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The purpose of this paper is to contribute to the literature in three ways: first, the authors investigate the impact of the sampling errors on optimal portfolio weights and on financial investment decision. Second, the authors advance a comparative analysis between various domestic and international diversification strategies to define a stochastic optimal choice. Third, the authors propose a new methodology combining the re-sampling method, stochastic optimization algorithm, and nonparametric stochastic dominance (SD) approach to analyze a stochastic optimal portfolio choice for risk-averse American investors who care about benefits of domestic diversification relative to international diversification. The authors propose a new portfolio optimization model involving SD constraints on the portfolio return rate. The authors define a portfolio with return dominating the benchmark portfolio return in the second-order stochastic dominance (SSD) and having maximum expected return. The authors combine re-sampling procedure and stochastic optimization to establish more flexibility in the investment decision rule.

The authors apply the re-sampling procedure to consider the sampling error in the optimization process. The authors try to resolve the problem of the stochastic optimal investment strategy choice using the nonparametric SD test by Linton et al. (2005) based on sub-sampling simulated p values. The authors apply the stochastic portfolio optimization algorithm with SSD constraints to define optimal diversified portfolios beating benchmark indices.

First, the authors find that reducing sampling error increases the dominance relationships between different portfolios, which, in turn, alters portfolio investment decisions. Though international diversification is preferred in some cases, the study’s results show that for risk-averse US investors, in general, there is no difference between the diversification strategies; this implies that there is no increase in the expected utility of international diversification for the period before and after the 2007-2008 financial crisis. Nevertheless, the authors find that stochastic diversification in domestic, global, and Europe, Australasia, and Far East markets delivers better risk returns for the US risk averters during the crisis period.

The originality of the idea in this paper is to introduce a new methodology combining the concept of portfolio re-sampling, stochastic portfolio optimization with SSD constraints, and the nonparametric SD test by Linton et al. (2005) based on subsampling simulated p values to analyze the impact of sampling errors on optimal portfolio returns and to investigate the problem of stochastic optimal choice between international and domestic diversification strategies. The authors try to prove more coherence in the portfolio choice with the stochastically and the uncertainty characters of the paper.

The liquefied natural gas (LNG) business comprises a number of economic activities with inherent risks. The purpose of this paper is to propose an integrated modelling approach, as part of the investment decision‐making process, for optimising economic returns from LNG whilst taking into account uncertainty in various key input parameters.

Inter‐linked cash flow and pricing models of the LNG chain were constructed. Net present value was maximised based on selection of netback pricing variables and level of investment shareholding. Constraints were placed on the minimum acceptable returns. The risk affinity of the decision maker was captured in the form of a chance‐constrained optimisation problem. A genetic algorithm was applied for numerical optimisation, in combination with Monte Carlo simulations to account for the stochastic nature of the problem.

Based on the results of a case study, the deterministic solution, having no consideration to uncertainty, was found to be both sub‐optimal and provided an unsatisfactory risk outcome. The stochastic approach yielded an optimal solution with due consideration to risk. Various scenarios show that the choice of the decision variables significantly impacts the trade‐off between risk and returns along the LNG chain to government and investor.

The suitability of the methodology to the operational phase of the LNG business which incorporates different elements of risk, such as market dynamics and logistics, is as yet untested.

This framework may be useful in the formulation of optimal commercial structure of firms, investment portfolio and gas/LNG pricing arrangements for host governments involved in the LNG business.

This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.

ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows.

First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1−T¯ _TSI )×100, where T¯ _TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy.

Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.

The purpose of this paper is to formulate the reliability optimization problem in stochastic and interval domain and also to solve the same under different stochastic set up.

Stochastic programming technique has been used to convert the chance constraints into deterministic form and the corresponding problem is transformed to mixed-integer constrained optimization problem with interval objective. Then the reduced problem has been converted to unconstrained optimization problem with interval objective by Big-M penalty technique. The resulting problem has been solved by advanced real coded genetic algorithm with interval fitness, tournament selection, intermediate crossover and one-neighbourhood mutation.

