Robust optimization

This paper proposes a new technique to analyze the electricity and transport sectors within a single integrated framework to realize an environmentally and economically sustainable integration of plug-in hybrid electric vehicles (PHEVs) into the electric grid, considering the most relevant planning uncertainties. The method is based on a comprehensive robust optimization planning that considers the constraints of both the electricity grid and the transport sector. The proposed model is justified and described in some detail, applying it to the real case of Ontario, Canada, to determine Ontario's grid potential to support PHEVs for the planning horizon 2008-2025.

This paper presents a phrase-based speech translation system that combines phrasal lexicon, language, and acoustic model features in a loglinear model. Automatic speech recognition and machine translation are coupled by using large word lattices as the input for translation. For the first time, all features are directly integrated into the decoding process. The feature weights are iteratively optimized for an objective error measure. We prove that acoustic recognition scores of the recognized words in the lattices together with a source language model score positively and significantly affect the translation quality. We show the advantage of using loglinear model combination for a robust optimization of scaling factors. We report consistent improvements compared with translations of single best recognition output on an Italian-to-English translation task. First encouraging results were also obtained on a large vocabulary task of translating European parliamentary speeches.

A methodology is presented to include financial risk management in the framework of two-stage stochastic programming for planning under uncertainty. A known probabilistic definition of financial risk is adapted to be used in this framework and its relation to downside risk is analyzed. Using these definitions, new two-stage stochastic programming models that manage financial risk are presented. Computational issues related to these models are also discussed.

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.

While investing in foreign assets may bring additional benefits in terms of risk diversification, it may also expose the portfolio to a further source of risk derived from changes in the value of the foreign currencies. Hedging strategies for international portfolios have usually focused on the use of forward contracts to mitigate the currency risk. We propose an alternative formulation aimed at the reduction of the overall portfolio risk by assuming the returns are uncertain and maximizing the portfolio return for the worst possible outcome of the returns. This technique known as robust optimization provides a first guarantee on the portfolio value thanks to the non-inferiority property. We further complement our approach with forward contracts on the foreign exchange rates and options on the assets. Because the total return on any asset will be the product of its local return and currency return, the models proposed are bilinear and non convex. A reformulation of both the uncertainty set and the objective function as a semidefinite problem will yield an approximate tractable model. We compare the hedging alternatives proposed with simulated and historical market data and conclude on their relative benefits.

The term "robust optimization" is quite popular, and the descriptor "robust" so commonly applied in the water resources literature that its specific meaning, and its implications for model results, have become elusive. We here provide a brief summary of the applications of robust optimization to water resources planning and management problems in the past 15 years. We describe and demonstrate concerns regarding Mulvey et al.'s (1995) multi-objective approach to robust optimization. We evaluate the idea of minimization of the expected costs as the primary design criterion by contrasting solutions to a simple robust optimization problem in terms of common performance measures, including reliability, vulnerability, and sustainability.

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.

Owning to similar business nature, it should be possible to directly migrate successful airline revenue management techniques to the hotel domain. However, one of the salient di erences between airlines and hotels is rarely highlighted-the network structure of length of stay or the displacement e ect. The hotel patrons go from a ÿrst stay-over night to a last stay-over night in consecutive night stays. The arrival demands for multi-night stays and the lengths of stay are stochastic in nature. In this paper, we propose a network optimization model for hotel revenue management under an uncertain environment. The network optimization is in a stochastic programming formulation so as to capture the randomness of the unknown demand (unknown number of arrivals and length of stays). A novel approach of robust optimization techniques for stochastic programming is applied to solve the problem. We also discuss the strategies for hotel management to take into account of risk trade-o ; di erent pricing policies; cancellations and no-show; early check-outs; extended stay and over-booking are discussed. We showed that our proposed model can be modiÿed to adopt these strategic considerations.

We investigate a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network to support all possible traffic matrices while minimizing the total reservation cost. The problem admits several versions depending on the desired topology of the reserved links, and the nature of the ...

