On the risk-averse optimization of service level in a supply chain under disruption risks

The worst-case optimization of service level in the presence of supply chain disruption risks is considered for the two different service levels measures: the expected worst-case demand fulfillment rate and the expected worst-case order fulfillment rate. The optimization problem is formulated as a joint selection of suppliers and stochastic scheduling of customer orders under random disruptions of supplies. The suppliers are located in different geographic regions and the supplies are subject to random local and regional disruptions. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional service-at-risk as a worst-case service level measure. The risk-averse solutions that optimize the worst-case performance of a supply chain are compared for the two service level measures. In addition, to demonstrate the impact on the cost in the process of optimizing the worst-case service level, a joint optimization of expected cost and conditional service-at-risk using a weighted-sum approach is considered and illustrated with numerical examples. The findings indicate that the worst-case order fulfillment rate shows a higher service performance than the worst-case demand fulfillment rate. Maximization of the expected worst-case fraction of fulfilled customer orders better mitigates the impact of disruption risks. The supply portfolio is more diversified and the expected worst-case fraction of fulfilled orders is greater for most confidence levels. Finally, the results clearly show that worst-case service level is in opposition to cost.     

Distributionally robust optimization for engineering design under uncertainty

This paper addresses the challenge of design optimization under uncertainty when the designer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out-of-sample performance (ie, performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design problem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design problem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample-average approximation and multiobjective optimization incorporating a risk reduction objective. In contrast with the multiobjective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather specifies a so-called ambiguity set of possible distributions and optimizes against the worst-case distribution in this set. Our results show that the DRO designs, in some cases, significantly outperform those designs found using the sample-average or the multiobjective approach.     

Optimal design and control of a reactive distillation system

This article presents the design and control of a reactive distillation system utilizing recent advances in mixed integer dynamic optimization. A high fidelity dynamic model is used to predict the behavior of the process under time-varying disturbances. Design and control decisions, involving both discrete and continuous variables, are simultaneously optimized leading to a more economically attractive and better controlled system than that obtained by following a sequential optimization approach. It is shown that the resulting design and control scheme can guarantee feasible operation under bounded uncertainty at a minimum total average cost, representing ～17% savings over the original design.     

Approaching maximum-likelihood performance with reduced complexity for a double space?time transmit diversity system

A reduced-complexity detector approaching maximum-likelihood (ML) detection performance is presented for the double space-time transmit diversity system. The proposed scheme exploits both the special structure of equivalent channel matrix and decision-feedback detection. This accounts for accomplishing near-ML or ML performance with significantly relieved computational loads. Moreover, to moderate the average complexity, several distance metric selection criteria are proposed. We can control performance and computational savings according to different distance metric selection rules. Numerical results show that the proposed detector requires significantly fewer computations than that of the Schnorr-Euchner sphere-decoding algorithm in terms of both the worst-case and the average complexity.     

Worst-Case Optimal Static Output Feedback for Uncertain Systems

This paper proposes a worst-case optimal approach to the synthesis of a static output feedback for a linear, time-invariant, multivariable system depending on uncertain parameters which nonlinearly affect a given state-space model. The aim is to seek an output-to-input feedback matrix that robustly stabilizes the closed-loop system while minimizing, over the uncertain parameter domain, the (worst-case) maximum of a composite quadratic index. The emerging minimax problem is shown to be exactly equivalent to a semi-infinite optimization problem for which an estimate of a global solution is obtained through a genetic/interval algorithm. This is a hybrid algorithm that combines a genetic algorithm (at the upper level) with an interval procedure (acting at the lower level). Computational results for a two-input two-output (TITO) system are included.     

Multi-product inventory planning with downward substitution, stochastic demand and setup costs

In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective (98.8% on average) and can handle industrial-sized problems efficiently. We also provide several new qualitative insights on issues such as the effect of demand variance and cost parameters on the optimal number of products setup, the amount produced or inventoried, and the benefits of allowing substitution.     

Minimization of acquisition and operational costs in horizontal material handling system design

This paper considers the problem of minimizing the fixed cost of acquiring material handling transporter:; and the operational cost of material transfer in a manufacturing system. This decision problem, which arises during manufacturing facility design, is modeled using an integer programming formulation. Since the problem is NP-complete, two efficient heuristics are developed to solve it. Computational complexity, worst-case performance analysis, and extensive computational tests are provided for both heuristics. The results indicate that the proposed methods are well suited for large-scale manufacturing applications.     

Robust Controller Design of a Dual-Stage Disk Drive Servo System With an Instrumented Suspension

This paper proposes a robust track-following controller design method for a dual-stage servo system in magnetic hard disk drives (HDDs). The method formulates the problem of minimizing track misregistration (TMR) in the presence of plant uncertainty and variation as a multiobjective optimization problem. Tracking error minimization is naturally formulated as an$H_2$norm minimization problem, while the robust stability issue is addressed by some$H_infty$norm bounds. This mixed$H_2/H_infty$control problem can then be formulated as a set of linear matrix inequalities (LMIs) and be efficiently solved through convex optimization algorithms. To enhance the system's tracking performance and stability robustness, the method explicitly takes attenuation of airflow-excited suspension vibration into consideration by an inner loop fast rate damping and compensation controller that utilizes the output of a strain gauge sensor on the suspension surface. Analysis and simulation show that a system designed by this method can achieve good tracking performance while still keeping stability robustness to plant variation and high-frequency spillover.     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design—determining well placement, number of fracturing stages, and fracture lengths—is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.     