A new optimization technique has been developed in stochastic domain and the concept of interval valued parameters has been integrated with the stochastic setup so as to increase the applicability of the resultant solution to the interval valued nonlinear optimization problems.

The concept of probability distribution with interval valued parameters has been introduced. This concept will motivate the researchers to carry out the research in this new direction.

The application of genetic algorithm is extended to solve the reliability optimization problem in stochastic and interval domain.

The purpose of this paper is to expose computational methods as applied to engineering systems and evolutionary processes with randomness in external actions and inherent parameters.

In total, two approaches are distinguished that rely on solvers from deterministic algorithms. Probabilistic analysis is referred to as the approximation of the response by a Taylor series expansion about the mean input. Alternatively, stochastic simulation implies random sampling of the input and statistical evaluation of the output.

Beyond the characterization of random response, methods of reliability assessment are discussed. Concepts of design improvement are presented. Optimization for robustness diminishes the sensitivity of the system to fluctuating parameters.

Deterministic algorithms available for the primary problem are utilized for stochastic analysis by statistical Monte Carlo sampling. The computational effort for the repeated solution of the primary problem depends on the variability of the system and is usually high. Alternatively, the analytic Taylor series expansion requires extension of the primary solver to the computation of derivatives of the response with respect to the random input. The method is restricted to the computation of output mean values and variances/covariances, with the effort determined by the amount of the random input. The results of the two methods are comparable within the domain of applicability.

The present account addresses the main issues related to the presence of randomness in engineering systems and processes. They comprise the analysis of stochastic systems, reliability, design improvement, optimization and robustness against randomness of the data. The analytical Taylor approach is contrasted to the statistical Monte Carlo sampling throughout. In both cases, algorithms known from the primary, deterministic problem are the starting point of stochastic treatment. The reader benefits from the comprehensive presentation of the matter in a concise manner.

This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.

The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.

New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.

In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

The purpose of this paper is to present a stochastic p-robust data envelopment analysis (DEA) model for decision-making units (DMUs) efficiency estimation under uncertainty. The main contribution of this paper consists of the development of a more robust system for the estimation of efficiency in situations of inputs uncertainty. The proposed model is used for the efficiency measurement of a commercial Iranian bank.

This paper has been arranged to launch along the following steps: the classical Charnes, Cooper, and Rhodes (CCR) DEA model was briefly reviewed. After that, the p-robust DEA model is introduced and then calculated the priority weights of each scenario for CCR DEA output oriented method. To compute the priority weights of criteria in discrete scenarios, the analytical hierarchy analysis process (AHP) is used. To tackle the uncertainty of experts’ opinion, a synthetic technique is applied based on both robust and stochastic optimizations. In the sequel, stochastic p-robust models are proposed for the estimation of efficiency, with particular attention being paid to DEA models.

The proposed method provides a more encompassing measure of efficiency in the presence of synthetic uncertainty approach. According to the results, the expected score, relative regret score and stochastic P-robust score for DMUs are obtained. The applicability of the extended model is illustrated in the context of the analysis of an Iranian commercial bank performance. Also, it is shown that the stochastic p-robust DEA model is a proper generalization of traditional DEA and gained a desired robustness level. In fact, the maximum possible efficiency score of a DMU with overall permissible uncertainties is obtained, and the minimal amount of uncertainty level under the stochastic p-robustness measure that is required to achieve this efficiency score. Finally, by an example, it is shown that the objective values of the input and output models are not inverse of each other as in classical DEA models.

This research showed that the enormous decrease in maximum possible regret makes only a small addition in the expected efficiency. In other words, improvements in regret can somewhat affect the expected efficiency. The superior issue this kind of modeling is to permit a harmful effect to the objective to better hedge against the uncertain cases that are commonly ignored.