After having described the development of new models for the energy equipment used in industrial utility systems in the first part of this paper, this second part explains how such a modelling framework has been developed into an integrated methodology for the design and optimization of utility plants that exploits the flexibility of these systems. The different types of problems to be addressed (i.e., grassroots design, retrofit and operational) are identified in terms of their major issues and tradeoffs, giving emphasis to the fact that these tasks require a robust optimization procedure to handle industrial cases. Mechanical driver selection is incorporated in the proposed strategy. Several examples demonstrate the applicability and the potential of the suggested approach to provide significant economic benefits when applied to industrial problems.

Portfolio optimization is to build your portfolio in such a way that you maximize potential returns from investments while still not exceeding the amount of risk you’re willing to carry. Creating a balanced portfolio with many different investments, such as stocks, bonds, mutual funds, etc., is the best way to spread out assets to maintain a riskto-reward ratio. The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution towards one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-CVaR problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation

Esta tesis aborda el Problema Árbol de Expansión con incertidumbre intervalar en los costos,utilizando el criterio de Min-Max Regret. Varios algoritmos son implementados, tanto exactos como heurísticos. Con respecto a los algoritmos exactos, se implementan Descomposición de Benders y Branch and Cut , ambos incluyen variantes. Branch and Cut logra superar al resto de los algoritmos, incluso obteniendo gaps menores a un 10%, para 100 nodos, en un conjunto de instancias. En relación a las heurísticas, se desarrolla una heurística constructiva, la que utiliza la información de los intervalos,a diferencia de todas las aproximaciones de la literatura. Se proponen metaheurísticas basadas enBúsqueda Local (Mejora iterativa, Simulated Annealing
y GRASP), se obtienen gaps de calidad,incluso para las instancias más complejas.Se realiza una comparación desde un punto de vista experimental, mostrando un buen desempeño, pues se igualan o mejoran los resultados existentes.

This paper focuses on the design of a distribution network problem in a three-tiered supply chain under uncertainty. The objective is to determine the optimal number, locations and capacities of plants and warehouses to minimize the overall network costs over a variety of economic growth scenarios. For this purpose, a mixed integer linear programming model is extended in a robust optimization framework and then three heuristic approaches based on genetic and memetic algorithms and a mathematical programming approach are used to solve this problem. The effectiveness of the proposed heuristics and the trade-off between model robustness and solution robustness is investigated and directions for further researches are presented.

Strategies, models, and algorithms facilitating such models are explored to provide transportation network managers and planners with more flexibility under uncertainty. Network design problems with non-stationary stochastic OD demand are formulated as real option investment problems and dynamic programming solution methodologies are used to obtain the value of flexibility to defer and re-design a network. The design premium is shown to reflect the opportunity cost of committing to a “preferred alternative” in transportation planning. Both network option and link option design problems are proposed with solution algorithms and tested on the classical Sioux Falls, SD network. Results indicate that allowing individual links to be deferred can have significant option value. A resource relocation model using non-stationary stochastic variables as chance constraints is proposed. The model is applied to air tanker relocation for initial attack of wildfires in California, and results show that the flexibility to switch locations with non-stationary stochastic variables providing 3-day or 7-day forecasts is more cost-effective than relocations without forecasting. Due to the computational costs of these more complex network models, a faster converging heuristic based on radial basis functions is evaluated for continuous network design problems for the Anaheim, CA network with a 31-dimensional decision variable. The algorithm is further modified and then proven to converge for multi-objective problems. Compared to other popular multi-objective solution algorithms in the literature such as the genetic algorithm, the proposed multi-objective radial basis function algorithm is shown to be most effective. The algorithm is applied to a flexible robust toll pricing problem, where toll pricing is proposed as a strategy to manage network robustness over multiple regimes of link capacity uncertainty. A link degradation simulation model is proposed that uses multivariate Bernoulli random variables to simulate correlated link failures. The solution to a multi-objective mean-variance toll pricing problem is obtained for the Sioux Falls network under low and high probability seasons, showing that the flexibility to adapt the Pareto set of toll solutions to changes in regime – e.g. hurricane seasons, security threat levels, etc – can increase value in terms of an epsilon indicator.