集中交互式多传感器联合概率数据互联算法

为了解决杂波环境下多传感器多机动目标跟踪问题,本文提出了一种集中交互式多传感器联合概率数据互联算法。本文提出的算法首先应用广义S-D分配的规则对每个传感器送来的观测数据进行排列组合,并对所有的测量组合进行有效性判断,然后应用数据压缩的方法将每个有效量测组合压缩成一个等效量测点并根据每个等效量测点的联合似然函数计算其联合互联概率,最后在此基础上应用交互式多模型算法的思想以处理目标出现机动的问题。本文最后给出了该算法的分析,仿真结果表明,本文算法能够很好地解决杂波环境下多传感器多机动目标的跟踪问题。     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

Improving sensitivity and selectivity of SnO/sub 2/ gas sensors by temperature variation

A microcontroller-based gas-sensing system is presented in this paper. The analysis presented here exploits the differences in the steady-state performance of SnO/sub 2/ gas sensors at different operating temperatures and the potential use of such differences for improving their selectivity and sensitivity. Sets of experimental measurements of sensitivity versus temperature are used for the detailed presentation of the proposed approach. The results indicate that selective identification and rather accurate measurement of a mixture of CH/sub 4/ and CO gases are quite possible. Finally, a microcontroller-based configuration is presented as a working example of a small-size implementation, which may offer measurements of improved sensitivity and selectivity along with high accuracy and reliability.     

Factor-based robust index tracking

We consider a robust optimization approach for the problem of tracking a benchmark portfolio. A strict subset of assets are selected from the benchmark such that the expected return is maximized subject to both risk and tracking error limits. A robust version of the Fama-French 3 factor model is developed whereby uncertatiny sets for the expected return and factor loading matrix are generated. The resulting model is a mixed integer second-order conic problem. Computational results in tracking the S&P 100 out of sample show that the robust model can generate tracking portfolios that have better tracking error and Sharpe ratio than those generated by the nominal model.     

Redundancy allocation for series-parallel systems using a max-min approach

The redundancy allocation problem is formulated with the objective of maximizing the minimum subsystem reliability for a series-parallel system. This is a new problem formulation that offers several distinct benefits compared to traditional problem formulations. Since time-to-failure of the system is dictated by the minimum subsystem time-to-failure, a logical design strategy is to increase the minimum subsystem reliability as high as possible, given constraints on the system. For some system design problems, a preferred design objective may be to maximize the minimum subsystem reliability. Additionally, the max-min formulation can serve as a useful and efficient surrogate for optimization problems to maximize system reliability. This is accomplished by sequentially solving a series of max-min subproblems by fixing the minimum subsystem reliability to create a new problem. For this new formulation, it becomes possible to linearize the problem and use integer programming methods to determine system design configurations that allow mixing of functionally equivalent component types within a subsystem. This is the first time the mixing of component types has been addressed using integer programming. The methodology is demonstrated on three problems.     

Robust multi-objective optimization for energy production scheduling in microgrids

In order to achieve better economic and environmental benefits of microgrids (MGs) under multiple uncertainties in renewable energy resources and loads, a novel energy production scheduling method is proposed based on robust multi-objective optimization with minimax criterion. Firstly, a mixed integer minimax multi-objective formulation is developed to capture uncertainties as well as minimize economic and environmental objectives. Secondly, the primal problem is decomposed into a bi-level optimization problem, which attempts to seek robust scheduling scheme set under the worst-case realization of uncertainties in a multi-objective framework. Finally, a hierarchical meta-heuristic solution strategy, including multi-objective cross entropy algorithm and δ+ indicator, is designed to solve the reconstructed problem. Numerical results demonstrate that the proposed scheduling method can effectively attenuate the disturbance of uncertainties as well as reduce energy costs and emissions, as compared with single-objective robust optimization and multi-objective optimization scheduling approaches. This study could offer useful insights which help decision-makers balance robustness and comprehensive benefits in the operation of MGs.     

On the robust decision-making in a supply chain under disruption risks

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.     

Design of a bias magnetic system of a magnetostrictive sensor for flexural wave measurement

We report on an investigation of the voltage output from a magnetostrictive sensor for the measurement of elastic flexural waves in a cylindrical steel waveguide. Since the sensor performance is strongly influenced by the bias magnetic field, the bias field optimization is one of the most critical issues in the design of magnetostrictive sensors. For a magnetic system consisting of a yoke and an electromagnet, we formulate a method for optimizing yoke topology in order to maximize the sensor output. Both linear and nonlinear magnetization relations are considered in our analysis. For the verification of the performance of the proposed sensors, we conducted several experiments involving flexural waves to assess the performance of the optimized sensors, and we analyze their results here.     

Statistical approach for detection and localization of a fluorescing mouse tumor in Intralipid

We present a method for detecting and localizing a fluorescing tumor obscured underneath several millimeters of a multiply scattering, homogeneous medium from fluorescence measurements made above the surface. Using a statistical model of the measurement system, we develop approaches for detection by use of a binary hypothesis testing approach and localization by use of maximum-likelihood estimation. We also compute the probability of tumor detection and the Cramér-Rao lower bound for the localization estimate error, which are performance metrics that could potentially be optimized in an experimental design. We validate the methods in an experimental study involving an excised mouse tumor tagged with a new folate-indocyanine dye and obscured under a tissue-simulating lipid suspension.     

多传感器多目标粒子滤波算法

为了能够有效解决非线性、非高斯环境中多传感器多目标跟踪问题,提出了一种基于粒子滤波的多传感器联合概率数据互联粒子滤波算法(MJPDAP)。该算法应用广义S-D分配的规则对每个传感器送来的观测数据进行排列组合以形成等效量测点,并计算所有等效量测点的联合似然函数。在此基础上,结合联合概率数据互联(JPDA)的思想计算各个粒子权值,以获得最终的跟踪结果。仿真结果表明,与单传感器联合概率数据互联粒子滤波算法(SJPDAP)相比,该算法位置跟踪精度能提高20m左右。