应用基因遗传算法优化单分散荧光微球制备工艺

以偶氮二异丁腈为引发剂,乙醇为反应介质的单分散聚合法制得了粒径为4.5μm的高度单分散聚苯乙烯(polystyrene)微球.用三氯甲烷和正丙醇将PS微球溶胀,同时吸附荧光素-罗丹明和吖啶橙,制得的微球在荧光显微镜下可观察到被激发出红、绿、蓝等多种颜色的荧光,其发射光谱范围为505到610nm.红外光谱分析表明荧光素被吸收到PS微球内部,而表面没有检测到残余荧光素.从平行试验数据中选出几组最佳条件,采用基因遗传算法优化了溶胀过程中的反应参数,在第六代时得到一组最优反应条件,即10%(wt)的三氯甲烷,15 mmol的荧光素(其中含有33%的吖啶橙),溶胀时间为24h.     

OPTAC: a portable software package for analyzing and comparing optimization methods by visualization

A software package for analyzing and comparing optimization methods is presented. This package displays, using different colors, the regions of convergence to the minima of a given function for various optimization methods. It displays also the rate of their convergence as well as the regions of divergence of these methods. Moreover, this package gives quantitative information regarding the total convergence area in a specific domain for various minima.     

Maximum-throughput dynamic network flows

This paper presents and solves the maximum throughput dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which the flow on each arc not only has an associated upper and lower bound but also an associated transit time. Flow is to be sent through the network in each period so as to satisfy the upper and lower bounds and conservation of flow at each node from some fixed period on. The objective is to maximize the throughput, the net flow circulating in the network in a given period, and this throughput is shown to be the same in each period. We demonstrate that among those flows with maximum throughput there is a flow which repeats every period. Moreover, a duality result shows the maximum throughput equals the minimum capacity of an appropriately defined cut. A special case of the maximum dynamic network flow problem is the problem of minimizing the number of vehicles to meet a fixed periodic schedule. Moreover, the elegantsolution derived by Ford and Fulkerson for the finite horizon maximum dynamic flow problem may be viewed as a special case of the infinite horizon maximum dynamic flow problem and the optimality of solutions which repeat every period.     

Worst-case analysis of greedy algorithms for the subset-sum problem

Given a set ofn positive integers and another positive integerW, the Subset-Sum Problem is to find that subset whose sum is closest to, without exceeding,W. We present a polynomial approximation scheme for this problem and prove that its worst-case performance dominates that of Johnson's well-known scheme. Research supported by Ministero Pubblica Istruzion, Italy.     

Linear programming via a quadratic penalty function

We use quadratic penalty functions along with some recent ideas from linearl ₁ estimation to arrive at a new characterization of primal optimal solutions in linear programs. The algorithmic implications of this analysis are studied, and a new, finite penalty algorithm for linear programming is designed. Preliminary computational results are presented.Research supported by grant No. 11-0505 from the Danish Natural Science Research Council SNF.     

A quasi-Newton method can be obtained from a method of conjugate directions

In a recent paper McCormick and Ritter consider two classes of algorithms, namely methods of conjugate directions and quasi-Newton methods, for the problem of minimizing a function ofn variablesF(x). They show that the former methods possess ann-step superlinear rate of convergence while the latter are every step superlinear and therefore inherently superior. In this paper a simple and computationally inexpensive modification of a method of conjugate directions is presented. It is shown that the modified method is a quasi-Newton method and is thus every step superlinearly convergent. It is also shown that under certain assumptions on the second derivatives ofF the rate of convergence of the modified method isn-step quadratic.This work was supported by the National Research Council of Canada under Research Grant A8189.     

The average quality of greedy-algorithms for the Subset-Sum-Maximization Problem

This paper deals with the quality of approximative solutions for the Subset-Sum-Maximization-Problem maximize $$\sum\limits_{i = l}^n {a_i x_i } $$ subject to $$\sum\limits_{i = l}^n {a_i x_i } \leqslant b$$ wherea _l,...,a_n,bεR⁺ andx _l,...x_nε{0,1}. produced by certain heuristics of a Greedy-type. Every heuristic under consideration realizes a feasible solution (x ₁, ..., x_n) whose objective value is less or equal the optimal value, which is of course not greater thanb. We use the gap between capacityb and realized value as an upper bound for the error made by the heuristic and as a criterion for quality. Under the stochastic model:a ₁, ..., a_n, b independent,a ₁...,a_n uniformly distributed on [0, 1], b uniformly distributed on [0,n] we derive the gap-distributions and the expected size of the gaps. The analyzed algorithms include four algorithms which can be done in linear time and four heuristics which require sorting, which means that they are done inO(nlnn) time.     

On accelerating PL continuation algorithms by predictor—corrector methods

We consider path following methods designed to trace the zeroes of a continuous or differentiable mapF:R ⁿ⁺¹ R ⁿ . These methods are applicable e.g. in the numerical study of nonlinear eigenvalue and bifurcation problems. Traditionally a simplicial algorithm is based on a fixed triangulationT ofR ⁿ⁺¹ and a corresponding piecewise linear approximationF _T :R ⁿ⁺¹ R ⁿ .4 A fixed triangulation algorithm then traces the zeroes ofF _T via a complementary pivoting procedure. We present two kinds of hybrid algorithms that have the structure of a predictor—corrector method using simplicial methods to carry out the corrector steps. Numerical experience is reported showing the improvement in efficiency as compared to the fixed triangulation algorithm.     

Homeomorphisms of triangulations with applications to computing fixed points

In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are shrinking to a point. This paper proposes a new method for shrinking the simplexes. It is shown that under certain conditions, the function whose fixed point is sought may be used to control this shrinking process. A computational method for implementing these ideas is also suggested and several examples are solved using this approach.An abstract appears in the November, 1978 issue of Notices of the American Mathematical Society.