Showing papers on "Optimal design published in 2011"

Constructive Nonlinear Control

Abstract: 1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation -- 2 Passivity Concepts as Design Tools -- 2.1 Dissipativity and Passivity -- 2.2 Interconnections of Passive Systems -- 2.3 Lyapunov Stability and Passivity -- 2.4 Feedback Passivity -- 2.5 Summary -- 2.6 Notes and References -- 3 Stability Margins and Optimality -- 3.1 Stability Margins for Linear Systems -- 3.2 Input Uncertainties -- 3.3 Optimality, Stability, and Passivity -- 3.4 Stability Margins of Optimal Systems -- 3.5 Inverse Optimal Design -- 3.6 Summary -- 3.7 Notes and References -- 4 Cascade Designs -- 4.1 Cascade Systems -- 4.2 Partial-State Feedback Designs -- 4.3 Feedback Passivation of Cascades -- 4.4 Designs for the TORA System -- 4.5 Output Peaking: an Obstacle to Global Stabilization -- 4.6 Summary -- 4.7 Notes and References -- 5 Construction of Lyapunov functions -- 5.1 Composite Lyapunov functions for cascade systems -- 5.2 Lyapunov Construction with a Cross-Term -- 5.3 Relaxed Constructions -- 5.4 Stabilization of Augmented Cascades -- 5.5 Lyapunov functions for adaptive control -- 5.6 Summary -- 5.7 Notes and references -- 6 Recursive designs -- 6.1 Backstepping -- 6.2 Forwarding -- 6.3 Interlaced Systems -- 6.4 Summary and Perspectives -- 6.5 Notes and References -- A Basic geometric concepts -- A.1 Relative Degree -- A.2 Normal Form -- A.3 The Zero Dynamics -- A.4 Right-Invertibility -- A.5 Geometric properties -- B Proofs of Theorems 3.18 and 4.35 -- B.1 Proof of Theorem 3.18 -- B.2 Proof of Theorem 4.35.

