorithms. However, there are some insufficiencies in solving complex problems, such as poor population diversity and slow convergence speed in the later stage. To overcome these shortcomings, we propose an improved BBO (IBBO) algorithm integrating a new improved migration operator, Gaussian mutation operator, and self-adaptive clear duplicate operator. The improved migration operator simultaneously adopts more information from other habitats, maintains population diversity, and preserves exploitation ability. The self-adaptive clear duplicate operator can clear duplicate or almost identical habitats, while also preserving population diversity through a self-adaptation threshold within the evolution process. Simulation results and comparisons from the experimental tests conducted on 23 benchmark functions show that IBBO achieves excellent performance in solving complex problems compared with other variants of the BBO algorithm and other evolutionary algorithms. The performance of the improved migration operator is also discussed.     

Hybrid adaptive differential evolution for mobile robot localization

This paper introduces a new evolutionary optimization algorithm named hybrid adaptive differential evolution (HADE) and applies it to the mobile robot localization problem. The behaviour of evolutionary algorithms is highly dependent on the parameter selection. This algorithm utilizes an adaptive method to tune the mutation parameter to enhance the rate of convergence and eliminate the need for manual tuning. A hybrid method for mutation is also introduced to give more diversity to the population. This method which constantly switches between two mutation schemes guarantees a sufficient level of diversity to avoid local optima. We use a well-known test set in continuous domain to evaluate HADE’s performance against the standard version of differential evolution (DE) and a self-adaptive version of the algorithm. The results show that HADE outperforms DE and self-adaptive DE in three of four benchmarks. Moreover, we investigate the performance of HADE in the well-known localization problem of mobile robots. Results show that HADE is capable of estimating the robot’s pose accurately with a decreased number of individuals needed for convergence compared with DE and particle swarm optimization methods. Comparative study exposes HADE algorithm as a competitive method for mobile robot localization.