Bicriteria Scheduling on a Series-Batching Machine to Minimize Makespan and Total Weighted Completion Time with Equal Length Job

It is known that the problem of minimizing total weighted completion time on a series-batching machine is NP-hard. We consider a series-batching bicriteria scheduling problem of minimizing makespan and total weighted completion time with equal length job simultaneously. A batching machine can handle up to b jobs in a batch, where b is called the batch capacity of the machine. We study the unbounded model with b ≥ n, where n denotes the number of jobs. A dynamic programming algorithm is proposed to solve the unbounded model, which can find all Pareto optimal schedules in O(n3) time.

Bicriteria Approximation Algorithm for Quarantining-vaccination-cure Problem

In this paper, we propose a model for the epidemic control problem, the goal of which is to minimize the total cost of quarantining, vaccination and cure under the constraint on the maximum number of infected people allowed. A (1+ε+ε3 , 1+ ε+1/ε )- bicriteria approximation algorithm is given.

Bicriteria Scheduling on Single Machine with Outsourcing

Scheduling with outsourcing is studied in this paper. It is assumed that both manufacturer and subcontractor have a single machine to process n jobs. The manufacturer needs to determine simultaneously a set of outsourced jobs and the schedule of the jobs in-house such that two criterias, i.e., outsourcing cost and production cost, are minimized.The production cost is measured by the number of tardy jobs or the total tardiness of jobs in-house, and the outsourcing cost is proportional to the total processing time of jobs outsourced. Two kinds of problems with different criterias are considered. We analyze the computational complexity and provide pseudo-polynomial time optimization algorithms for the NP-hard version of the problems.

Fast Computation of Pareto Set for Bicriteria Linear Programs with Application to a Diet Formulation Problem

In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.

A Flexible Space-Time Tradeoff on Hybrid Index with Bicriteria Optimization

Inverted indexes are widely adopted in the vast majority of information systems. Growing requirements for efficient query processing have motivated the development of various compression techniques with different spacetime characteristics. Although a single encoder yields a relatively stable point in the space-time tradeoff curve,flexibly transforming its characteristic along the curve to fit different information retrieval tasks can be a better way to prepare the index. Recent research comes out with an idea of integrating different encoders within the same index,namely, exploiting access skewness by compressing frequently accessed regions with faster encoders and rarely accessed regions with succinct encoders, thereby improving the efficiency while minimizing the compressed size.However, these methods are either inefficient or result in coarse granularity. To address these issues, we introduce the concept of bicriteria compression, which aims to formalize the problem of optimally trading the compressed size and query processing time for inverted index. We also adopt a Lagrangian relaxation algorithm to solve this problem by reducing it to a knapsack-type problem, which works in O(n log n)time and O(n)space, with a negligible additive approximation. Furthermore, this algorithm can be extended via dynamic programming pursuing improved query efficiency. We perform an extensive experiment to show that, given a bounded time/space budget, our method can optimally trade one for another with more efficient indexing and query performance.

Bicriteria Algorithms for Approximately Submodular Cover Under Streaming Model

In this paper,we mainly investigate the optimization model that minimizes the cost function such that the cover function exceeds a required threshold in the set cover problem,where the cost function is additive linear,and the cover function is non-monotone approximately submodular.We study the problem under streaming model and propose three bicriteria approximation algorithms.Firstly,we provide an intuitive streaming algorithm under the assumption of known optimal objective value.The intuitive streaming algorithm returns a solution such that its cover function value is no less thanα(1−ϵ)times threshold,and the cost function is no more than(2+ϵ)^(2)/(ϵ^(2)ω^(2))⋅κ,whereκis a value that we suppose for the optimal solution andαis the approximation ratio of an algorithm for unconstrained maximization problem that we can call directly.Next we present a bicriteria streaming algorithm scanning the ground set multi-pass to weak the assumption that we guess the optimal objective value in advance,and maintain the same bicriteria approximation ratio.Finally we modify the multi-pass streaming algorithm to a single-pass one without compromising the performance ratio.Additionally,we also propose some numerical experiments to test our algorithm’s performance comparing with some existing methods.

