Deriving operating policies for multi-objective reservoir systems: Application of Self-Learning Genetic Algorithm

Optimal multi-reservoir operation is a multi-objective problem in nature and some of its objectives are nonlinear, non-convex and multi-modal functions. There are a few areas of application of mathematical optimization models with a richer or more diverse history than in reservoir systems optimization. However, actual implementations remain limited or have not been sustained.Genetic Algorithms (GAs) are probabilistic search algorithms that are capable of solving a variety of complex multi-objective optimization problems, which may include non-linear, non-convex and multi-modal functions. GA is a population based global search method that can escape from local optima traps and find the global optima. However GAs have some drawbacks such as inaccuracy of the intensification process near the optimal set.In this paper, a new model called Self-Learning Genetic Algorithm (SLGA) is presented, which is an improved version of the SOM-Based Multi-Objective GA (SBMOGA) presented by Hakimi-Asiabar et al. (2009) [45]. The proposed model is used to derive optimal operating policies for a three-objective multi-reservoir system. SLGA is a new hybrid algorithm which uses Self-Organizing Map (SOM) and Variable Neighborhood Search (VNS) algorithms to add a memory to the GA and improve its local search accuracy. SOM is a neural network which is capable of learning and can improve the efficiency of data processing algorithms. The VNS algorithm can enhance the local search efficiency in the Evolutionary Algorithms (EAs).To evaluate the applicability and efficiency of the proposed methodology, it is used for developing optimal operating policies for the Karoon-Dez multi-reservoir system, which includes one-fifth of Iran's surface water resources. The objective functions of the problem are supplying water demands, generating hydropower energy and controlling water quality in downstream river.     

Learning the Search Range for Evolutionary Optimization in Dynamic Environments

Conventional evolutionary algorithms operate in a fixed search space with limiting parameter range, which is often predefined via a priori knowledge or trial and error in order to ‘guess’ a suitable region comprising the global optimal solution. This requirement is hard, if not impossible, to fulfil in many real-world optimization problems since there is often no clue of where the desired solutions are located in these problems. Thus, this paper proposes an inductive–deductive learning approach for single- and multi-objective evolutionary optimization. The method is capable of directing evolution towards more promising search regions even if these regions are outside the initial predefined space. For problems where the global optimum is included in the initial search space, it is capable of shrinking the search space dynamically for better resolution in genetic representation to facilitate the evolutionary search towards more accurate optimal solutions. Validation results based on benchmark optimization problems show that the proposed inductive–deductive learning is capable of handling different fitness landscapes as well as distributing nondominated solutions uniformly along the final trade-offs in multi-objective optimization, even if there exist many local optima in a high-dimensional search space or the global optimum is outside the predefined search region. Received 15 January 2001 / Revised 8 June 2001 / Accepted in revised form 24 July 2001     

一种函数优化问题的混合遗传算法

将传统的局部搜索算法和遗传算法相结合,可以较好地解决遗传算法在达到全局最优解前收敛慢的问题.文章给出一种结合可变多面体法和正交遗传算法的混合算法.实验表明,它通过对问题的解空间交替进行全局和局部搜索,能更有效地求解函数优化问题.     

Self-adjusting the intensity of assortative mating in genetic algorithms

Mate selection plays a crucial role in both natural and artificial systems. While traditional Evolutionary Algorithms (EA) usually engage in random mating strategies, that is, mating chance is independent of genotypic or phenotypic distance between individuals, in natural systems non-random mating is common, which means that somehow this mechanism has been favored during the evolutionary process. In non-random mating, the individuals mate according to their parenthood or likeness. Previous studies indicate that negative assortative mating (AM)—also known as dissortative mating—, which is a specific type of non-random mating, may improve EAs performance by maintaining the genetic diversity of the population at a higher level during the search process. In this paper we present the Variable Dissortative Mating Genetic Algorithm (VDMGA). The algorithm holds a mechanism that varies the GA’s mating restrictions during the run by means of simple rule based on the number of chromosomes created in each generation and indirectly influenced by the genetic diversity of the population. We compare VDMGA not only with traditional Genetic Algorithms (GA) but also with two preceding non-random mating EAs: the CHC algorithm and the negative Assortative Mating Genetic Algorithm (nAMGA). We intend to study the effects of the different methods in the performance of GAs and verify the reliability of the proposed algorithm when facing an heterogeneous set of landscapes. In addition, we include the positive Assortative Mating Genetic Algorithm (pAMGA) in the experiments in order test both negative and positive AM mechanisms, and try to understand if and when negative AM (or DM) speeds up the search process or enables the GAs to escape local optima traps. For these purposes, an extensive set of optimization test problems was chosen to cover a variety of search landscapes with different characteristics. Our results confirm that negative AM is effective in leading EAs out of local optima traps, and show that the proposed VDMGA is at least as efficient as nAMGA when applied to the range of our problems, being more efficient in very hard functions were traditional GAs usually fail to escape local optima. Also, scalability tests have been made that show VDMGA ability to decrease optimal population size, thus reducing the amount of evaluations needed to attain global optima. We like to stress that only two parameters need to be hand-tuned in VDMGA, thus reducing the tuning effort present in traditional GAs and nAMGA.     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

