Solving Linear Unconstrained Problems of Combinatorial Optimization on Arrangements Under Stochastic Uncertainty

Linear unconstrained problem of combinatorial optimization on arrangements under stochastic uncertainty is being solved. The minimum is defined as the result of sequential comparison of numerical characteristics of random variables. The properties of the solution of the optimization problem under study are obtained. These properties use the properties of special constructed deterministic problems. The authors also propose the reduction method to solve linear unconstrained problem of combinatorial stochastic optimization, which is based on obtained solution’s properties.     

Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients

We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method, and demonstrate numerically its superiority. The asymptotic cost of solving the stochastic problem with the multilevel method is always significantly lower than that of the standard method and grows only proportionally to the cost of solving the deterministic problem in certain circumstances. Numerical calculations demonstrating the effectiveness of the method for one- and two-dimensional model problems arising in groundwater flow are presented.     

Assessing the benefits of group-buying-based combinatorial reverse auctions

Combinatorial reverse auctions represent a popular business model in procurement. For multiple buyers, different procurement models based on combinatorial reverse auctions may be applied. For example, each buyer may hold one combinatorial reverse auction independently. Alternatively, the buyers may delegate the auction to a group-buyer and let the group-buyer hold only one combinatorial reverse auction on behalf of all the buyers. A combination of a combinatorial reverse auctions with the group-buying model makes it possible to reduce the overall cost to acquire the required items significantly due to complementarities between items. However, combinatorial reverse auctions suffer from high computational complexity. To assess the advantage of combining group-buying with combinatorial reverse auctions, three issues must be addressed, including performance, computational efficiency and the scheme to reward the buyers. This motivates us to compare the performance and efficiency of the aforementioned two different combinatorial reverse auction models and to study the possible schemes to reward the buyers. To achieve these objectives, we first illustrate the advantage of group-buying-based combinatorial reverse auctions over multiple independent combinatorial reverse auctions. We then formulate the problems for these two combinatorial reverse auction models and propose solution algorithms for them. We compare performance and computational efficiency for these two combinatorial reverse auction models. Our analysis indicates that a group-buying-based combinatorial reverse auction not only outperforms multiple independent combinatorial reverse auctions but also is more efficient than multiple independent combinatorial reverse auctions. We also propose a non-uniform scheme to reward the buyers in group-buying based combinatorial reverse auctions.     

Combinatorial auction under fuzzy environment

Combinatorial auction (CA) mechanism allows bundling of multiple items in packages, which can be solved through a clearing method termed as the winner determination problem (WDP). However, to date, there has yet to be a CA model that accounts for the fuzziness of bidders’ submitted prices. The imprecision in submitted prices is the result of the time gap between bid placement and winning bid announcement, which reflects the bidders’ expected values of the goods at the point of contract sale. Despite this common understanding, conventional CA modeling still treats the prices as deterministic. This causes a major shortcoming when an uncertain environment is assumed to be deterministic and solved through conventional WDP. This study shows that a fuzzy environment modeled via a deterministic WDP approach provides overly optimistic revenue for the auctioneer. A method of using possibilistic distributions of submitted prices to account for price uncertainty is proposed and formalized as Fuzzy Combinatorial Auction Winner Determination Problem (Fuzzy CA WDP). The difference in optimal solutions in deterministic WDP and fuzzy WDP reflects the amount of over estimation when a fuzzy situation is treated as though it is precise. It also reflects the information value when the uncertainty inherent in the fuzzy environment is resolved. Given that the information value is quantified in unit dollars, the fuzzy WDP approach allows the auctioneer to estimate its “true” revenue despite price uncertainties.     

蚁群优化算法在求解随机组合优化问题中的应用综述*

不确定条件下的优化问题更贴近真实世界环境,因而日益受到广泛关注。综述了蚁群优化在求解一组不确定条件下的组合优化问题,即随机组合优化问题方面的应用。首先介绍了不确定条件下组合优化问题的概念分类模型,给出了随机组合优化问题的一般定义;然后指出了其与求解传统确定性组合优化问题的不同之处,即目标函数的计算存在不确定性,并详细论述了目前解决方法的进展;最后分析了该领域值得重点关注的几个研究方向,并对其未来发展进行了展望。     

