Operation and preventive maintenance scheduling for containerships: Mathematical model and solution algorithm

This paper considers the problem of determining operation and maintenance schedules for a containership equipped with various subsystems during its sailing according to a pre-determined navigation schedule. The operation schedule, which specifies working time of each subsystem, determines the due-date of each maintenance activity and the maintenance schedule specifies the actual start time of each maintenance activity. The main constraints are subsystem requirements, workforce availability, working time limitation, and inter-maintenance time. To represent the problem mathematically, a mixed integer programming model is developed. Then, due to the complexity of the problem, we suggest a heuristic algorithm that minimizes the sum of earliness and tardiness between the due-date and the actual start time for each maintenance activity. Computational experiments were done on various test instances and the results are reported. In particular, a case study was done on a real instance and a significant amount of improvement is reported over the experience based conventional method.     

Two improved formulations for the minimum latency problem

In network problems, latency is associated with the metric used to evaluate the length of the path from a root vertex to each vertex in the network. In this work we are dealing with two applications or variations of the minimum latency problem known as the repairman problem and the deliveryman problem. We have developed two integer formulations for the minimum latency problem and compared them with other two formulations from the literature for the time-dependent traveling salesman problem. The present work highlights the similarities and differences between the different formulations. In addition, we discuss the convenience of including a set of constraints in order to reduce the computation time needed to reach the optimal solution. We have carried out extensive computational experimentation on asymmetrical instances, since they provide the characteristics of the deliveryman and repairman problems in a better way.     

On duality concepts in fractional programming

The paper (Part I) describes an approach to duality in fractional programming on the basis of another kind of conjugate functions. The connections to some duality concepts (the Lagrange-duality and duality concepts of Craven and Schaible) are investigated and some new proofs of strong duality theorems are given.     

Path-following barrier and penalty methods for linearly constrained problems

In the present paper some barrier and penalty methods (e.g. logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex problems are studied, in particular, the radius of convergence of Newton’s method depending on the barrier and penalty para-meter is estimated, Unlike using self-concordance properties the convergence bounds are derived by direct estimations of the solutions of the Newton equations. The obtained results establish parameter selection rules which guarantee the overall convergence of the considered barrier and penalty techniques with only a finite number of Newton steps at each parameter level. Moreover, the obtained estimates support scaling method which uses approximate dual multipliers as available in barrier and penalty methods     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

概率约束下最优解的统计影响函数

本文把稳健统计的影响函数概念引入到了概率约束下的随机规划模型中．在一定条件下,得到了三个模型最优解的影响函数表达式．     

基于可靠度的结构优化的序列近似规划算法

基于可靠度的优化的最直观解法是把可靠度和优化的各自算法搭配一起形成嵌套两层次迭代。为改善其收敛性提高计算效率,人们提出了功能测度法、半无限规划法、单层次算法等多种改进方法。本文对传统结构优化界的经典序列近似规划法改造并扩展应用于求解基于可靠度的结构优化问题,构造该问题的序列近似规划模型和求解过程;其核心思想是在每个近似规划子问题中采用近似可靠度指标对设计变量的线性近似,在优化迭代过程中同步更新设计变量和随机空间中的近似验算点坐标,以达到可靠度分析和优化迭代同步收敛的目标。为了算法的实施,还推导出近似可靠度指标的半解析灵敏度计算公式,编制了程序,最终实现与通用软件的连接。论文用算例证实算法的有效性。