Optimal Design of Experiments: A Case Study Approach

Abstract: Preface. Acknowledgments. 1 A simple comparative experiment. 1.1 Key concepts. 1.2 The setup of a comparative experiment. 1.3 Summary. 2 An optimal screening experiment. 2.1 Key concepts. 2.2 Case: an extraction experiment. 2.2.1 Problem and design. 2.2.2 Data analysis. 2.3 Peek into the black box. 2.3.1 Main-effects models. 2.3.2 Models with two-factor interaction effects. 2.3.3 Factor scaling. 2.3.4 Ordinary least squares estimation. 2.3.5 Significance tests and statistical power calculations. 2.3.6 Variance inflation. 2.3.7 Aliasing. 2.3.8 Optimal design. 2.3.9 Generating optimal experimental designs. 2.3.10 The extraction experiment revisited. 2.3.11 Principles of successful screening: sparsity, hierarchy, and heredity. 2.4 Background reading. 2.4.1 Screening. 2.4.2 Algorithms for finding optimal designs. 2.5 Summary. 3 Adding runs to a screening experiment. 3.1 Key concepts. 3.2 Case: an augmented extraction experiment. 3.2.1 Problem and design. 3.2.2 Data analysis. 3.3 Peek into the black box. 3.3.1 Optimal selection of a follow-up design. 3.3.2 Design construction algorithm. 3.3.3 Foldover designs. 3.4 Background reading. 3.5 Summary. 4 A response surface design with a categorical factor. 4.1 Key concepts. 4.2 Case: a robust and optimal process experiment. 4.2.1 Problem and design. 4.2.2 Data analysis. 4.3 Peek into the black box. 4.3.1 Quadratic effects. 4.3.2 Dummy variables for multilevel categorical factors. 4.3.3 Computing D-efficiencies. 4.3.4 Constructing Fraction of Design Space plots. 4.3.5 Calculating the average relative variance of prediction. 4.3.6 Computing I-efficiencies. 4.3.7 Ensuring the validity of inference based on ordinary least squares. 4.3.8 Design regions. 4.4 Background reading. 4.5 Summary. 5 A response surface design in an irregularly shaped design region. 5.1 Key concepts. 5.2 Case: the yield maximization experiment. 5.2.1 Problem and design. 5.2.2 Data analysis. 5.3 Peek into the black box. 5.3.1 Cubic factor effects. 5.3.2 Lack-of-fit test. 5.3.3 Incorporating factor constraints in the design construction algorithm. 5.4 Background reading. 5.5 Summary. 6 A "mixture" experiment with process variables. 6.1 Key concepts. 6.2 Case: the rolling mill experiment. 6.2.1 Problem and design. 6.2.2 Data analysis. 6.3 Peek into the black box. 6.3.1 The mixture constraint. 6.3.2 The effect of the mixture constraint on the model. 6.3.3 Commonly used models for data from mixture experiments. 6.3.4 Optimal designs for mixture experiments. 6.3.5 Design construction algorithms for mixture experiments. 6.4 Background reading. 6.5 Summary. 7 A response surface design in blocks. 7.1 Key concepts. 7.2 Case: the pastry dough experiment. 7.2.1 Problem and design. 7.2.2 Data analysis. 7.3 Peek into the black box. 7.3.1 Model. 7.3.2 Generalized least squares estimation. 7.3.3 Estimation of variance components. 7.3.4 Significance tests. 7.3.5 Optimal design of blocked experiments. 7.3.6 Orthogonal blocking. 7.3.7 Optimal versus orthogonal blocking. 7.4 Background reading. 7.5 Summary. 8 A screening experiment in blocks. 8.1 Key concepts. 8.2 Case: the stability improvement experiment. 8.2.1 Problem and design. 8.2.2 Afterthoughts about the design problem. 8.2.3 Data analysis. 8.3 Peek into the black box. 8.3.1 Models involving block effects. 8.3.2 Fixed block effects. 8.4 Background reading. 8.5 Summary. 9 Experimental design in the presence of covariates. 9.1 Key concepts. 9.2 Case: the polypropylene experiment. 9.2.1 Problem and design. 9.2.2 Data analysis. 9.3 Peek into the black box. 9.3.1 Covariates or concomitant variables. 9.3.2 Models and design criteria in the presence of covariates. 9.3.3 Designs robust to time trends. 9.3.4 Design construction algorithms. 9.3.5 To randomize or not to randomize. 9.3.6 Final thoughts. 9.4 Background reading. 9.5 Summary. 10 A split-plot design. 10.1 Key concepts. 10.2 Case: the wind tunnel experiment. 10.2.1 Problem and design. 10.2.2 Data analysis. 10.3 Peek into the black box. 10.3.1 Split-plot terminology. 10.3.2 Model. 10.3.3 Inference from a split-plot design. 10.3.4 Disguises of a split-plot design. 10.3.5 Required number of whole plots and runs. 10.3.6 Optimal design of split-plot experiments. 10.3.7 A design construction algorithm for optimal split-plot designs. 10.3.8 Difficulties when analyzing data from split-plot experiments. 10.4 Background reading. 10.5 Summary. 11 A two-way split-plot design. 11.1 Key concepts. 11.2 Case: the battery cell experiment. 11.2.1 Problem and design. 11.2.2 Data analysis. 11.3 Peek into the black box. 11.3.1 The two-way split-plot model. 11.3.2 Generalized least squares estimation. 11.3.3 Optimal design of two-way split-plot experiments. 11.3.4 A design construction algorithm for D-optimal two-way split-plot designs. 11.3.5 Extensions and related designs. 11.4 Background reading. 11.5 Summary. Bibliography. Index.