Deterministic Bicriteria Model for Stochastic Variational Inequalities

We propose a deterministic bicriteria model for stochastic variational inequalities based on some existing deterministic models.We reformulate the bicriteria model into a single objective problem involving a conditional value-at-risk(CVaR)term and introduce two approximation methods for solving the single objective problem,which are based on the primal and dual formulations of CVaR,respectively.In particular,for the primal problem,we introduce a smooth approximation of CVaR and establish some properties for this approximation problem.Then,we use sample average approximation methods to deal with the single objective problem and investigate the limiting behaviors of optimal solutions and stationary points.For the dual problem,we regularize the inner maximization problem and demonstrate the convergence of the approximation.

A Note on Relations between Linear Bilevel Programming and Linear Bicriteria Programming

In this short note.we discuss the relations between linear bilevel programming and linear bicriteria programming.A counter example is comtructed to illustrate the the main result in Wen and Hsu[3]is not correct.A sufficient condition is also presented to guarantee at least of optimal solution of a linear bilevel programming problem is also an efficient solution of the corresponding bicriteria programming problem.

一个多物资网络流问题的逼近算法

给出最小满意率最大双标准最大多物资网络流问题,并证明其解存在.建构辅助网络,运用Korte和Vygen于2000年在Young,Garg和Kφnemann等工作的基础上给出的求最大多种物资网络流问题的ε—逼近解的完全多项式算法作子程序和二分收索方法做出一个求所给问题的解的拟多项式逼近算法.分析算法的复杂性,给出并证明算法的逼近程度.

双目标函数下需要安装时间的平行多功能机排序问题

讨论了双目标函数下需要安装时间的平行多功能机排序问题。在该问题中,每个工件对应机器集合的一个子集,且每个工件只能在相应子集中的任一台机器上加工,工件分组,不同组中的工件连续加工需要安装时间,目标函数为极小化最大完工时间和安装次数。根据实际应用背景确定双目标排序问题的形式,并证明了该问题是NP—难的。设计了一个求启发式有效解的算法,首先按照特定的规则将所有工件组都整组地安排到各台机器上,然后逐步改进最大完工时间和拆分工件组,从而得到一系列的启发式有效解。实验表明,该算法是实用而有效的。

关于工期分配与加权误工数的双指标排序问题（英文）

排序问题中工期分配的目的是处理分配费用与性能指标的利益平衡,由此提出工期分配的双目标排序问题.关于工期分配与加权误工数的单机双指标排序问题,文献中只研究了其线性组合形式.针对该问题,本文针对约束形式及Pareto优化形式进一步研究了更多的模型.主要结果包括NP-困难性、多项式可解情形以及多项式时间近似方案等结果.通过这些结果,一个多目标优化问题的特征得以完整地刻画.

最大一致流问题的一个逼近算法

通过建构辅助网络,以Korte和Vygen于2000年所给出的一个求最大多种物资网络流问题的逼近解的完全多项式算法作为子程序进行二分搜索,给出了一个新的求解最大一致流问题的逼近算法.然后,进行算法分析,说明了所建立的算法是拟多项式算法,并且给出与证明了一个有关输出的流与输入问题的解之间的逼近关系.该项工作表明从一个多种物资网络流问题的算法出发通过变换求解其他有关问题是可行的,并且为研究网络流问题提供了一种新的方法.

带有惩罚和软容量约束的下界设施选址问题的双标准近似算法研究(英文)

研究带惩罚和软容量约束的下界设施选址问题.扩展Guha等(Guha S,Meyerson A,Munagala K.Hierarchical placement and network design problems[C]//Proceedings of Foundations of Computer Science,2000:892328,DOI:10.1109/SFCS.2000.892328)和Karger等(Karger D R,Minkoff M.Building steiner trees with incomplete global knowledge[C]//Proceedings of Foundations of Computer Science,2000:892329,DOI:10.1109/SFCS.2000.892329)的工作到带有惩罚的下界约束设施选址问题,提出了一个新的双标准近似算法,得到了同样的近似比(1+α)/(1-α)ρ.进一步考虑带惩罚和软容量约束的下界设施选址问题,得到了近似比为2(1+α)/(1-α)ρ的双标准近似算法.