大规模分布式资源搜索技术研究进展*

针对分布式资源搜索技术及其分类的特点,分别从基于网格的搜索技术的穷举式、集中式、路由式,以及基于P2P系统的搜索技术的集中式、全分布式非结构化、混合式、全分布式结构化等几个方面,对当前研究的分布式资源搜索技术进行了归纳总结,并且对该研究领域需要解决的问题进行了总结,对进一步研究的方向进行了展望。     

产品设计方案费效权衡的随机机会约束规划模型

针对产品设计方案费效权衡中由于未考虑生产过程中不确定性因素影响而导致的权衡结果易产生偏差的问题, 提出将不确定优化理论引入产品设计方案费效权衡模型中。在对关键设计参数敏感性分析的基础上,将敏感性变量以及费用估算的偏差描述为随机变量,构建基于以产品设计方案费效权衡的随机机会约束规划模型,并采用嵌入蒙特卡洛模拟的遗传算法求解,得到考虑不确定因素影响的最优产品设计方案。最后以混凝土泵车为实例,验证了模型的有效性。研究表明,采用费效权衡随机机会约束规划模型得到的产品设计方案,更能反映生产实际,可以最大程度保证不确定条件下产品设计决策目标的实现。     

应急物资采购及代储服务交易的逆向组合拍卖机制设计

建立市场化的政企联合储备模式已经成为应急物资储备体系建设的重要方式.基于此,着眼于应急物资采购及代储服务的交易问题,设计一个逆向组合拍卖机制.在此拍卖机制中,政府是拍卖的买方兼委托人,企业是拍卖的卖方兼竞拍者,应急物资采购及代储服务是拍卖商品.首先,通过一个报童模型建立政府决策行为与拍卖活动之间的关系,并提出企业的投标策略;其次,建立最小化供需偏差和最大化供给数量的竞胜标决定模型;最后,提出一个符合实际背景的数值算例对拍卖机制进行模拟和验证.研究表明,所提出的逆向组合拍卖机制不仅具有经济效率,还能够促进政府一次性达成与多家企业在多个周期的合作.由此可见,运用拍卖机制解决应急物资政企联合储备的交易问题具备理论的优越性和现实的适用性.     

基于NSGA-II算法的认知无线电频谱分配

认知无线电中,频谱拍卖是解决动态频谱分配的有效方法,其主要目的是最大化所有主用户的收益。然而,主用户间的收益是存在冲突的,给拍卖算法的优化带来了困难。为此,提出一种新的拍卖方案,来解决获胜者确定问题(Winner Determination Problem, WDP)。在该方案中,动态频谱拍卖问题被建模成多背包问题,并通过非支配排序遗传算法II (NSGA-II)得到最终的解决方案。最后,仿真实验结果表明,就解决WDP问题而言,与贪心算法相比,NSGA-II算法有更好的表现。     

基于光伏预测的微电网能源随机优化调度

可再生能源的间歇性和负荷的随机性对微电网能源管理系统（ EMS）产生了巨大的挑战。在随机环境下的能源优化调度问题在微电网的研究中具有重要意义。以微电网中光伏发电系统的功率预测为基础,将光伏预测误差当做随机变量,建立了一种基于期望模型的能源随机优化调度模型。用Monte Carlo模拟方法生成了光伏发电预测误差的情景集,应用粒子群优化算法来解决随机优化调度模型。通过与确定性模型产生的调度方案相对比,证明了随机优化调度模型更加有效。     

流程工业配料过程的随机优化模型及求解算法

针对配料过程原料质量参数存在的不确定性,以原料消耗成本最小为优化目标,将不确定质量参数以随机数的形式引入质量指标约束中,建立了一种配料过程随机优化模型．考虑传统蒙特卡洛抽样方法的不足,采用一种更高效的Hammersley sequence sampling（HSS）技术,获得随机优化模型对应的期望值优化模型．将HSS技术用于遗传算法的种群初始化和交叉、变异操作,以保证种群分布的均匀性,实现随机优化问题的有效求解．工业应用实验结果表明,所提方法不仅能够有效降低原料的消耗成本,而且能够保证产品质量指标满足生产要求,优化结果具有较好的鲁棒性,为配料过程的随机优化控制提供了一个优化模式．     

Multiple task assignments for cooperating uninhabited aerial vehicles using genetic algorithms

