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We present two new approaches to address the optimization problem associated with engine calibration. In this area, the tuning parameters are traditionally determined in a local way, i.e., at each engine operating point, via a single-objective minimization problem. To overcome these restrictions, the first method we propose is able to cope with several objective functions simultaneously in the local formulation. The second method we put forward relies on a global formulation, which allows the whole driving cycle to be taken into account while remaining single-objective. At the practical level, the two methods are implemented by combining various existing techniques such as the LoLiMoT (Local Linear Model Tree) parameterization and the MO-CMA-ES (Multi-Objective Covariance Matrix Adaptation Evolution Strategy) algorithm. A better compromise appears to be achieved on real case applications.

The Nelder-Mead (NM) method is a popular derivative-free optimization algorithm owing to its fast convergence and robustness. However, it is known that the method often fails to converge or costs a long time for a large-scale optimization. In the present study, the NM method has been improved using direct inversion in iterative subspace (DIIS). DIIS is a technique to accelerate an optimization method, extrapolating a better intermediate solution from linear-combination of the known ones. We compared runtimes of the new method (NM-DIIS) and the conventional NM method using unimodal test functions with various dimensions. The NM-DIIS method showed better results than the original NM on average when the dimension of the objective function is high. Long tails of the runtime distributions in the NM method have disappeared when DIIS was applied. DIIS has also been implemented in the quasi-gradient method, which is an improved version of the NM method developed by Pham et al. [IEEE Trans. Ind. Informatics, 7 (2011) 592]. The combined method also performed well especially in an upwardly convex test function. The present study proposes a practical optimization strategy and proves the versatility of DIIS.

Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.

In this work, metamodel-based robust optimization is performed using measured scatter of noise variables. Principal component analysis is used to describe the input noise using linearly uncorrelated principal components. Some of these principal components follow a normal probability distribution, others however deviate from a normal probability distribution. In that case, for more accurate description of material scatter, a multimodal distribution is used. An analytical method is implemented to propagate the noise distribution via metamodel and to calculate the statistics of the response accurately and efficiently. The robust optimization criterion as well as the constraints evaluation are adjusted to properly deal with multimodal response. Two problems are presented to show the effectiveness of the proposed approach and to validate the method. A basketball free throw in windy weather condition and forming of B-pillar component are presented. The significance of accounting for non-normal distribution of input variables using multimodal distributions is investigated. Moreover, analytical calculation of response statistics, and adjustment of the robust optimization problem are presented and discussed.

This paper studies the dual relation between risk-sensitive control and large deviation control of maximizing the probability for out-performing a target for Markov Decision Processes. To derive the desired duality, we apply a non-linear extension of the Krein-Rutman Theorem to characterize the optimal risk-sensitive value and prove that an optimal policy exists which is stationary and deterministic. The right-hand side derivative of this value function is used to characterize the specific targets which make the duality to hold. It is proved that the optimal policy for the “out-performing” probability can be approximated by the optimal one for the risk-sensitive control. The range of the (right-hand, left-hand side) derivative of the optimal risk-sensitive value function plays an important role. Some essential differences between these two types of optimal control problems are presented.

The design of dynamic Label-Switched Paths (LSP’s) in MultiProtocol Label Switched (MPLS) networks is an NP-hard optimization problem. An LSP is a logical path between two nodes in the network. This path has a pre-reserved amount of bandwidth that defines its size. The LSP design problem consists of determining the number of these logical links and configuring the physical path and the size of each LSP. This paper presents an optimization model based on game theory. In this approach, connection requests are modeled as competitive players in a noncooperative game context. The transport network bandwidth constitutes the resource for which optimization is sought. The outcome of this optimization is a set of LSPs upon which the competing connections are routed.

At present, black-box and simulation-based optimization problems with multiple objective functions are becoming increasingly common in the engineering context. In many cases, the functional relationships that define the objective and constraints are only known as black-boxes, cannot be differentiated accurately, and may be subject to unexpected failures. Directional direct search techniques, in particular the direct multisearch (DMS) methodology, may be applied to identify Pareto fronts for such problems. In this work, we propose a mechanism for adaptively selecting search directions in the DMS framework, with the goal of reducing the number of black-box evaluations required during the optimization. Our method relies on the concept of simplex derivatives in order to define search directions that are optimal for a local, linear model of the objective function. We provide a detailed description of the resulting algorithm and offer several practical recommendations for efficiently solving the associated subproblems. The overall performance in an academic context is assessed via a standard benchmark. Through a realistic case study, involving the bi-objective design optimization of a mechatronic quarter-car suspension, the performance of the novel method in a multidisciplinary engineering setting is tested. The results show that our method is competitive with standard implementations of DMS and other state-of-the-art multi-objective direct search methods.

In this paper the line search procedure within the method of feasible directions is parallelized and used in the solution of constrained structural optimization problems. As the objective function is linear in the variables, the step size problem reduces to a zero finding problem. That is, the step size is the distance along the direction vector to the nearest constraint boundary. Zero finding is accomplished in two steps—a ‘march’ along the direction vector to bracket the zero followed by an interval reduction scheme. Both these steps are parallelized using MPI for message passing. When implemented on a cluster of workstations, for a convergence parameter of 10−6, the time for optimization of composite pressure vessel reduces from 3 $$\frac{1}{2}$$ hours to $$\frac{1}{2}$$ hour when 64 processors are utilized, with a speedup of 7.0.

We propose solution methods for multidisciplinary design optimization (MDO) under uncertainty. This is a class of stochastic optimization problems that engineers are often faced with in a realistic design process of complex systems. Our approach integrates solution methods for reliability-based design optimization (RBDO) with solution methods for deterministic MDO problems. The integration is enabled by the use of a deterministic equivalent formulation and the first order Taylor’s approximation in these RBDO methods. We discuss three specific combinations: the RBDO methods with the multidisciplinary feasibility method, the all-at-once method, and the individual disciplinary feasibility method. Numerical examples are provided to demonstrate the procedure.

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.