Optimal Design of Microgrids in Autonomous and Grid-Connected Modes Using Particle Swarm Optimization

Abstract: The dynamic nature of the distribution network challenges the stability and control effectiveness of the microgrids in both grid-connected and autonomous modes. In this paper, linear and nonlinear models of microgrids operating in different modes are presented. Optimal design of LC filter, controller parameters, and damping resistance is carried out in case of grid-connected mode. On the other hand, controller parameters and power sharing coefficients are optimized in case of autonomous mode. The control problem has been formulated as an optimization problem where particle swarm optimization is employed to search for optimal settings of the optimized parameters in each mode. In addition, nonlinear time-domain-based as well as eigenvalue-based objective functions are proposed to minimize the error in the measured power and to enhance the damping characteristics, respectively. Finally, the nonlinear time-domain simulation has been carried out to assess the effectiveness of the proposed controllers under different disturbances and loading conditions. The results show satisfactory performance with efficient damping characteristics of the microgrid considered in this study. Additionally, the effectiveness of the proposed approach for optimizing different parameters and its robustness have been confirmed through the eigenvalue analysis and nonlinear time-domain simulations.

Metamodeling Method Using Dynamic Kriging for Design Optimization

Abstract: Metamodeling has been widely used for design optimization by building surrogate models for computationally intensive engineering application problems. Among all the metamodeling methods, the kriging method has gained significant interest for its accuracy.However, in traditional krigingmethods, themean structure is constructed using a fixed set of polynomial basis functions, and the optimization methods used to obtain the optimal correlation parameter may not yield an accurate optimum. In this paper, a new method called the dynamic kriging method is proposed to fit the true model more accurately. In this dynamic kriging method, an optimal mean structure is obtainedusing thebasis functions that are selected bya genetic algorithm from the candidate basis functions based on a new accuracy criterion, and a generalized pattern search algorithm is used to find an accurate optimum for the correlation parameter. The dynamic kriging method generates a more accurate surrogate model than other metamodeling methods. In addition, the dynamic kriging method is applied to the simulation-based design optimization with multiple efficiency strategies. An engineering example shows that the optimal design obtained by using the surrogate models from the dynamic kriging method can achieve the same accuracy as the one obtained by using the sensitivity-based optimization method.

Multiphysic Modeling of a High-Speed Interior Permanent-Magnet Synchronous Machine for a Multiobjective Optimal Design

Abstract: High-speed electric drive design is concerned with paying particular attention to thermal and mechanical design of the machine. Therefore, this paper proposes a multiphysic modeling of an interior permanent-magnet synchronous machine (IPMSM) dedicated to high speed, including magnetic, electric, thermal, and mechanical aspects. The proposed analytical models are verified using finite-element (FE) computations. These models are then subjected to a multiobjective optimization-based on genetic algorithm-to design an IPMSM for a high-speed compressor application that develops 30 kW at 20 000 r/min. The design is formulated as a constrained optimization problem consisting of maximizing the machine efficiency while minimizing its weight. The result of this process is a Pareto front between efficiency and weight of the machine allowing the designer to make a posteriori choice. A particular optimal machine is chosen and its performances are validated with FE analysis. This study carries out an optimal multiphysic and multiobjective design approach that allows rationalization of the design process in a realistic computation time thanks to the analytical models involved.

Bayesian optimal designs for discrete choice experiments with partial profiles

Abstract: In a discrete choice experiment, each respondent chooses the best product or service sequentially from many groups or choice sets of alternative goods. The alternatives are described by levels of a set of predefined attributes and are also referred to as profiles. Respondents often find it difficult to trade off prospective goods when every attribute of the offering changes in each comparison. Especially in studies involving many attributes, respondents get overloaded by the complexity of the choice task. To overcome respondent fatigue, it is better to simplify the choice tasks by holding the levels of some of the attributes constant in every choice set. The resulting designs are called partial profile designs. In this paper, we construct D-optimal partial profile designs for estimating main-effects models. We use a Bayesian design algorithm that integrates the D-optimality criterion over a prior distribution of likely parameter values. To determine the constant attributes in each choice set, we generalize the approach that makes use of balanced incomplete block designs. Our algorithm is very flexible because it produces partial profile designs of any choice set size and allows for attributes with any number of levels and any number of constant attributes. We provide an illustration in which we make recommendations that balance the loss of statistical information and the burden imposed on the respondents.