A problem of assigning cooperating uninhabited aerial vehicles to perform multiple tasks on multiple targets is posed as a new combinatorial optimization problem. A genetic algorithm for solving such a problem is proposed. The algorithm allows us to efficiently solve this NP-hard problem that has prohibitive computational complexity for classical combinatorial optimization methods. It also allows us to take into account the unique requirements of the scenario such as task precedence and coordination, timing constraints, and trajectory limitations. A matrix representation of the genetic algorithm chromosomes simplifies the encoding process and the application of the genetic operators. The performance of the algorithm is compared to that of deterministic branch and bound search and stochastic random search methods. Monte Carlo simulations demonstrate the viability of the genetic algorithm by showing that it consistently and quickly provides good feasible solutions. This makes the real time implementation for high-dimensional problems feasible.     

A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service

On-time shipment delivery is critical for just-in-time production and quick response logistics. Due to uncertainties in travel and service times, on-time arrival probability of vehicles at customer locations can not be ensured. Therefore, on-time shipment delivery is a challenging job for carriers in congested road networks. In this paper, such on-time shipment delivery problems are formulated as a stochastic vehicle routing problem with soft time windows under travel and service time uncertainties. A new stochastic programming model is proposed to minimize carrier’s total cost, while guaranteeing a minimum on-time arrival probability at each customer location. The aim of this model is to find a good trade-off between carrier’s total cost and customer service level. To solve the proposed model, an iterated tabu search heuristic algorithm was developed, incorporating a route reduction mechanism. A discrete approximation method is proposed for generating arrival time distributions of vehicles in the presence of time windows. Several numerical examples were conducted to demonstrate the applicability of the proposed model and solution algorithm.     

Solving multiple scenarios in a combinatorial auction

As part of its social policy, the government of Chile provides more than 1.8 million meals daily to public schoolchildren under the authority of Junta Nacional de Auxilio Escolar y Becas (JUNAEB), the state agency responsible for the program, at an annual cost of 360 million dollars. The service is provided by private firms chosen through an annual public auction. In order to capture economies of scale, a combinatorial auction design is implemented, allowing suppliers to bid on different sets of geographical units within the country. The bid evaluation process must solve multiple scenarios of a difficult combinatorial optimization model. To date, more than 2 billion dollars have been awarded under this methodology. In this paper, we describe the 2006 auction process and report that solution times can be significantly improved if the scenarios are solved in an appropriate order and the optimal solution to one scenario is employed as the initial solution of another. Results reflecting these improvements are given for real instances of the 2006 auction.     

基于多目标两阶段随机规划方法的电热联合系统调度

针对电热综合能源系统由于风电出力的随机性和波动性而难以有效调度的问题,提出了以成本最小化和弃风最小化为目标的一种多目标两阶段随机规划方法(multi-objective and two-stage stochastic programming,MOTSP),其中采用两阶段的随机规划模型对成本最小化部分进行建模分析,第一阶段以火电机组的启停成本为调度目标,第二阶段以机组运行成本为调度目标。最后采用多目标算法NSGA-Ⅱ中对解的筛选机制求解随机规划问题。该方法利用高斯分布描述负荷和风力发电预测误差来解决风电出力的不确定性,采用蒙特卡罗方法生成随机场景,并采用反向缩减技术对场景进行削减。仿真结果表明,所提的MOTSP算法比其他多种智能算法的解集更均匀广泛,收敛性更好,能够最大限度地减少弃风并使机组运营成本最小。     

A metaheuristic framework for stochastic combinatorial optimization problems based on GPGPU with a case study on the probabilistic traveling salesman problem with deadlines

In this work we propose a general metaheuristic framework for solving stochastic combinatorial optimization problems based on general-purpose computing on graphics processing units (GPGPU). This framework is applied to the probabilistic traveling salesman problem with deadlines (PTSPD) as a case study. Computational studies reveal significant improvements over state-of-the-art methods for the PTSPD. Additionally, our results reveal the huge potential of the proposed framework and sampling-based methods for stochastic combinatorial optimization problems.     