基于自适应Memetic算法的多目标复杂网络社区检测

针对提高复杂网络社区检测准确度问题, 提出了一种自适应Memetic算法的多目标社区检测算法。在全局搜索中利用Logistic函数来设置与全局优化相应的交叉概率和变异概率,并将多目标优化问题转化成同时最小优化Kernel K-Means和Ratio Cut这两个目标函数;在局部搜索中利用权重将两个目标函数合并成一个局部优化目标,并采用爬山搜索来寻找个体最优。在虚拟和真实网络实验平台下,与五个基于遗传算法的方法以及Fast Modularity算法相比,结果表明算法能有效提高社区检测准确度,具有更好的寻优效果。     

A hybrid variable neighborhood search for solving the hybrid flow shop scheduling problem

This paper proposes a hybrid variable neighborhood search (HVNS) algorithm that combines the chemical-reaction optimization (CRO) and the estimation of distribution (EDA), for solving the hybrid flow shop (HFS) scheduling problems. The objective is to minimize the maximum completion time. In the proposed algorithm, a well-designed decoding mechanism is presented to schedule jobs with more flexibility. Meanwhile, considering the problem structure, eight neighborhood structures are developed. A kinetic energy sensitive neighborhood change approach is proposed to extract global information and avoid being stuck at the local optima. In addition, contrary to the fixed neighborhood set in traditional VNS, a dynamic neighborhood set update mechanism is utilized to exploit the potential search space. Finally, for the population of local optima solutions, an effective EDA-based global search approach is investigated to direct the search process to promising regions. The proposed algorithm is tested on sets of well-known benchmark instances. Through the analysis of experimental results, the high performance of the proposed HVNS algorithm is shown in comparison with four efficient algorithms from the literature.     

一种混合自适应多目标Memetic算法

Memetic算法是求解多目标优化问题最有效的方法之一，融合了局部搜索和进化计算，具有较高的全局搜索能力．混合自适应多目标Memetic算法（HAMA）用基于模拟退火的加权法进行局部搜索，采用Pareto法实现交叉和变异，通过扰动增强算法的exploration能力，且进化过程可根据改善率自适应调整，以提高搜索效率并改善算法的鲁棒性．算例测试说明HAMA能产生更接近Pareto前沿且多样性更好的近似集．     

基于人类社交行为的动态多目标优化

为了提高多目标微粒群优化算法处理多目标优化问题的性能,降低计算复杂度,改善算法的收敛性,提出了一种基于人类社交行为的多目标动态微粒群优化算法。考虑到粒子寻优过程受到环境中精英粒子与平庸粒子的影响,分别对自身产生推力与阻力作用,并引入局部跳出策略,使算法具有很强的全局搜索能力和较好的鲁棒性能。通过典型的多目标优化函数对算法进行了测试验证,结果表明提出的多目标算法具有较快的收敛速度和较强的跳出局部最优能力,性能优越,可供许多领域优化问题求解借鉴。     

Adaptive directed mutation for real-coded genetic algorithms

Adaptive directed mutation (ADM) operator, a novel, simple, and efficient real-coded genetic algorithm (RCGA) is proposed and then employed to solve complex function optimization problems. The suggested ADM operator enhances the abilities of GAs in searching global optima as well as in speeding convergence by integrating the local directional search strategy and the adaptive random search strategies. Using 41 benchmark global optimization test functions, the performance of the new algorithm is compared with five conventional mutation operators and then with six genetic algorithms (GAs) reported in literature. Results indicate that the proposed ADM-RCGA is fast, accurate, and reliable, and outperforms all the other GAs considered in the present study.     