An extensive study of robust and optimal tuning of PID controllers for stable non-oscillating plants is presented. It is built on a set of well defined criteria related to output performance, stability margins and control activity. Different interesting properties of the closed loop systems are observed. A set of simple tuning rules is based on these observations. These rules are compared to a couple of well established tuning methods and are shown to give well competitive results, especially when simplicity, low control activity and high-frequency robustness are emphasized. Derivative action is shown to improve performance significantly compared to PI control, with equal stability margin and a moderate increase of control activity, for most plants, including those with significant time delay.

Designing a production process normally is involved with some important constraints such as uncertainty, trade-off between production costs and quality, customer's expectations and production tolerances. In this paper, a novel multi-objective robust optimization model is introduced to investigate the best levels of design variables. The primary objective is to minimize the production cost while increasing robustness and performance. The response surface methodology is utilized as a common approximation model to fit the relationship between responses and design variables in the worst-case scenario of uncertainties. The target mean ratio is applied to ensure the quality of the process by providing the robustness for all types of quality characteristics and with a trade-off between variability and deviance from the ideal point. The Lp metric method is used to integrate all objectives in one overall function. In order to estimate target value of the quality loss by considering production tolerances, the process capability ratio () is applied. At the end, a numerical chemical mixture problem is served to show the applicability of the proposed method.

Multi-Airport Systems (MAS), or Metroplexes, serve air traffic demand in cities with two or more airports. Due to the spatial proximity and operational interdependency of the airports , Metroplex airspaces are characterized by high complexity, and current system structures fail to provide satisfactory utilization of the available airspace resources. In order to support system-level design and management towards increased operational efficiency in such systems, an accurate depiction of major demand patterns is a prerequisite. This paper proposes a framework for the robust identification of significant air traffic flow patterns in Metroplex systems, which is aligned with the dynamic route service policy for the effective management of Metroplex operations. We first characterize deterministic demand through a spatio-temporal clustering algorithm that takes into account changes in the traffic flows over the planning horizon. Then, in order to handle uncertainties in the demand, a Distributionally Robust Optimization (DRO) approach is proposed, which takes into account demand variations and prediction errors in a robust way to ensure the reliability of the demand identification. The DRO-based approach is applied on pre-tactical (i.e. one-day planning) as well as operational levels (i.e. 2-h rolling horizon). The framework is applied to Time Based Flow Management (TBFM) data from the New York Metroplex. The framework and results are validated by Subject Matter Experts (SMEs).

Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.

With the expansion of electric power systems, the size and complexity of the network is increased. One of the most important drawbacks of network expansion is the reduction in the damping torque of the whole system. The lack of damping torque can lead to fluctuations and instability in the power system. With regard to this problem, power system stabilizers (PSSs) have been widely utilized to improve power system stability. However, due to some drawbacks of the conventional PSSs, the need for finding a better substitution still remains. Therefore, in this paper, the application of a hybrid controller based on the coordination of PSS with static synchronous compensator to improve dynamic stability of a two area multi-machines electric power system is presented, and this supplementary stabilizer signal based on STATCOM is incorporated.

