Heuristic methods for evolutionary computation techniques

Evolutionary computation techniques, which are based on a powerful principle of evolution—survival of the fittest, constitute an interesting category of heuristic search. In other words, evolutionary techniques are stochastic algorithms whose search methods model some natural phenomena: genetic inheritance and Darwinian strife for survival.Any evolutionary algorithm applied to a particular problem must address the issue of genetic representation of solutions to the problem and genetic operators that would alter the genetic composition of offspring during the reproduction process. However, additional heuristics should be incorporated in the algorithm as well; some of these heuristic rules provide guidelines for evaluating (feasible and infeasible) individuals in the population. This paper surveys such heuristics and discusses their merits and drawbacks.An abridged version of this paper appears in the volume entitled META-HEURISTICS: Theory & Application, edited by Ibrahim H. Osman and James P. Kelly, to be published by Kluwer Academic Publishers in March 1996.     

一个线性约束优化问题的广义梯度投影法

本文对线性约束优化问题提出了一个新的广义梯度投影法，该算法采用了非精确线性搜索，并在每次迭代运算中结合了广义投影矩阵和变尺度方法的思想确定其搜索方向．在通常的假设条件下，证明了该算法的整体收敛性和超线性收敛速度．     

Robust optimization with applications to game theory

In this article, we investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent's strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria.     

New Bundle Methods for Solving Lagrangian Relaxation Dual Problems

Bundle methods have been used frequently to solve nonsmooth optimization problems. In these methods, subgradient directions from past iterations are accumulated in a bundle, and a trial direction is obtained by performing quadratic programming based on the information contained in the bundle. A line search is then performed along the trial direction, generating a serious step if the function value is improved by or a null step otherwise. Bundle methods have been used to maximize the nonsmooth dual function in Lagrangian relaxation for integer optimization problems, where the subgradients are obtained by minimizing the performance index of the relaxed problem. This paper improves bundle methods by making good use of near-minimum solutions that are obtained while solving the relaxed problem. The bundle information is thus enriched, leading to better search directions and less number of null steps. Furthermore, a simplified bundle method is developed, where a fuzzy rule is used to combine linearly directions from near-minimum solutions, replacing quadratic programming and line search. When the simplified bundle method is specialized to an important class of problems where the relaxed problem can be solved by using dynamic programming, fuzzy dynamic programming is developed to obtain efficiently near-optimal solutions and their weights for the linear combination. This method is then applied to job shop scheduling problems, leading to better performance than previously reported in the literature.     

A dual-active-set algorithm for positive semi-definite quadratic programming

Because of the many important applications of quadratic programming, fast and efficient methods for solving quadratic programming problems are valued. Goldfarb and Idnani (1983) describe one such method. Well known to be efficient and numerically stable, the Goldfarb and Idnani method suffers only from the restriction that in its original form it cannot be applied to problems which are positive semi-definite rather than positive definite. In this paper, we present a generalization of the Goldfarb and Idnani method to the positive semi-definite case and prove finite termination of the generalized algorithm. In our generalization, we preserve the spirit of the Goldfarb and Idnani method, and extend their numerically stable implementation in a natural way. Supported in part by ATERB, NSERC and the ARC. Much of this work was done in the Department of Mathematics at the University of Western Australia and in the Department of Combinatorics and Optimization at the University of Waterloo.     

FEW: A workflow tool for free energy calculations of ligand binding

In the later stages of drug design projects, accurately predicting relative binding affinities of chemically similar compounds to a biomolecular target is of utmost importance for making decisions based on the ranking of such compounds. So far, the extensive application of binding free energy approaches has been hampered by the complex and time‐consuming setup of such calculations. We introduce the free energy workflow (FEW) tool that facilitates setup and execution of binding free energy calculations with the AMBER suite for multiple ligands. FEW allows performing free energy calculations according to the implicit solvent molecular mechanics (MM‐PB(GB)SA), the linear interaction energy, and the thermodynamic integration approaches. We describe the tool's architecture and functionality and demonstrate in a show case study on Factor Xa inhibitors that the time needed for the preparation and analysis of free energy calculations is considerably reduced with FEW compared to a fully manual procedure. © 2013 Wiley Periodicals, Inc.     

Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights

This paper deals with a general combinatorial optimization problem in which closed intervals and fuzzy intervals model uncertain element weights. The notion of a deviation interval is introduced, which allows us to characterize the optimality and the robustness of solutions and elements. The problem of computing deviation intervals is addressed and some new complexity results in this field are provided. Possibility theory is then applied to generalize a deviation interval and a solution concept to fuzzy ones.     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

带多面体控制锥的锥约束凸向量优化问题的有效解集的非空有界性的刻画

本文刻画了控制锥为多面凸锥的锥约束凸向量优化问题有效解集的非空有界性．然后将其中的一个重要条件应用于一类罚函数方法收敛性的研究．     

Equivalence of variational inequality problems to unconstrained minimization

In this paper we propose a class of merit functions for variational inequality problems (VI). Through these merit functions, the variational inequality problem is cast as unconstrained minimization problem. We estimate the growth rate of these merit functions and give conditions under which the stationary points of these functions are the solutions of VI. This work was supported by the state key project “Scientific and Engineering Computing”.