Optimal instrumental variable method for closed-loop identification

Abstract: This study presents in a new unified way, optimal instrumental variable methods for identifying discrete-time transfer function models when the system operates in a closed loop. The conditions for the optimal design of prefilters and instruments depending on common model structures are analysed and different approaches are developed according to whether the controller is known or not. The performance of the proposed approaches is evaluated by Monte-Carlo analysis in comparison with other alternative closed-loop estimation methods.

Single- and multiobjective design optimization of a fast multihull ship: numerical and experimental results

Abstract: Numerical optimization of the initial design of a fast catamaran (high-speed sealift research model B, HSSL-B) has been carried out through a simulation-based design (SBD) framework, based on an advanced free-surface unsteady Reynolds-averaged Navier–Stokes (URANS) solver and a potential flow solver, and global optimization (GO) algorithms. The potential flow computational fluid dynamics (CFD) SBD was used to guide the more expensive URANS CFD SBD. The fluid-dynamic analysis of the flow past the catamaran proved that the use of the URANS solver was fundamental in dealing with the multihull interference problem. In the case investigated, the separation distance was small and the viscous flow quite distorted by the proximity of the hulls, so that only viscous solvers could correctly capture the flow details. Sinkage and trim effects, due to the high speed range and again to the small separation distance investigated, are also relevant. The initial HSSL-B geometry and three optimization problems, including single- and multiobjective optimization problems, proposed by designers from Bath Iron Works, were successfully optimized/solved, and finally an experimental campaign was carried out to validate the optimal design. A new verification and validation methodology for assessing uncertainties and errors in simulation-based optimization was used based on the trends, i.e., the differences between the numerically predicted improvement of the objective function and the actual improvement measured in a dedicated experimental campaign, including consideration of numerical and experimental uncertainties. Finally, the success of the optimization processes was confirmed by the experimental measurements, and trends for total resistance, sinkage, and trim between the original and optimal designs were numerically and experimentally verified and validated.

The usefulness of Bayesian optimal designs for discrete choice experiments

Abstract: Recently, the use of Bayesian optimal designs for discrete choice experiments, also called stated choice experiments or conjoint choice experiments, has gained much attention, stimulating the development of Bayesian choice design algorithms. Characteristic for the Bayesian design strategy is that it incorporates the available information about people's preferences for various product attributes in the choice design. This is in contrast with the linear design methodology, which is also used in discrete choice design and which depends for any claims of optimality on the unrealistic assumption that people have no preference for any of the attribute levels. Although linear design principles have often been used to construct discrete choice experiments, we show using an extensive case study that the resulting utility‐neutral optimal designs are not competitive with Bayesian optimal designs for estimation purposes. Copyright (c) 2011 John Wiley & Sons, Ltd.

Fuzzy control optimized by a Multi-Objective Particle Swarm Optimization algorithm for vibration suppression of smart structures

Abstract: Smart structures include elements of active, passive or hybrid control. In this paper, a new Multi-Objective Particle Swarm Optimization (MOPSO), with a different velocity equation, for the calculation of the free parameters in active control systems is proposed and tested. A fuzzy control system is considered. Fuzzy control is a suitable tool for the systematic development of nonlinear active control strategies and can be fine tuned if no experience exists or if one designs more complicated control schemes. The usage of MOPSO with a combination of continuous and discrete variables for the optimal design of the controller is proposed. Numerical applications on smart piezoelastic beams are presented.

Efficient Designs With Minimal Aliasing.

Abstract: For some experimenters, a disadvantage of the standard optimal design approach is that it does not consider explicitly the aliasing of specified model terms with terms that are potentially important but are not included in the model. For example, when constructing an optimal design for a first-order model, aliasing of main effects and interactions is not considered. This can lead to designs that are optimal for estimation of the primary effects of interest, yet have undesirable aliasing structures. In this article, we construct exact designs that minimize the squared norm of the alias matrix subject to constraints on design efficiency. We demonstrate use of the method for the construction of screening and response surface designs.