Abstrak—Travelling Salesman Problem (TSP) merupakan permasalahan klasik dalam ilmu komputer. Dengan kemajuan teknologi, perhitungan rute terpendek untuk menyelesaikan TSP bukan hanya diperhitungkan, tetapi juga dapat dikomputasikan agar didapatkan hasil yang akurat dalam waktu yang relatif singkat. Pekan Paralimpiade Nasional (Peparnas) adalah turnamen olahraga tingkat nasional bagi atlet penyandang disabilitas di Indonesia. Pada tahun 2016, Jawa Barat menjadi tuan rumah pelaksanaan PON XIX dan Peparnas XV. Lokasi pertandingan Peparnas XV seluruhnya berada di Kota Bandung. Kunjungan lokasi pertandingan seyogyanya dilakukan oleh Ketua Pengurus Besar turnamen, yaitu Gubernur Jawa Barat. Kondisi dalam melakukan kunjungan ke setiap lokasi pertandingan selama hari pertandingan memenuhi aturan dalam TSP. Saat melakukan kunjungan dapat terjadi ketidakpastian, yang berhubungan dengan jarak tempuh yang disebabkan berbagai faktor. Ketidakpastian dapat diselesaikan dengan optimisasi robust. Dalam penelitian ini, aplikasi dikembangkan untuk mampu memberikan rute dengan jarak terpendek dengan menggunakan optimisasi robust dan metode branch and bound. Set ketidakpastian optimisasi robust yang digunakan dalam penelitian ini adalah ketidakpastian kotak. Pengembangan aplikasi dilakukan dengan menggunakan metode waterfall. Dengan aplikasi yang telah berhasil dikembangkan dengan bahasa pemrograman C#, mampu dihasilkan rute terpendek dan jarak yang perlu ditempuh. Nilai yang diperoleh dapat dipergunakan sebagai bahan pengambilan keputusan dalam melakukan kunjungan ke lokasi pertandingan selama pelaksanaan Peparnas. Kata kunci— ketidakpastian kotak; Kota Bandung; metode branch and bound; metode waterfall; optimisasi robust; Peparnas XV; travelling salesman problem. Abstract—Traveling Salesman Problem (TSP) is a classic problem in computer science. With advances in technology, the calculation of the shortest route to resolve TSP is not only to be calculated, but can also be computed in order to obtain accurate results in a relatively short time. National Paralympic Week (Peparnas) is a national-level sports tournament for athletes with disabilities in Indonesia. In 2016, West Java hosted the PON XIX and Peparnas XV. Venues of Peparnas XV all located in the city of Bandung. Venue visits should be conducted by the Chairman Board of the tournament, which is the Governor of West Java. The conditions of the visits to each venue during the week meet the problem of TSP. During a visit uncertainties can be happened, related to mileage caused by various factors. Uncertainty can be solved with robust optimization. In this study, the application was developed to be able to provide shortest route by using robust optimization and branch and bound method. Uncertainty set in robust optimization which is used in this study is the box uncertainty. Application development is done by using waterfall method. With applications that have been successfully developed with C# programming language, it is able to produce the shortest route and the distance that needs to be taken. The values obtained can be used as a part in the decision-making conduct a site visit during Peparnas. Kata kunci— Bandung City, box uncertainty, branch and bound method, robust optimization, Peparnas XV, travelling salesman problem, waterfall method. I. LATAR BELAKANG Travelling Salesman Problem (TSP) merupakan permasalahan klasik dalam ilmu komputer. Masalah ini tidak hanya menarik dalam bidang ilmu komputer tetapi juga dalam bidang matematika, khususnya karena begitu mudahnya kasus ini untuk dideskripsikan, namun cukup sulit untuk menyelesaikannya. Secara sederhana, TSP dapat dituliskan sebagai: jika seseorang ingin pergi tepat satu kali ke í µí±š kota (di mana biaya perjalanan dari kota í µí±– ke kota í µí±— adalah í µí± í µí±–í µí±—) dan kemudian kembali ke kota asal, maka akan ditentukan rute mana yang paling murah untuk ditempuh. Dalam ilmu komputer terutama menurut teori kompleksitas komputasional, TSP termasuk ke dalam kategori NP-complete. Hal ini tidak menunjukkan bahwa masalah dalam jumlah yang besar tidak dapat diselesaikan. Faktanya, kini berbagai pendekatan optimisasi telah mampu memberi jawaban atas berbagai permasalahan TSP dengan ukuran yang relatif besar.

The Train Timetabling Problem (TTP) consists in finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function which counts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough and one calls for a robust solution that is capable of absorbing as much as possible delays/disturbances on the network. In this paper we propose and analyze computationally four different methods to improve the robustness of a given TTP solution for the aperiodic (non cyclic) case. The approaches combine Linear Programming (LP) and ad-hoc Stochastic Programming/Robust Optimization techniques. We compare computationally the effectiveness and practical applicability of the four techniques under investigation on real-world test cases from the Italian railway company (Trenitalia). The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable quality with respect to the standard (but very time consuming) Stochastic Programming approach. Table 2. Comparison of different training methods with respect to computing time, percentage WAD and validation function (cumulative delay in minutes), for different lines and tradeoff α.

