Toward routine billion‐variable optimization using genetic algorithms

The push for better understanding and design of complex systems requires the solution of challenging optimization problems with large numbers of decision variables. This note presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of a genetic algorithm (GA). The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The genetic algorithm used—the compact GA—is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billion‐variable problems across the landscape of complexity science. © 2007 Wiley Periodicals, Inc. Complexity 12: 27–29, 2007     

Stock timing using genetic algorithms

In this paper, a genetic algorithm to search a set of technical trading rules which gives buying and selling advices about individual stocks is proposed. This approach is tested out of a sample of 24 French stocks among the most important stocks traded on the French market. We show that in most cases, the method outperforms a simple buy and hold strategy. However, we also illustrate the fact that the near‐optimal set of rules varies through time and across stocks. Copyright © 2002 John Wiley & Sons, Ltd.     

Improving crossover operator for real-coded genetic algorithms using virtual parents

The crossover operator is the most innovative and relevant operator in real-coded genetic algorithms. In this work we propose a new strategy to improve the performance of this operator by the creation of virtual parents obtained from the population parameters of localisation and dispersion of the best individuals. The idea consists of mating these virtual parents with individuals of the population. In this way, the offspring are created in the most promising regions. This strategy has been incorporated into several crossover operators. After analysing the results we can conclude that this strategy significantly improves the performance of the algorithm in most problems analysed.     

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.     

Global and local real-coded genetic algorithms based on parent-centric crossover operators

Parent-centric real-parameter crossover operators create the offspring in the neighbourhood of one of the parents, the female parent. The other parent, the male one, defines the range of the neighbourhood. With the aim of improving the behaviour of these crossover operators, we present three processes that are performed before their application. First, a female and male differentiation process determines the individuals in the population that may become female or/and male parents. Then, two different selection mechanisms choose the female and male parents from each group. In addition, we tackle the election of the most adequate evolution model to take out profit from these parent selection mechanisms. The experimental results confirm that these three processes may enhance the operation of the parent-centric crossover operators.     

Identification of fuzzy relation models using hierarchical fair competition-based parallel genetic algorithms and information granulation

The paper is concerned with a hybrid optimization of fuzzy inference systems based on hierarchical fair competition-based parallel genetic algorithms (HFCGA) and information granulation. The process of information granulation is realized with the aid of the C-Means clustering. HFCGA being a multi-population based parallel genetic algorithms (PGA) is exploited here to realize structure optimization and carry out parameter estimation of the fuzzy models. The HFCGA becomes helpful in the context of fuzzy models as it restricts a premature convergence encountered quite often in optimization problems. It concerns a set of parameters of the model including among others the number of input variables to be used, a specific subset of input variables, and the number of membership functions. In the hybrid optimization process, two general optimization mechanisms are explored. The structural development of the fuzzy model is realized via the HFCGA optimization and C-Means, whereas to deal with the parametric optimization we proceed with a standard least square method and the use of the HFCGA technique. A suite of comparative studies demonstrates that the proposed algorithm leads to the models whose performance is superior in comparison with some other constructs commonly used in fuzzy modeling.     

Multicriteria–multistage planning for the optimal path selection using hybrid genetic algorithms

The problem of the competence set expansion involves determining the optimal expansion path under the minimum cost and time. As we know, the conventional competence set model only considers the problems of the static situation and the single objective. However, the dynamic situation and the multicriteria should also be simultaneously considered in practice. In this paper, a multicriteria and multistage competence set model is proposed. In order to efficiently obtain an optimal expansion path, hybrid genetic algorithms (HGA) are employed. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations.     

CFD modeling and multi-objective optimization of cyclone geometry using desirability function,artificial neural networks and genetic algorithms

The low-mass loading gas cyclone separator has two performance parameters, the pressure drop and the collection efficiency (cut-off diameter). In this paper, a multi-objective optimization study of a gas cyclone separator has been performed using the response surface methodology (RSM) and CFD data. The effects of the inlet height, the inlet width, the vortex finder diameter and the cyclone total height on the cyclone performance have been investigated. The analysis of design of experiment shows a strong interaction between the inlet dimensions and the vortex finder diameter. No interaction between the cyclone height and the other three factors was observed. The desirability function approach has been used for the multi-objective optimization. A new set of geometrical ratios (design) has been obtained to achieve the best performance. A numerical comparison between the new design and the Stairmand design confirms the superior performance of the new design. As an alternative approach for applying RSM as a meta-model, two radial basis function neural networks (RBFNNs) have been used. Furthermore, the genetic algorithms technique has been used instead of the desirability function approach. A multi-objective optimization study using NSGA-II technique has been performed to obtain the Pareto front for the best performance cyclone separator.     

A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

Reducing the bandwidth of a sparse matrix with a genetic algorithm

Abstract

The matrix bandwidth minimization problem (MBMP) consists in finding a permutation of the lines and columns of a given sparse matrix in order to keep the non-zero elements in a band that is as close as possible to the main diagonal. Equivalently in terms of graph theory, MBMP is defined as the problem of finding a labelling of the vertices of a given graph G such that its bandwidth is minimized. In this paper, we propose an improved genetic algorithm (GA)-based heuristic for solving the matrix bandwidth minimization problem, motivated by its robustness and efficiency in a wide area of optimization problems. Extensively computational results are reported for an often used set of benchmark instances. The obtained results on the different instances investigated show improvement of the quality of the solutions and demonstrate the efficiency of our GA compared to the existing methods in the literature.     