Scheduling Multi-Mode Projects under Uncertainty to Optimize Cash Flows: A Monte Carlo Ant Colony System Approach

Project scheduling under uncertainty is a challenging field of research that has attracted increasing attention. While most existing studies only consider the single-mode project scheduling problem under uncertainty, this paper aims to deal with a more realistic model called the stochastic multi-mode resource constrained project scheduling problem with discounted cash flows (S-MRCPSPDCF). In the model, activity durations and costs are given by random variables. The objective is to find an optimal baseline schedule so that the expected net present value (NPV) of cash flows is maximized. To solve the problem, an ant colony system (ACS) based approach is designed. The algorithm dispatches a group of ants to build baseline schedules iteratively using pheromones and an expected discounted cost (EDC) heuristic. Since it is impossible to evaluate the expected NPV directly due to the presence of random variables, the algorithm adopts the Monte Carlo (MC) simulation technique. As the ACS algorithm only uses the best-so-far solution to update pheromone values, it is found that a rough simulation with a small number of random scenarios is enough for evaluation. Thus the computational cost is reduced. Experimental results on 33 instances demonstrate the effectiveness of the proposed model and the ACS approach.     

Progressive Latin Hypercube Sampling: An efficient approach for robust sampling-based analysis of environmental models

Efficient sampling strategies that scale with the size of the problem, computational budget, and users’ needs are essential for various sampling-based analyses, such as sensitivity and uncertainty analysis. In this study, we propose a new strategy, called Progressive Latin Hypercube Sampling (PLHS), which sequentially generates sample points while progressively preserving the distributional properties of interest (Latin hypercube properties, space-filling, etc.), as the sample size grows. Unlike Latin hypercube sampling, PLHS generates a series of smaller sub-sets (slices) such that (1) the first slice is Latin hypercube, (2) the progressive union of slices remains Latin hypercube and achieves maximum stratification in any one-dimensional projection, and as such (3) the entire sample set is Latin hypercube. The performance of PLHS is compared with benchmark sampling strategies across multiple case studies for Monte Carlo simulation, sensitivity and uncertainty analysis. Our results indicate that PLHS leads to improved efficiency, convergence, and robustness of sampling-based analyses.     

A multidimensional procurement auction for trading composite services

Recently, static value chains have gradually been giving way to highly agile service value networks. This involves novel economic and organizational challenges. Added value for customers is created by feasible compositions of distributed service components. This work focuses on the design of a multidimensional procurement auction for trading service compositions and the analysis of strategies for service providers that participate in the procurement process. The mechanism implementation is incentive-compatible, so that it results in an equilibrium in which revealing the true multidimensional type (quality of service and valuation) is a weakly-dominant strategy for all service providers. Due to combinatorial restrictions imposed by the underlying graph topology, the winner determination problem can be solved in polynomial time, in contrast to computationally-intractable combinatorial auctions which cannot be solved this way. Furthermore, we provide a simulation-based analysis based on a reinforcement learning model of bundling and unbundling strategies of service providers that participate in the auction. Based on our results we discuss strategic recommendations for service providers depending on how they are situated within the network.     

A Benders decomposition for the location-allocation and scheduling model in a healthcare system regarding robust optimization

The hospital location and service allocation is one of the most important aspects of healthcare systems. Due to lack of studies on covering location-allocation and scheduling problems with respect to the uncertain budget, this paper develops a bi-objective hybrid model to locate hospitals and allocate machines and services scheduled. The costs of establishing facilities are assumed to be uncertain, while a robust counterpart model is employed to overcome the uncertainty. Covering the demand of each service is limited as well. Moreover, hospitals have a limited space to the specialized equipment like CT scan and MRI machines, while there is a cost constraint on hospitals and the specialized equipment. The aim of this paper is to find a near-optimal solution including the number of hospitals and the specialized equipment, the location of hospitals, the assignment of demand of each service and the specialized equipment to hospitals, the determination of allowable number of each service of hospitals, the determination of demand that should be transferred from one hospital to another (patient transfer), and schedule services. As the proposed model, minimizing the total costs and the completion time of demand simultaneously, is an NP-hard problem, it is impossible to solve its large-scale version with exact methods in a reasonable time. Thus, a hybrid algorithm including simulated annealing optimization and the Benders decomposition is employed to solve it. The CPLEX optimizer verifies the presented algorithm to solve the proposed model. The sensitivity analysis is performed to validate the proposed robust model against of uncertain situations while the Monte Carlo simulation is used to analyze the quality and the robustness of solutions under uncertain situations. The results show that the uncertainty used in the proposed model properly formulates real-world situations compared to the deterministic case. Finally, the contributions and the future research are presented.