Determining the optimal scale size of a combined cycle power plant is inherently a complex problem often with multiple and conflicting criteria as well as uncertain factors. The complexity of the problem is compounded by the production of undesirable outputs and the presence of natural and managerial disposability. We propose a customized data envelopment analysis (DEA) method for solving the return to scale (RS) problem in the presence of uncertain data and undesirable outputs. A combined cycle power plant is considered a decision making unit (DMU) which consumes fuels to produce electricity and emissions. The uncertainty of the inputs and outputs are modeled with interval data and the emissions are assumed to be undesirable outputs. The proposed DEA method determines the interval efficiency scores of the DMUs and offers a practical benchmark for enhancing the efficiency scores. We demonstrate the applicability of the proposed method and exhibit the efficacy of the procedure with a six-year study of 17 combined cycle power plants in Iran. The main contributions of this paper are six fold: we (1) model the uncertainties in the input and output data using interval data; (2) consider undesirable outputs; (3) determine the efficiency scores of the DMUs as interval values; (4) develop a group of indices to distinguish between the efficient and inefficient DMUs; (5) determine the most economic scale size for the efficient DMUs; and (6) determine practical benchmarks for the inefficient DMUs.

This paper reviews the state-of-the-art in robust design optimization -the search for designs and solutions which are immune with respect to production tolerances, parameter drifts during operation time, model sensitivities and others. Starting with a short glimps of Taguchi's robust design methodology, a detailed survey of approaches to robust optimization is presented. This includes a detailed discussion on how to account for design uncertainties and how to measure robustness (i.e., how to evaluate robustness). The main focus will be on the different approaches to perform robust optimization in practice including the methods of mathematical programming, deterministic nonlinear optimization, and direct search methods such as stochastic approximation and evolutionary computation. It discusses the strenghts and weaknesses of the different methods, thus, providing a basis for guiding the engineer to the most appropriate techniques. It also addresses performance aspects and test scenarios for direct robust optimization techniques.

A reliability-based robust design optimization for resistance reduction and operability increase in head waves from a real ocean environment is formulated and solved. The analysis tool consists in a URANS solver coupled with uncertainty quantification methods for variable regular wave, based on a Monte Carlo simulation with metamodels. The design optimization methods include the Karhunen-Loève expansion of the geometry modification space, coupled with design of experiments and metamodels, and a multi-objective particle swarm optimization algorithm. To reduce the computational effort, a simplified model is introduced for the effects of sea state and speed on the subsystem's seakeeping responses. The application presented is a 100m Delft catamaran sailing in the North Pacific Ocean, with speed in the range Fr = 0.115 ÷ 0.575. An optimal design is selected, providing a 2.8% reduction for the expected value of the mean resistance and an 8.5% increase in operability, based on stochastic operations.

A comprehensive optimization study was carried out to evaluate the performance of a simulated moving bed reactor (SMBR) system for an industrially important biochemical reaction-separation problem, the inversion of Sucrose and the in situ separation of the products, glucose and fructose. Two modifications of SMBR are studied, one in which non-synchronous switching is used to vary the number of columns in different sections within a global switching period (the so-called Varicol ® process), while in the other the concept of distributed feed is studied in which the feed flow was distributed over the global switching period. Multi-objective optimization study is performed as it results in more meaningful solutions although the optimization for such complex processes is complicated owing to the complex interplay of relatively large number of decision variables, including continuous variables like switching time, flow rates and column length and discrete variables like number and distribution of columns in different sections. A state-of-the-art non-traditional but more versatile optimization technique based on genetic algorithm, non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG) was used. The optimization results in significant improvement for SMBR as well as its modification, Varicol and distributed feed systems, in terms of increasing productivity using less desorbent for both existing as well as at design stage.