基于弧长均值和方差的集装箱站场排队网络最短路问题研究

集装箱站场排队网络属于随机的动态服务系统,顾客从网络的起点进入一直到终点离开该系统的时间长短则反映集装箱站场的服务水平.为使顾客在这一过程花费的时间最短,根据稳态条件下的排队系统理论,结合多准则最短路问题,提出了一种基于弧长均值和方差的双准则最短路算法,并通过算例证明了该算法的可行性.文中提到的方法还适用于寻找随机路径问题中从起点到终点的最短路.

Some Remarks on Application of Sandwich Methods in the Minimum Cost Flow Problem

In this paper, two new sandwich algorithms for the convex curve approximation are introduced. The proofs of the linear convergence property of the first method and the quadratic convergence property of the second method are given. The methods are applied to approximate the efficient frontier of the stochastic minimum cost flow problem with the moment bicriterion. Two numerical examples including the comparison of the proposed algorithms with two other literature derivative free methods are given.

混合遗传算法求解双准则线性运输问题

针对传统的遗传算法求解双准则线性运输问题时非劣解容易陷入局部区域的不足之处,提出一种改进的混合遗传算法。该算法分别从初始化染色体、非劣解的寻找和选择算子三个方面对传统遗传算法进行改进。并且在选择算子中结合使用权重系数变化和最小境技术保证可行解的收敛性,增加非劣解的多样性,使所求的非劣解具有一定代表性。最后通过计算实例结果,表明改进的混合遗传算法能获得更多的有效非劣解。

高速铁路双准则客流分配方法研究

在考虑高速铁路旅客个性化乘车选择行为基础上,针对票价优化研究高速铁路双准则客流分配方法。基于高速列车运行图构建列车服务网络,在分析多层次客流选择行为基础上,提出服务网络的路径广义成本计算方法。引入旅客时间价值变量,建立时间-费用双准则客流分配模型,允许旅客在时间和票价2个择路原则之间做出偏向性选择,采用改进的基于迭代加权法(MSA)的蒙特卡罗模拟算法进行客流分配。以京沪高速铁路实际客票数据对模型和算法进行验证,结果表明,研究提出的双准则客流分配方法可以较好地反映特定票价下客流的分布情况。

一台串行批处理机上的一类有主次指标的排序问题

考虑一类带机器安装时间的单机双目标串行分批排序问题.对这样两个问题1,s|s-batch,B≥n,Cmax≤u|∑Cj和1,s|s-batch,B≥n,∑Cj≤v|Cmax,通过动态规划给出了多项式时间最优算法.

一台串行批处理机上的一类有主次指标的排序问题

考虑一类带机器安装时间的单机双目标串行分批排序问题。对解决这一排序问题所涉及的两个问题:1,s/s-batch,B≥n,Cmax≤u|∑Cj和1,s/s-batch,B≥n,Cj≤v|∑Cmax,通过动态规划给出了多项式时间最优算法。

双准则最短路径问题的算法实现与对比分析

双准则最短路径问题旨在寻找路网两节点间所含路段总权重最小化的路径,其中路段权重需综合考虑如时间、金钱在内的两种准则。考虑出行者的异质性假设,研究中通常采用一个连续分布刻画同一起讫点(origin-destination,OD)出行者的时间价值。尽管将连续分布均等离散化并将每个分段近似成单一值后可以使用如Dijkstra算法等标准最短路径算法求解,但较少离散类别下这种近似处理致使部分出行者的路径选择被错误刻画,而过多的离散类别又会大大降低算法效率。因此,研究者们致力于精确求解连续双准则最短路径问题。但现有研究在算法的网络拓扑解释方面仍有欠缺,对不同算法性能的比较也较为缺乏。本文详细分析了连续双准则最短路径问题的三种求解算法,首先阐述了基于OD对和基于起点两类双准则最短路径算法的原理以及实现步骤,进一步分析基于起点的“转轴”加速策略。通过一系列数值实验分析测试算法性能,结果表明,基于起点的算法配合“转轴”加速策略在不同规模的测试网络中均展现出较高的计算效率,而基于OD对的算法在大型网络中表现较差。此外,本文还在网络规模、收费路段数量、收费尺度、需求水平等维度全面测试了三种算法,并分析不同要素对算法性能的影响。结果显示,收费增加和网络拥挤均会在一定程度上降低三种算法的求解效率。本研究不仅有助于加深对双准则路径选择行为的理解,还为解决多用户多准则网络均衡、多目标网络优化等复杂优化问题奠定了基础。