Worst-case analysis of a scheduling algorithm

In this note, a heuristic proposed by Ibarra and Kim (IK) for scheduling independent tasks on unrelated processors is analyzed. The heuristic may create a schedule which finishes a time $\text{m 1 OPT}$, where m is the number of processors, and OPT is the time used in the optimal schedule. This compares unfavorably with the heuristics described by Davis and Jaffe [2], which have worst-case behavior which is $\text{O(OPT 1 m}{}^{0.5}\text{)}$.     

New TSP Construction Heuristics and Their Relationships to the 2-Opt

Correction heuristics for the traveling salesman problem (TSP), with the 2-Opt applied as a postprocess, are studied with respect to their tour lengths and computation times. This study analyzes the 2-Opt dependency, which indicates how the performance of the 2-Opt depends on the initial tours built by the construction heuristics. In accordance with the analysis, we devise a new construction heuristic, the recursive-selection with long-edge preference (RSL) method, which runs faster than the multiple-fragment method and produces a comparable tour when they are combined with the 2-Opt.     

Greedy Randomized Adaptive Search Procedures

Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.     

基于彩色离焦模糊图像清晰度评价的启发式调焦算法

运用启发式搜索策略提出了一种基于彩色离焦模糊图像清晰度评价的启发式调焦算法。算法采用了以2为模的Sobel算子梯度建立图像清晰度评价函数的数学模型。该评价函数具有无偏性好,单峰性强,灵敏度高,在焦平面变化趋势明显等特点。我们给出了结合启发式搜索策略的具体算法。实验结果证明,所提出的启发式调焦算法精度高,可重复性强,并对图像噪声具有良好的鲁棒性。     

Effective Heuristics for the GPS Survey Network of Malta: Simulated Annealing and Tabu Search Techniques

A GPS network can be defined as a set of stations, co-ordinated by a series of sessions formed by placing receivers on the stations. This paper shows how to search for the best order in which to observe these sessions giving the cheapest schedule. The complexity of observing GPS networks increases with their size and become highly difficult to solve effectively. To obtain good methods to solve this problem a new area of research is implemented. This area is based on developed heuristic techniques that provide an optimal or near optimal solution for large networks. Comparing their outcome in terms of solution quality and computational effort proves the performance of the developed techniques.     

一类速度不同的具有m台通用机的n组工件的排序问题

研究的目的在于解决实践中对多组任务的优化排序问题,即在最短的时间内完成所有给定的任务,由于这类问题往往都是NP完全问题,人们通常寻求其近似算法．文中提出了一种改进的LPT算法,利用。首先空闲”准则,讨论了将n组工件安排在n台速度不同的专用机,m台速度小于专用机的通用机上的C‰。。问题,得到了利用该近似算法所得的解T与最优解T＊的—个估计：T/T＊≤2＋（n-2）/（m＋1）     

Twenty years of linear programming based portfolio optimization

Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features.     

Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs

For comparing random designs and Latin hypercube designs, this paper con- siders a wrap-around version of the L₂-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete.     

Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method

The reliability-redundancy allocation problem is an optimization problem that achieves better system reliability by determining levels of component redundancies and reliabilities simultaneously. The problem is classified with the hardest problems in the reliability optimization field because the decision variables are mixed-integer and the system reliability function is nonlinear, non-separable, and non-convex. Thus, iterative heuristics are highly recommended for solving the problem due to their reasonable solution quality and relatively short computation time. At present, most iterative heuristics use sensitivity factors to select an appropriate variable which significantly improves the system reliability. The sensitivity factor represents the impact amount of each variable to the system reliability at a designated iteration. However, these heuristics are inefficient in terms of solution quality and computation time because the sensitivity factor calculations are performed only at integer variables. It results in degradation of the exploration and growth in the number of subsequent continuous nonlinear programming (NLP) subproblems. To overcome the drawbacks of existing iterative heuristics, we propose a new scaling method based on the multi-path iterative heuristics introduced by Ha (2004). The scaling method is able to compute sensitivity factors for all decision variables and results in a decreased number of NLP subproblems. In addition, the approximation heuristic for NLP subproblems helps to avoid redundant computation of NLP subproblems caused by outlined solution candidates. Numerical experimental results show that the proposed heuristic is superior to the best existing heuristic in terms of solution quality and computation time.     

流水车间作业排序问题蚁群算法研究

本文运用蚁群算法研究辨台处理机、目标函数为时间表长最小的同顺序排列流水车间作业排序问题，设计出解决该问题的算法步骤与流程。最后，通过仿真比较该算法与解决该问题的其它启发式算法性能，计算效果比较满意。