Optimal design of arch dams subjected to earthquake loading by a combination of simultaneous perturbation stochastic approximation and particle swarm algorithms

Abstract: An efficient optimization procedure is introduced to find the optimal shapes of arch dams considering fluid-structure interaction subject to earthquake loading. The optimization is performed by a combination of simultaneous perturbation stochastic approximation (SPSA) and particle swarm optimization (PSO) algorithms. This serial integration of the two single methods is termed as SPSA-PSO. The operation of SPSA-PSO includes three phases. In the first phase, a preliminary optimization is accomplished using the SPSA. In the second phase, an optimal initial swarm is produced using the first phase results. In the last phase, the PSO is employed to find the optimum design using the optimal initial swarm. The numerical results demonstrate the high performance of the proposed strategy for optimal design of arch dams. The solutions obtained by the SPSA-PSO are compared with those of SPSA and PSO. It is revealed that the SPSA-PSO converges to a superior solution compared to the SPSA and PSO having a lower computation cost.

Optimal experiment design for open and closed-loop system identification

Abstract: This article reviews the development of experiment design in the field of identification of dynamical systems, from the early work of the seventies on input design for open loop identification to the developments of the last decade that were spurred by the research on identification for control. While the early work focused entirely on criteria based on the asymptotic parameter covariance, the results of the last decade aim at minimizing a wide range of possible criteria, including measures of the estimated transfer function, or of functions of this estimated transfer function. Two important recent developments are the solution of the experiment design problem for closed loop identification, and the formulation and solution of the dual optimal design problem in which the cost of identification is minimized subject to a quality constraint on the estimated model. We shall conclude this survey with new results on the optimal closed loop experiment design problem, where the optimization is performed jointly with respect to the controller and the spectrum of the external excitation.

Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis

Abstract: In this paper, we analyze an improved suspension system with the incorporated inerter device of the quarter-car model to obtain optimal design parameters for maximum comfort level for a driver and passengers. That is achieved by finding the analytical solution for the system of ordinary differential equations, which enables us to generate an optimization problem whose objective function is based on the international standards of admissible acceleration levels (ISO 2631-1, Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration–Part 1, 1997). The considered approach ensures the highest level of comfort for the driver and passengers due to a favorable reduction in body vibrations. Numerical examples, based on actually measured road profiles, are presented at the end of the paper to prove the validity of the proposed approach and its suitability for the problem at hand.

Optimization and design of disk-type MR brakes

Abstract: In this paper, first a new design for a disk-type magneto-rheological (MR) brake for automotive applications is proposed and then, a finite element analysis is performed to analyze the resulting magnetic field intensity distribution within the MR brake configuration This finite element model of the brake is then utilized in a optimization process which incorporates Genetic Algorithm (GA) to obtain optimal design parameters The optimization process goal is to increase the braking torque capacity of the brake while keeping the weight of the brake as low as possible Although, the braking torque of the present design is larger compared to the previous designs, the braking toque capacity of the present design is still smaller than the required braking torque for automobiles

D-optimal designs

Abstract: D-optimal designs are constructed to minimize the generalized variance of the estimated regression coefficients. In the multiple regression setting, the matrix X is often used to represent the data matrix of independent variables. D-optimal designs minimize the overall variance of the estimated regression coefficients by maximizing the determinant of X’X. Designs that are D-optimal have been shown to be nearly optimal for several other criteria that have been proposed as well.

Optimum design of structures using an improved firefly algorithm

Abstract: Nature-inspired search algorithms have proved to be successful in solving real-world optimization problems. Firefly algorithm is a novel meta-heuristic algorithm which simulates the natural behavior of fireflies. In the present study, optimum design of truss structures with both sizing and geometry design variables is carried out using the firefly algorithm. Additionally, to improve the efficiency of the algorithm, modifications in the movement stage of artificial fireflies are proposed. In order to evaluate the performance of the proposed algorithm, optimum designs found are compared to the previously reported designs in the literature. Numerical results indicate the efficiency and robustness of the proposed approach.