Automatic clustering using genetic algorithms

In face of the clustering problem, many clustering methods usually require the designer to provide the number of clusters as input. Unfortunately, the designer has no idea, in general, about this information beforehand. In this article, we develop a genetic algorithm based clustering method called automatic genetic clustering for unknown K (AGCUK). In the AGCUK algorithm, noising selection and division-absorption mutation are designed to keep a balance between selection pressure and population diversity. In addition, the Davies-Bouldin index is employed to measure the validity of clusters. Experimental results on artificial and real-life data sets are given to illustrate the effectiveness of the AGCUK algorithm in automatically evolving the number of clusters and providing the clustering partition.     

Robustness in multi-objective optimization using evolutionary algorithms

This work discusses robustness assessment during multi-objective optimization with a Multi-Objective Evolutionary Algorithm (MOEA) using a combination of two types of robustness measures. Expectation quantifies simultaneously fitness and robustness, while variance assesses the deviation of the original fitness in the neighborhood of the solution. Possible equations for each type are assessed via application to several benchmark problems and the selection of the most adequate is carried out. Diverse combinations of expectation and variance measures are then linked to a specific MOEA proposed by the authors, their selection being done on the basis of the results produced for various multi-objective benchmark problems. Finally, the combination preferred plus the same MOEA are used successfully to obtain the fittest and most robust Pareto optimal frontiers for a few more complex multi-criteria optimization problems.     

Minimizing flow time variance in a single machine system using genetic algorithms

In this paper, we address an n-job, single machine scheduling problem with an objective to minimize the flow time variance. We propose heuristic procedure based on genetic algorithms with the potential to address more generalized objective function such as weighted flow time variance. The development and implementation of the algorithm is supported with literature review and statistical analysis of the results. Some general guidelines to select the parameter values of the genetic algorithm are also developed using an experimental design approach.     

On the effect of selection in genetic algorithms

To study the effect of selection with respect to mutation and mating in genetic algorithms, we consider two simplified examples in the infinite population limit. Both algorithms are modeled as measure valued dynamical systems and are designed to maximize a linear fitness on the half line. Thus, they both trivially converge to infinity. We compute the rate of their growth and we show that, in both cases, selection is able to overcome a tendency to converge to zero. The first model is a mutation‐selection algorithm on the integer half line, which generates mutations along a simple random walk. We prove that the system goes to infinity at a positive speed, even in cases where the random walk itself is ergodic. This holds in several strong senses, since we show a.s. convergence, L^p convergence, convergence in distribution, and a large deviations principle for the sequence of measures. For the second model, we introduce a new class of matings, based upon Mandelbrot martingales. The mean fitness of the associated mating‐selection algorithms on the real half line grows exponentially fast, even in cases where the Mandelbrot martingale itself converges to zero. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 185–200, 2001     

Routing and wavelength assignment in optical networks using bin packing based algorithms

This paper addresses the problem of routing and wavelength assignment (RWA) of static lightpath requests in wavelength routed optical networks. The objective is to minimize the number of wavelengths used. This problem has been shown to be NP-complete and several heuristic algorithms have been developed to solve it. We suggest very efficient, yet simple, heuristic algorithms for the RWA problem developed by applying classical bin packing algorithms. The heuristics were tested on a series of large random networks and compared with an efficient existing algorithm for the same problem. Results indicate that the proposed algorithms yield solutions significantly superior in quality, not only with respect to the number of wavelength used, but also with respect to the physical length of the established lightpaths. Comparison with lower bounds shows that the proposed heuristics obtain optimal or near optimal solutions in many cases.     

Integrated crossover rules in real coded genetic algorithms

Modifications in crossover rules and localization of searches are suggested to the real coded genetic algorithms for continuous global optimization. Central to our modifications is the integration of different crossover rules within the genetic algorithm. Numerical experiments using a set of 50 test problems indicate that the resulting algorithms are considerably better than the previous version considered and offer a reasonable alternative to many currently available global optimization algorithms, especially for problems requiring ‘direct search type’ methods.     

On-line algorithms for networks of temporal constraints

We consider a semi-dynamic setting for the Temporal Constraint Satisfaction Problem (TCSP), where we are requested to maintain the path-consistency of a network under a sequence of insertions of new (further) constraints between pairs of variables. We show how to maintain the path-consistency in O(nR³) amortized time on a sequence of Θ(n²) insertions, where n is the number of vertices of the network and R is its range, defined as the maximum size of the minimum interval containing all the intervals of a single constraint.Furthermore we extend our algorithms to deal with more general temporal networks where variables can be points and/or intervals and constraints can also be defined on pairs of different kinds of variables. For such cases our algorithms maintain their performance. Finally, we adapt our algorithms to also maintain the arc-consistency of such generalized networks in O(R) amortized time for Θ(n²) insertions.     

Test driving three 1995 genetic algorithms: New test functions and geometric matching

Genetic algorithms have attracted a good deal of interest in the heuristic search community. Yet there are several different types of genetic algorithms with varying performance and search characteristics. In this article we look at three genetic algorithms: an elitist simple genetic algorithm, the CHC algorithm and Genitor. One problem in comparing algorithms is that most test problems in the genetic algorithm literature can be solved using simple local search methods. In this article, the three algorithms are compared using new test problems that are not readily solved using simple local search methods. We then compare a local search method to genetic algorithms for geometric matching and examine a hybrid algorithm that combines local and genetic search. The geometric matching problem matches a model (e.g., a line drawing) to a subset of lines contained in a field of line fragments. Local search is currently the best known method for solving general geometric matching problems.     

一种基于自适应混合遗传算法的非线性函数优化方法

遗传算法因其具有的特性,它采用交换、复制和突变等方法,获取的解为全局最优解,而且无需计算函数的导数,是一种只考虑输入与输出关系的黑箱问题,适用于处理各种复杂问题.此文基于最优保存的思想,把最速下降法与最优保存和自适应遗传算法相结合,用于求解非线性函数优化问题,提出一种基于自适应混合遗传算法的非线性函数全局优化方法.