Gene selection in class space for molecular classification of cancer

Gene selection (feature selection) is generally pertormed in gene space(feature space), where a very serious curse of dimensionality problem always existsbecause the number of genes is much larger than the number of samples in gene space(G-space). This results in difficulty in modeling the data set in this space and the lowconfidence of the result of gene selection. How to find a gene subset in this case is achallenging subject. In this paper, the above G-space is transformed into its dual space,referred to as class space (C-space) such that the number of dimensions is the verynumber of classes of the samples in G-space and the number of samples in C-space isthe number of genes in G-space. it is obvious that the curse of dimensionality in C-spacedoes not exist. A new gene selection method which is based on the principle of separatingdifferent classes as far as possible is presented with the help of Principal ComponentAnalysis (PCA). The experimental results on gene selection for real data set areevaluat     

Gene boosting for cancer classification based on gene expression profiles

Gene selection is one of the important issues for cancer classification based on gene expression profiles. Filter and wrapper approaches are widely used for gene selection, where the former is hard to measure the relationship between genes and the latter requires lots of computation. We present a novel method, called gene boosting, to select relevant gene subsets by integrating filter and wrapper approaches. It repeatedly selects a set of top-ranked informative genes by a filtering algorithm with respect to a temporal training dataset constructed according to the classification result for the original training dataset. Empirical results on three microarray benchmark datasets have shown that the proposed method is effective and efficient in finding a relevant and concise gene subset. It achieved competitive performance with fewer genes in a reasonable time, as well as led to the identification of some genes frequently getting selected.     

Grasshopper optimization algorithm with principal component analysis for global optimization

The Journal of Supercomputing - As one of the latest meta-heuristic algorithms, the grasshopper optimization algorithm (GOA) has extensive applications because of its efficiency and simplicity....     

A hybrid grasshopper optimization algorithm with bat algorithm for global optimization

Multimedia Tools and Applications - This paper introduces a hybrid grasshopper optimization algorithm with bat algorithm (BGOA) for global optimization. In the BGOA, the Levy flight with variable...     

Hybrid arithmetic optimization algorithm with hunger games search for global optimization

Multimedia Tools and Applications - Recently, many population-dependent methods have been proposed. Despite their acceptance in many applications, we are still exploring suggested methods to solve...     

A classification approach to efficient global optimization in presence of non-computable domains

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.     

Pseudorandom lattices for global optimization

Rationalization processes are proposed to improve uniformity in small samples for pseudorandom lattices in (0,1)ⁿ constructed from sequences produced by random number generators. On this basis, the space filtration and space contraction algorithms are developed for the solution of multimodal global optimization problems. Strong convergence to the global minimum value and convergence in measure onto the set of all global minimizers are proved. Numerical experiments are presented to illustrate a better uniformity provided by a rationalization process and the use of the space filtration algorithm for global optimization.     

Adaptive comprehensive learning particle swarm optimization with spatial weighting for global optimization

Multimedia Tools and Applications - Although particle swarm optimization (PSO) algorithm shows excellent performance in solving optimization problems, how to balance exploration and exploitation is...     

Improved global-best-guided particle swarm optimization with learning operation for global optimization problems

In this paper, an improved global-best-guided particle swarm optimization with learning operation (IGPSO) is proposed for solving global optimization problems. The particle population is divided into current population, historical best population and global best population, and each population is assigned a corresponding searching strategy. For the current population, the global neighborhood exploration strategy is employed to enhance the global exploration capability. A local learning mechanism is used to improve local exploitation ability in the historical best population. Furthermore, stochastic learning and opposition based learning operations are employed to the global best population for accelerating convergence speed and improving optimization accuracy. The effects of the relevant parameters on the performance of IGPSO are assessed. Numerical experiments on some well-known benchmark test functions reveal that IGPSO algorithm outperforms other state-of-the-art intelligent algorithms in terms of accuracy, convergence speed, and nonparametric statistical significance. Moreover, IGPSO performs better for engineering design optimization problems.     

A multi-start central force optimization for global optimization

Central force optimization (CFO) is an efficient and powerful population-based intelligence algorithm for optimization problems. CFO is deterministic in nature, unlike the most widely used metaheuristics. CFO, however, is not completely free from the problems of premature convergence. One way to overcome local optimality is to utilize the multi-start strategy. By combining the respective advantages of CFO and the multi-start strategy, a multi-start central force optimization (MCFO) algorithm is proposed in this paper. The performance of the MCFO approach is evaluated on a comprehensive set of benchmark functions. The experimental results demonstrate that MCFO not only saves the computational cost, but also performs better than some state-of-the-art CFO algorithms. MCFO is also compared with representative evolutionary algorithms. The results show that MCFO is highly competitive, achieving promising performance.     

Prototype optimization for nearest-neighbor classification

A novel neuralnet-based method of constructing optimized prototypes for nearest-neighbor classifiers is proposed. Based on an effective classification oriented error function containing class classification and class separation components, the corresponding prototype and feature weight update rules are derived. The proposed method consists of several distinguished properties. First, not only prototypes but also feature weights are constructed during the optimization process. Second, several instead of one prototype not belonging to the genuine class of input sample x are updated when x is classified incorrectly. Third, it intrinsically distinguishes different learning contribution from training samples, which enables a large amount of learning from constructive samples, and limited learning from outliers. Experiments have shown the superiority of this method compared with LVQ2 and other previous works.     

Reduction constraints for the global optimization of NLPs

Convergence of branch‐and‐bound algorithms for the solution of NLPs is obtained by finding ever‐nearer lower and upper bounds to the objective function. The lower bound is calculated by constructing a convex relaxation of the NLP. Reduction constraints are new linear problem constraints which are (a) linearly independent from the existing constraints; (b) redundant with reference to the original NLP formulation; (c) not redundant with reference to its convex relaxation. Thus, they can be successfully employed to reduce the feasible region of the convex relaxation without cutting the feasible region of the original NLP.     