基于跳跃辅助工作策略的混流装配线排产优化

为了使混流装配线高效运作, 研究了一类基于跳跃辅助工作策略的混流装配线排产优化问题. 以同时优化空闲费用和辅助工作费用为目标, 建立了一类基于跳跃辅助工作策略的混流装配线排产优化模型, 给出了执行跳跃辅助工作策略的一个必要条件和辅助工作费用的一个下界. 然后证明了该类优化问题是强NP难的, 由于该问题的强NP难性, 提出了一种嵌入式变邻域类电磁机制(Variable neighborhood search-electromagnetism-like mechanism, VNS-EM)混合算法求解该模型, 为了避免算法陷入局部最优, 在类电磁机制算法的每次迭代过程中嵌入改进的变邻域搜索算法, 利用变邻域搜索算法较好的局部搜索能力对最好个体的邻域进行精细搜索, 从而提高了解的质量. 仿真结果验证了该方法的可行性和有效性.     

Truss optimization on shape and sizing with frequency constraints based on parallel genetic algorithm

Truss shape and sizing optimization under frequency constraints is extremely useful when improving the dynamic performance of structures. However, coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to slow convergence or even divergence. Because shape and sizing variables coupled increase the number of design variables and the changes of shape and sizing variables are of widely different orders of magnitude. Otherwise, multiple frequency constraints often cause difficult dynamic sensitivity analysis. Thus optimal criteria and mathematical programming methods have considerable limitations on solving the problems because of needing complex dynamic sensitivity analysis and being easily trapped into the local optima. Genetic Algorithms (GAs) show great potentials to solve the truss shape and sizing optimization problems. Since GAs adopt global probabilistic population search techniques and require no gradient information. The improved genetic algorithms can effectively increase the solution quality. However, the serial GA is computationally expensive and is limited on gaining higher quality solutions. To solve the truss shape and sizing optimization problems with frequency constraints more effectively and efficiently, a Niche Hybrid Parallel Genetic Algorithm (NHPGA) is proposed to significantly reduce the computational cost and to further improve solution quality. The NHPGA is to blend the advantages of parallel computing, simplex search and genetic algorithm with niche technique. Several typical truss optimization examples demonstrate that NHPGA can significantly reduce computing time and attain higher quality solutions. It also suggests that the NHPGA provide a potential algorithm architecture, which effectively combines the robust and global search characteristics of genetic algorithm, strong exploitation ability of simplex search and computational speedup property of parallel computing.     

A HYBRID METAHEURISTIC FOR THE SINGLE-MACHINE TOTAL WEIGHTED TARDINESS PROBLEM

This article presents a new hybrid algorithm for combinatorial optimization that combines differential evolution (DE) with variable neighborhood search (VNS). DE (a population heuristic for optimization over continuous search spaces) is used as global optimizer for solution evolution guiding the search toward the optimal regions of the search space; VNS (a random local search heuristic based on the systematic change of neighborhood) is used as a local optimizer performing a sequence of local changes on individual DE solutions until a local optimum is found. The effectiveness of a DE-VNS approach is demonstrated on the solution of the single-machine total weighted tardiness scheduling problem. The concepts of Lamarckian and Baldwinian learning are also investigated and discussed. Experiments on known benchmark data sets show that DE-VNS with Lamarckian learning can produce high-quality schedules in a rather short computation time. DE-VNS uses a self-adapted mechanism for tuning the required control parameters, a critical feature rendering it applicable to real-life scheduling problems.     

一种求解多目标组合优化的遗传局部搜索算法

为改善遗传算法求解多目标组合优化问题的搜索效率,提出一种新的遗传局部搜索算法.算法采取非劣解并行局部搜索策略以及基于分散度的精英选择策略,并采用基于NSGA-Ⅱ的适应度赋值方式和二元赌轮选择操作,以提高算法收敛性,保持群体多样性.实验结果表明,新算法能够产生数量较多分布较广的近似Pareto最优解.     