We are developing an aircraft Flight Plan Manager (FPM) that incorporates a variable autonomy plan repair algorithm and provides real-time trajectory adaptation in response to both performance degradation and traffic and weather conflicts. FPM reduces environmental impact, improves safety, and simplifies personal air vehicle (PAV) operation by coupling realistic performance and noise models with intuitive pilot interfaces and robust optimization algorithms. Enhanced situational awareness and detailed procedural guidance improve safety and reduce reliance on specialized pilot knowledge. Reuse of existing navigation and autopilot systems will minimize production cost. Our long-term goal is to develop and validate the models and methods that will make FPM part of every PAV cockpit.

The optimization of batch processes has attracted attention in recent years because, in the face of growing competition, it is a natural choice for reducing production costs, improving product quality, meeting safety requirements and environmental regulations. This paper starts with a brief overview of the analytical and numerical tools that are available to analyze and compute the optimal solution. The originality of the overview lies in the classification of the various methods. The interpretation of the optimal solution represents the novel element of the paper: the optimal solution is interpreted in terms of constraints and compromises on the one hand, and in terms of path and terminal objectives on the other. This characterization is key to the utilization of measurements in an optimization framework, which will be the subject of the companion paper. #

A BAYESIAN DESIGN SPACE 1331 . These guidelines rely on the use of information and prior knowledge gained during pharmaceutical development studies to provide a scientific rationale about the manufacturing process of a product. In particular, the concept of design space (DS) is defined as "the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality."

The aim of this paper is to investigate the use of heuristic information to efficiently solve to optimality the robust shortest path problem. Starting from the exact algorithm proposed by Murty and Her, we describe how this algorithm can be enhanced by using heuristic rules and evaluation functions to guide the search. The efficiency of the proposed enhanced approach is tested over a range of random generated instances. Our computational results indicate that the use of heuristic criteria is able to speed up considerably the search and that the enhanced exact solution method outperforms the state-of-the-art algorithm proposed by Murty and Her in most of the instances.

In this paper, we evaluate the performance of a supply chain (SC) under uncertainty with different components such as direct costs, operational costs, transaction expenses, order lead time, product flexibility and net profit. Data Envelopment Analysis (DEA) can be used for measuring the performance of supply chain problems. On the other hand, robust optimization approach is a powerful technique for handling problems faced with various environmental uncertainties. This paper combines these two concepts and proposes a method to evaluate SCs performance. The results of the proposed method, under any different environmental situation, show which ranking of SC's performance is better in a network. The preliminary results of the implementation of a real-world case study indicates that the method could be successfully used for performance measurement.

We create a formulation and a solution procedure for fleet sizing under uncertainty in future demands and operating conditions. The formulation focuses on robust optimization, using a partial moment measure of risk. This risk measure is incorporated into the expected recourse function of a two-stage stochastic programming formulation, and stochastic decomposition is used as a solution procedure. A numerical example illustrates the importance of including uncertainty in the fleet sizing problem formulation, and the nature of the fundamental tradeoff between acquiring more vehicles and accepting the risk of potentially high costs if insufficient resources are available.

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound. ᭧

Structural optimization for vehicle door signifies one of the key topics of research to continuously improve its performances. However, majority of the studies to date have not considered uncertainties whilst it has been known that a deterministic optimization may lead to an unreliable design in practice. In this paper, a multiobjective reliability-based design optimization (MORBDO) procedure is proposed to explore the design of vehicle door. To improve the efficiency of optimization, response surface method (RSM) is used to replace the time-consuming finite element simulations. In conjunction with Monte Carlo simulation and descriptive sampling technique, probabilistic sufficiency factor is adopted as a design constraint. The multiobjective particle swarm optimization (MOPSO) algorithm is employed to perform the optimization. The results demonstrate that the proposed optimization procedure is capable of generating a well-distributed Pareto frontier of reliable solutions, and it is suggested to select an optimum from relative insensitive regions. Moreover, the influence of varying the uncertainty and increasing the target reliability level in the optimization results is analyzed, which provided decisionmakers with insightful design information.