An application of multi-objective stochastic optimisation to structural design

An application to structural design of an innovative method for optimising stochastic systems is introduced in the paper. The proposed method allows one to carry out both the multi-objective optimisation of a structural element and to improve the robustness of the design. The innovative method is rather general. To show its effectiveness, an ideal cantilever has been designed in order to minimise both mass and deflection. The cantilever is shaped as a beam and is subject to random loads acting at its free end. The beam geometrical dimensions and material properties vary stochastically due to manufacturing tolerances. Different beam cross sections and two different materials (aluminium alloy and steel) have been considered. From the optimisation, it turned out that the optimal solutions are the O and the I beam, depending on the required lightness and stiffness. Compared to steel, aluminium alloy beams have provided better (or at least equal) performance.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

Finite Horizon Minimax Optimal Control of Nonlinear Continuous Time Systems with Stochastic Uncertainty

This paper develops a general continuous-time stochastic framework for robustness analysis and robust control synthesis. We consider a stochastic minimax optimization problem for general stochastic uncertain systems. A general method is presented for converting problems of performance analysis or controller synthesis into unconstrained optimization problems.     

考虑混合型号托盘的托盘共用调度随机规划模型

如何将托盘科学地在系统内调度是目前托盘共用系统管理者们亟待解决的问题。面对各类参数的随机性和多种多样的托盘,管理者很难仅凭经验做出科学的决策。利用随机机会约束规划的方法,构建了考虑混合型号托盘的托盘共用系统调度随机规划模型,使用确定性等价转化的方法将机会约束转化为了其确定等价形式,通过算例进行了数值求解和分析,验证了模型的有效性,提出了决策策略建议。     

Optimal apparel supplier selection with forecast updates under carbon emission taxation scheme

Carbon emission tax is an important measure for sustainable supply chain management. This paper studies an optimal supplier selection problem in the fashion apparel supply chain in the presence of carbon emission tax. We consider the scenario in which there are multiple suppliers in the market. In the basic model, each supplier offers a supply lead time and a wholesale pricing contract to the fashion retail buyer. For the fashion retail buyer, the supplier which offers a shorter lead time allows it to postpone the ordering decision with updated and better forecast, and also a smaller carbon tax. However, the wholesale price is usually larger. We propose a two-phase optimal supplier selection scheme in which phase one filters the inferior suppliers and phase two helps to select the best supplier among the set of non-inferior suppliers by multi-stage stochastic dynamic programming. The impacts brought by different formats of carbon emission tax are explored. Finally, we examine an extended model in which there is a local supplier who offers a buyback contract and accepts product returns. Insights from the analysis are discussed.     

不确定条件下应急资源布局的鲁棒双层优化模型

针对非常规突发事件中应急资源布局问题,在受灾点需求不确定和应急救援过程分为多个阶段的情景下,建立了省市两级应急储备仓库定位和物资配置的鲁棒双层规划模型。运用相对鲁棒优化方法,将上述具有不确定性系数的双层规划模型转化为从者无关联的确定性线性双层规划,提出了一种混合遗传算法进行求解,实现了省市两级应急资源布局的协同优化。通过实例验证了模型及算法的可行性和有效性。     

动态多项目选择计划管理及其免疫优化决策

针对资源受限情况下动态多项目选择计划管理问题,探讨其数学模型,并设计免疫优化算法对其求解。算法设计中,分别引入基因块的随机漂移与确定性漂移两种变异方式,以及个体的亲和选择与激励选择两种选择方案。最后,数值实验验证了模型的合理性以及各算法的有效性。     

供应商选择的双层规划模型及求解分析

为了促使供应商在降低产品成本的同时,提高服务质量,提出了利用双层规划建立供应商选择模型。上层规划以制造企业的采购费用最小为目标,下层以选择的供应商的服务质量最大为目标。其中,下层规划中供应商的服务质量用综合评价得分体现先计算出各影响因素的权重,乘以标准判断矩阵得出各供应商的综合得分。最后,结合模型特点设计了双层迭代的算法,并结合实例验证了模型和算法的有效性。     

A Pricing Mechanism for Resource Management in Grid Computing

We consider the problem of efficient resource allocation in a grid computing environment. Grid computing is an emerging paradigm that allows the sharing of a large number of a heterogeneous set of resources. We propose an auction mechanism for decentralized resource allocation. The problem is modeled as a multistage stochastic programming problem. Convergence of the auction allocations to the social optimum is established. Numerical experiments illustrate the efficacy of the method.     

Mathematical Programming in Data Mining

Mathematical programming approaches to three fundamental problems will be described: feature selection, clustering and robust representation. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. This creates a lean model that often generalizes better to new unseen data. Computational results on real data confirm improved generalization of leaner models. Clustering is exemplified by the unsupervised learning of patterns and clusters that may exist in a given database and is a useful tool for knowledge discovery in databases (KDD). A mathematical programming formulation of this problem is proposed that is theoretically justifiable and computationally implementable in a finite number of steps. A resulting k-Median Algorithm is utilized to discover very useful survival curves for breast cancer patients from a medical database. Robust representation is concerned with minimizing trained model degradation when applied to new problems. A novel approach is proposed that purposely tolerates a small error in the training process in order to avoid overfitting data that may contain errors. Examples of applications of these concepts are given.