Empirical investigation of the benefits of partial Lamarckianism

Genetic algorithms (GAs) are very efficient at exploring the entire search space; however, they are relatively poor at finding the precise local optimal solution in the region in which the algorithm converges. Hybrid GAs are the combination of improvement procedures, which are good at finding local optima, and GAs. There are two basic strategies for using hybrid GAs. In the first, Lamarckian learning, the genetic representation is updated to match the solution found by the improvement procedure. In the second, Baldwinian learning, improvement procedures are used to change the fitness landscape, but the solution that is found is not encoded back into the genetic string. This paper examines the issue of using partial Lamarckianism (i.e., the updating of the genetic representation for only a percentage of the individuals), as compared to pure Lamarckian and pure Baldwinian learning in hybrid GAs. Multiple instances of five bounded nonlinear problems, the location-allocation problem, and the cell formation problem were used as test problems in an empirical investigation. Neither a pure Lamarckian nor a pure Baldwinian search strategy was found to consistently lead to quicker convergence of the GA to the best known solution for the series of test problems. Based on a minimax criterion (i.e., minimizing the worst case performance across all test problem instances), the 20% and 40% partial Lamarckianism search strategies yielded the best mixture of solution quality and computational efficiency.     

一种新的并行文化微粒群优化算法

为了避免微粒群优化算法在解决复杂优化问题时陷入局部最优,提高算法种群的多样性。将微粒群优化算法纳入文化算法框架,提出了一种新的基于文化算法框架的并行微粒群优化算法。在文化算法框架中,由微粒群组成的群体空间和信念空间各自独立并行演化,并相互影响,有效地提高了种群的多样性,降低了陷入局部极值的可能性。通过对不同测试函数的仿真实验表明,新提出的并行文化微粒群优化算法比标准微粒群优化算法更容易找到全局最优解,提高了微粒群优化算法的全局寻优能力。     

An improved particle swarm optimization with decline disturbance index (DDPSO) for multi-objective job-shop scheduling problem

As same with many evolutional algorithms, performance of simple PSO depends on its parameters, and it often suffers the problem of being trapped in local optima so as to cause premature convergence. In this paper, an improved particle swarm optimization with decline disturbance index (DDPSO), is proposed to improve the ability of particles to explore the global and local optimization solutions, and to reduce the probability of being trapped into the local optima. The correctness of the modification, which incorporated a decline disturbance index, was proved. The key question why the proposed method can reduce the probability of being trapped in local optima was answered. The modification improves the ability of particles to explore the global and local optimization solutions, and reduces the probability of being trapped into the local optima. Theoretical analysis, which is based on stochastic processes, proves that the trajectory of particle is a Markov processes and DDPSO algorithm converges to the global optimal solution with mean square merit. After the exploration based on DDPSO, neighborhood search strategy is used in a local search and an adaptive meta-Lamarckian strategy is employed to dynamically decide which neighborhood should be selected to stress exploitation in each generation. The multi-objective combination problems with DDPSO for finding the pareto front was presented under certain performance index. Simulation results and comparisons with typical algorithms show the effectiveness and robustness of the proposed DDPSO.     

A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.     

A genetic algorithm with disruptive selection

Genetic algorithms are a class of adaptive search techniques based on the principles of population genetics. The metaphor underlying genetic algorithms is that of natural evolution. Applying the “survival-of-the-fittest” principle, traditional genetic algorithms allocate more trials to above-average schemata. However, increasing the sampling rate of schemata that are above average does not guarantee convergence to a global optimum; the global optimum could be a relatively isolated peak or located in schemata that have large variance in performance. In this paper we propose a novel selection method, disruptive selection. This method adopts a nonmonotonic fitness function that is quite different from traditional monotonic fitness functions. Unlike traditional genetic algorithms, this method favors both superior and inferior individuals. Experimental results show that GAs using the proposed method easily find the optimal solution of a function that is hard for traditional GAs to optimize. We also present convergence analysis to estimate the occurrence ratio of the optima of a deceptive function after a certain number of generations of a genetic algorithm. Experimental results show that GAs using disruptive selection in some occasions find the optima more quickly and reliably than GAs using directional selection. These results suggest that disruptive selection can be useful in solving problems that have large variance within schemata and problems that are GA-deceptive     

Genetic learning automata for function optimization

Stochastic learning automata and genetic algorithms (GAs) have previously been shown to have valuable global optimization properties. Learning automata have, however, been criticized for having a relatively slow rate of convergence. In this paper, these two techniques are combined to provide an increase in the rate of convergence for the learning automata and also to improve the chances of escaping local optima. The technique separates the genotype and phenotype properties of the GA and has the advantage that the degree of convergence can be quickly ascertained. It also provides the GA with a stopping rule. If the technique is applied to real-valued function optimization problems, then bounds on the range of the values within which the global optima is expected can be determined throughout the search process. The technique is demonstrated through a number of bit-based and real-valued function optimization examples.