This research study aims to minimize autonomous flight cost and maximize autonomous flight performance of a slung load carrying rotary wing mini unmanned aerial vehicle (i.e. UAV) by stochastically optimizing autonomous flight control system (AFCS) parameters. For minimizing autonomous flight cost and maximizing autonomous flight performance, a stochastic design approach is benefitted over certain parameters (i.e. gains of longitudinal PID controller of a hierarchical autopilot system) meanwhile lower and upper constraints exist on these design parameters.

A rotary wing mini UAV is produced in drone Laboratory of Iskenderun Technical University. This rotary wing UAV has three blades main rotor, fuselage, landing gear and tail rotor. It is also able to carry slung loads. AFCS variables (i.e. gains of longitudinal PID controller of hierarchical autopilot system) are stochastically optimized to minimize autonomous flight cost capturing rise time, settling time and overshoot during longitudinal flight and to maximize autonomous flight performance. Found outcomes are applied during composing rotary wing mini UAV autonomous flight simulations.

By using stochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads over previously mentioned gains longitudinal PID controller when there are lower and upper constraints on these variables, a high autonomous performance having rotary wing mini UAV is obtained.

Approval of Directorate General of Civil Aviation in Republic of Türkiye is essential for real-time rotary wing mini UAV autonomous flights.

Stochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads is properly valuable for recovering autonomous flight performance cost of any rotary wing mini UAV.

Establishing a novel procedure for improving autonomous flight performance cost of a rotary wing mini UAV carrying slung loads and introducing a new process performing stochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads meanwhile there exists upper and lower bounds on design variables.

The purpose of this paper is to consider various possible constraints of the problem of production and maintenance planning control for a multi-machine under subcontracting constraint, in order to bring the manufacturer industry closer to real mode. In this paper, we present an efficient and feasible optimal solution, by comparing optimization procedures.

Our manufacturing system is composed of parallel machines producing a single product, to satisfy a random demand under a given service level. In fact, the demand is greater than the total capacity of the set of machines; hence there rises a necessity of subcontracting to complete the missing demand. In addition, we consider that the unit cost of subcontracting is a variable depending on the quantity subcontracted. As a result, we have developed a stochastic optimal control model. Then, to solve the problem we compared three optimization methods: (exact/approximate), the genetic algorithm (GA), the Pattern Search (PS) and finally fmincon. Thus, we validate our approach via a numerical example and a sensitivity analysis.

This paper defines an internal production plan, a subcontracting plan and an optimal maintenance strategy. The optimal solution presented in this paper significantly improves the ability of the decision maker to consider larger instances of the integrated model. In addition, the decision maker can answer the following question: Which is the most optimal subcontractor to choose?

The approach developed deals with the case of the real-mode manufacturing industry, taking into consideration different constraints and determining decision variables which allow it to expand the profits of the manufacturing industry in different domains such as automotive, aeronautics, textile and pharmacies.

This paper is one of the few documents dealing with the integrated maintenance in subcontracting constraint production which considers the complex aspect of the multi-machine manufacturing industry. We also dealt with the stochastic aspect of demand and failures. Then, we covered the impact of the unit cost variation of subcontracting on the total cost. Finally, we shed light on a comparison between three optimization methods in order to arrive at the most optimal solution.

This study proposes targeted modernization of the Department of Defense (DoD's) Joint Forces Ammunition Logistics information system by implementing the optimized innovative information technology open architecture design and integrating Radio Frequency Identification Device data technologies and real-time optimization and control mechanisms as the critical technology components of the solution. The innovative information technology, which pursues the focused logistics, will be deployed in 36 months at the estimated cost of $568 million in constant dollars. We estimate that the Systems, Applications, Products (SAP)-based enterprise integration solution that the Army currently pursues will cost another $1.5 billion through the year 2014; however, it is unlikely to deliver the intended technical capabilities.