A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

二维椭圆型方程反问题中优化算法的比较

近年来，决定椭圆型方程系数反问题在地磁、地球物理、冶金和生物等实际问题上有着广泛的应用．本文讨论了二维的决定椭圆型方程系数反问题的数值求解方法．由误差平方和最小原则，这个反问题可化为一个变分问题，并进一步离散化为一个最优化问题，其目标函数依赖于要决定的方程系数．本文着重考察非线性共轭梯度法在此最优化问题数值计算中的表现，并与拟牛顿法作为对比．为了提高算法的效率我们适当选择加快收敛速度的预处理矩阵．同时还考察了线搜索方法的不同对优化算法的影响．数值实验的结果表明，非线性共轭梯度法在这类大规模优化问题中相对于拟牛顿法更有效．     

Searching in trees

In (Discrete Math. 17 (1977)181) Rivest introduced the search complexity of binary trees and proved that among all binary trees with a fixed search complexity the smallest ones are the so-called Fibonacci trees. This result is extended for q-trees. The structure of the smallest q-trees is again Fibonacci-like but more complicated than in the binary case. In addition an upper bound for the asymptotic growth of these trees is given.     

Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

Heuristic Algorithms and Scatter Search for the Cardinality Constrained P||Cmax Problem

We consider the generalization of the classical P||C_max problem (assign n jobs to m identical parallel processors by minimizing the makespan) arising when the number of jobs that can be assigned to each processor cannot exceed a given integer k. The problem is strongly NP-hard for any fixed k > 2. We briefly survey lower and upper bounds from the literature. We introduce greedy heuristics, local search and a scatter search approach. The effectiveness of these approaches is evaluated through extensive computational comparison with a depth-first branch-and-bound algorithm that includes new lower bounds and dominance criteria.     

Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Protein Conformation of a Lattice Model Using Tabu Search

We apply tabu search techniques to the problem of determining the optimal configuration of a chain of protein sequences on a cubic lattice. The problem under study is difficult to solve because of the large number of possible conformations and enormous amount of computations required. Tabu search is an iterative heuristic procedure which has been shown to be a remarkably effective method for solving combinatorial optimization problems. In this paper, an algorithm is designed for the cubic lattice model using tabu search. The algorithm has been tested on a chain of 27 monomers. Computational results show that our method outperforms previously reported approaches for the same model.     

Feature Selection using Fuzzy Support Vector Machines

The feature selection consists of obtaining a subset of these features to optimally realize the task without the irrelevant ones. Since it can provide faster and cost-effective learning machines and also improve the prediction performance of the predictors, it is a crucial step in machine learning. The feature selection methods using support machines have obtained satisfactory results, but the noises and outliers often reduce the performance. In this paper, we propose a feature selection approach using fuzzy support vector machines and compare it with the previous work, the results of experiments on the UCI data sets show that feature selection using fuzzy SVM obtains better results than using SVM.