Gene selection and prediction for cancer classification using support vector machines with a reject option

In cancer classification based on gene expression data, it would be desirable to defer a decision for observations that are difficult to classify. For instance, an observation for which the conditional probability of being cancer is around 1/2 would preferably require more advanced tests rather than an immediate decision. This motivates the use of a classifier with a reject option that reports a warning in cases of observations that are difficult to classify. In this paper, we consider a problem of gene selection with a reject option. Typically, gene expression data comprise of expression levels of several thousands of candidate genes. In such cases, an effective gene selection procedure is necessary to provide a better understanding of the underlying biological system that generates data and to improve prediction performance. We propose a machine learning approach in which we apply the l₁ penalty to the SVM with a reject option. This method is referred to as the l₁ SVM with a reject option. We develop a novel optimization algorithm for this SVM, which is sufficiently fast and stable to analyze gene expression data. The proposed algorithm realizes an entire solution path with respect to the regularization parameter. Results of numerical studies show that, in comparison with the standard l₁ SVM, the proposed method efficiently reduces prediction errors without hampering gene selectivity.     

Efficient global optimization for image registration

The image registration problem of finding a mapping that matches data from multiple cameras is computationally intensive. Current solutions to this problem tolerate Gaussian noise, but are unable to perform the underlying global optimization computation in real time. This paper expands these approaches to other noise models and proposes the Terminal Repeller Unconstrained Subenergy Tunneling (TRUST) method, originally introduced by B.C. Cetin et al. (1993), as an appropriate global optimization method for image registration. TRUST avoids local minima entrapment, without resorting to exhaustive search by using subenergy-tunneling and terminal repellers. The TRUST method applied to the registration problem shows good convergence results to the global minimum. Experimental results show TRUST to be more computationally efficient than either tabu search or genetic algorithms     

Free Pattern Search for global optimization

An efficient algorithm named Pattern search (PS) has been used widely in various scientific and engineering fields. However, even though the global convergence of PS has been proved, it does not perform well on more complex and higher dimension problems nowadays. In order to improve the efficiency of PS and obtain a more powerful algorithm for global optimization, a new algorithm named Free Pattern Search (FPS) based on PS and Free Search (FS) is proposed in this paper. FPS inherits the global search from FS and the local search from PS. Two operators have been designed for accelerating the convergence speed and keeping the diversity of population. The acceleration operator inspired by FS uses a self-regular management to classify the population into two groups and accelerates all individuals in the first group, while the throw operator is designed to avoid the reduplicative search of population and keep the diversity. In order to verify the performance of FPS, two famous benchmark instances are conducted for the comparisons between FPS with Particle Swarm Optimization (PSO) variants and Differential Evolution (DE) variants. The results show that FPS obtains better solutions and achieves the higher convergence speed than other algorithms.     

Path relinking for large-scale global optimization

In this paper we consider the problem of finding a global optimum of a multimodal function applying path relinking. In particular, we target unconstrained large-scale problems and compare two variants of this methodology: the static and the evolutionary path relinking (EvoPR). Both are based on the strategy of creating trajectories of moves passing through high-quality solutions in order to incorporate their attributes to the explored solutions. Computational comparisons are performed on a test-bed of 19 global optimization functions previously reported with dimensions ranging from 50 to 1,000, totalizing 95 instances. Our results show that the EvoPR procedure is competitive with the state-of-the-art methods in terms of the average optimality gap achieved. Statistical analysis is applied to draw significant conclusions.     

Constrained global optimization for wine blending

Assemblage consists in blending base wines in order to create target wines. Recent developments in aroma analysis allow us to measure chemical compounds impacting the taste of wines. This chemical analysis makes it possible to design a decision tool for the following problem: given a set of target wines, determine which volumes must be extracted from each base wine to produce wines that satisfy constraints on aroma concentration, volumes, alcohol contents and price. This paper describes the modeling of wine assemblage as a mixed constrained optimization problem, where the main goal is to minimize the gap to the desired concentrations for every aromatic criterion. The deterministic branch and bound solvers Couenne and IbexOpt behave well on the wine blending problem thanks to their interval constraint propagation/programming and polyhedral relaxation methods. We also study the performance of other optimization goals that could be embedded in a configuration tool, where the different possible interactions amount to solving the same constraints with different objective functions. We finally show on a recent generic wine blending instance that the proposed optimization process scales up well with the number of base wines.     

求解全局优化问题的遗传退火算法

针对全局优化过程中,算法计算时间长、收敛时机不成熟、容易陷入局部最优等现象,在分析模拟退火算法和遗传算法优缺点的基础上提出了新的遗传退火混合算法,并将新的交叉、变异策略和诱导微调方法应用于算法中,通过10组非线性约束函数的测试表明,该算法能够在保持较高精度的前提下快速收敛。     

Deterministic global optimization for FNN training

This paper addresses the issue of training feedforward neural networks by global optimization. The main contributions include characterization of global optimality of a network error function, and formulation of a global descent algorithm to solve the network training problem. A network with a single hidden-layer and a single-output unit is considered. By means of a monotonic transformation, a sufficient condition for global optimality of a network error function is presented. Based on this, a penalty-based algorithm is derived directing the search towards possible regions containing the global minima. Numerical comparison with benchmark problems from the neural network literature shows superiority of the proposed algorithm over some local methods, in terms of the percentage of trials attaining the desired solutions. The algorithm is also shown to be effective for several pattern recognition problems.