Dimension Reduction for Aerodynamic Design Optimization

Abstract: The search for an optimal design in a high-dimensional design space of a multivariate problem requires a sample size proportional or even exponential to the number of variables of the problem. This ‘curse of dimensionality’ places a computational burden on the cost of optimization, especially when the problem uses expensive high fidelity simulations and may force one to try to reduce the dimensions of a problem. Traditional variable screening techniques reduce the dimensionality of the problem by removing variables that seem irrelevant to the design problem. This practice fails when all the variables are equally relevant in the problem or when some variables are relevant only in some parts of the design space. The present work describes a dimension reduction method called generative topographic mapping based on non-linear latent models which transform a high-dimensional data set into a low-dimensional latent space, without removing any variables. It is first illustrated on a two dimensional Branin function and then applied to a thirty-dimensional airfoil problem. The method is then compared with a global optimizer (a genetic algorithm), other dimension reduction methods (principle component analysis and Gaussian process latent variable models) and with Kriging surrogate models. The method improves when the initial sample used for dimension reduction is filtered to contain only good designs.

Bayesian conjoint choice designs for measuring willingness to pay

Abstract: In this paper, we propose a new criterion for selecting efficient conjoint choice designs when the interest is in quantifying willingness to pay (WTP). The new criterion, which we call the WTP-optimality criterion, is based on the c-optimality criterion which is often used in the optimal experimental design literature. We use a simulation study to evaluate the designs generated using the WTP-optimality criterion and discuss the design of a real-life conjoint experiment from the literature. The results show that the new criterion leads to designs that yield more precise estimates of the WTP than Bayesian D-optimal conjoint choice designs, which are increasingly being seen as the state-of-the-art designs for conjoint choice studies, and to a substantial reduction in the occurrence of unrealistically high WTP estimates.

Optimal design of stationary supercapacitors storage devices for light electrical transportation systems

Abstract: Recently a great interest has been paid in the relevant literature to the use of energy storage systems for the performance improvement of electrified light transit systems. In this context, the main targets are the increase of the energetic efficiency and the reduction of pantograph voltage drops. Therefore, it can be very interesting the determination of the optimal characteristics of a storage device for satisfying these objectives, both in stationary and onboard case. In this paper, this problem is approached for a sample case study, by showing that the optimal design of a stationary storage device can be regarded as a classical isoperimetric problem, whose solution is very attractive in order to determine also the optimal allocation of the storage device. For more complex configurations of the transit system, the methodology presented can be extended by solving a constrained optimization problem, which in a quite general manner is capable of matching all the assigned technical requirements. The reported simulations confirm the validity of the proposed design approach.

Comparison of optimal design methods in inverse problems

Abstract: Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix A fundamental approximation theory is also included in this framework A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework We compare this new design criterion with the more traditional D-optimal and E-optimal designs The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh We use three examples to illustrate ideas: the Verhulst–Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am J Physiol 236 E667–77; De Gaetano A and Arino O 2000 J Math Biol 40 136–68; Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979–90)

Response-adaptive dose-finding under model uncertainty

Abstract: Dose-finding studies are frequently conducted to evaluate the effect of different doses or concentration levels of a compound on a response of interest. Applications include the investigation of a new medicinal drug, a herbicide or fertilizer, a molecular entity, an environmental toxin, or an industrial chemical. In pharmaceutical drug development, dose-finding studies are of critical importance because of regulatory requirements that marketed doses are safe and provide clinically relevant efficacy. Motivated by a dose-finding study in moderate persistent asthma, we propose response-adaptive designs addressing two major challenges in dose-finding studies: uncertainty about the dose-response models and large variability in parameter estimates. To allocate new cohorts of patients in an ongoing study, we use optimal designs that are robust under model uncertainty. In addition, we use a Bayesian shrinkage approach to stabilize the parameter estimates over the successive interim analyses used in the adaptations. This approach allows us to calculate updated parameter estimates and model probabilities that can then be used to calculate the optimal design for subsequent cohorts. The resulting designs are hence robust with respect to model misspecification and additionally can efficiently adapt to the information accrued in an ongoing study. We focus on adaptive designs for estimating the minimum effective dose, although alternative optimality criteria or mixtures thereof could be used, enabling the design to address multiple objectives. In an extensive simulation study, we investigate the operating characteristics of the proposed methods under a variety of scenarios discussed by the clinical team to design the aforementioned clinical study.