Multiple-objective Optimal Designs Research Articles

Nature-inspired Metaheuristics for finding Optimal Designs for the Continuation-Ratio Models

The continuation-ratio (CR) model is frequently used in dose response studies to model a three-category outcome as the dose levels vary. Design issues for a CR model defined on an unrestricted dose interval have been discussed for estimating model parameters or a selected function of the model parameters. This paper uses metaheuristics to address design issues for a CR model defined on any compact dose interval when there are one or more objectives in the study and some are more important than others. Specifically, we use an exemplary nature-inspired metaheuristic algorithm called particle swarm optimization (PSO) to find locally optimal designs for estimating a few interesting functions of the model parameters, such as the most effective dose ($MED$), the maximum tolerated dose ($MTD$) and for estimating all parameters in a CR model. We demonstrate that PSO can efficiently find locally multiple-objective optimal designs for a CR model on various dose intervals and a small simulation study shows it tends to outperform the popular deterministic cocktail algorithm (CA) and another competitive metaheuristic algorithm called differential evolutionary (DE). We also discuss hybrid algorithms and their flexible applications to design early Phase 2 trials or tackle biomedical problems, such as different strategies for handling the recent pandemic.

Using CVX to Construct Optimal Designs for Biomedical Studies with Multiple Objectives

ABSTRACT Model-based optimal designs for regression problems with multiple objectives are common in practice. The traditional approach is to construct an optimal design for the most important objective and hope that the design performs well for the other objectives. Analytical approaches are challenging because the objectives are often competitive and their relative importance has to be incorporated at the onset of the design construction. There are also no general and efficient algorithms for searching such designs for user-specified nonlinear models and criteria. We propose a new and effective approach for finding multiple-objective optimal designs via the CVX software and demonstrate it can efficiently find different types of multiple-objective optimal designs after the optimization problems are carefully formulated as convex optimization problems appropriate for CVX use. We provide three biomedical applications and show our MATLAB code producing the same few multiple-objective optimal designs reported in the statistical literature. MATLAB code files are available online in the supplementary materials of this article.

Optimal designs for group randomized trials and group administered treatments with outcomes at the subject and group level.

With group randomized trials complete groups of subject are randomized to treatment conditions. Such grouping also occurs in individually randomized trials where treatment is administered in groups. Outcomes may be measured at the level of the subject, but also at the level of the group. The optimal design determines the number of groups and the number of subjects per group in the intervention and control conditions. It is found by taking a budgetary constraint into account, where costs are associated with implementing the intervention and control, and with taking measurements on subject and groups. The optimal design is found such that the effect of treatment is estimated with highest efficiency, and the total costs do not exceed the budget that is available. The design that is optimal for the outcome at the subject level is not necessarily optimal for the outcome at the group level. Multiple-objective optimal designs consider both outcomes simultaneously. Their aim is to find a design that has high efficiencies for both outcome measures. An Internet application for finding the multiple-objective optimal design is demonstrated on the basis of an example from smoking prevention in primary education, and another example on consultation time in primary care.

On multiple-objective optimal designs

Experiments with multiple objectives form a staple diet of modern scientific research. Deriving optimal designs with multiple objectives is a long-standing challenging problem with few tools available. The few existing approaches cannot provide a satisfied solution in general: either the computation is very expensive or a satisfied solution is not guaranteed. A novel algorithm is proposed to address this literature gap. We prove convergence of this algorithm, and show in various examples that the new algorithm can derive the true solutions with high speed.

VNM: An R Package for Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model

A multiple-objective optimal design is useful for dose-response studies because it can incorporate several objectives at the design stage. Objectives can be of varying interests and a properly constructed multiple-objective optimal design can provide user-specified efficiencies, delivering higher efficiencies for the more important objectives. In this work, we introduce the VNM package written in R for finding 3-objective locally optimal designs for the 4-parameter logistic (4PL) model widely used in education, bioscience and in the manufacturing industry. The package implements the methodology to construct multipleobjective optimal designs in Hyun and Wong (2015). As illustrative examples, we focus on a biomedical application where our objectives are to estimate: (1) the shape of the dose-response curve, (2) the median effective dose level (ED50) and (3) the minimum effective dose level (MED) in the 4PL model. Our VNM package uses a state-of-theart algorithm to generate multiple-objective optimal designs that meet the user-specified efficiency requirement for each objective, provides tools for calculating the efficiency of the generated design under each objective and also a plot for confirming optimality of the VNM-generated design. The package can also be used to determine an optimal scheme for allocating subjects to the various doses when the number and doses of the drug are fixed in advance.

A survey on automating configuration and parameterization in evolutionary design exploration

AbstractConfiguration and parameterization of optimization frameworks for the computational support of design exploration can become an exclusive barrier for the adoption of such systems by engineers. This work addresses the problem of defining the elements that constitute a multiple-objective design optimization problem, that is, design variables, constants, objective functions, and constraint functions. In light of this, contributions are reviewed from the field of evolutionary design optimization with respect to their concrete implementation for design exploration. Machine learning and natural language processing are supposed to facilitate feasible approaches to the support of configuration and parameterization. Hence, the authors further review promising machine learning and natural language processing methods for automatic knowledge elicitation and formalization with respect to their implementation for evolutionary design optimization. These methods come from the fields of product attribute extraction, clustering of design solutions, relationship discovery, computation of objective functions, metamodeling, and design pattern extraction.

Bayesian Optimal Designs for a Quantal Dose-Response Study with Potentially Missing Observations

In a dose-response study, there are frequently multiple goals and not all planned observations are realized at the end of the study. Subjects drop out and the initial design can be quite different from the final design. Consequently, the final design can be inefficient. Single- and multiple-objective Bayesian optimal designs that account for potentially missing observations in quantal response models were recently proposed in Baek (2005). In this work, we investigate the efficiencies of the conventional optimal designs that do not incorporate potential missing information relative to our proposed designs. Furthermore, we examine the impact of restricted dose range on the resulting optimal designs. As an application, we used missing data information from a study by Yocum et al. (2003) to design a study for estimating dose levels of tacrolimus that will result in a certain percentage of rheumatoid arthritis patients having an ACR20 response at 6 months.

Robustness Properties of Multiple-Objective Optimal Designs for a Bi-Exponential Model

We first discuss a design strategy for constructing locally optimal designs when there are several competing objectives in the study. Using a bi-exponential compartmental model as an illustrative example, we investigate robustness properties of the multiple-objective optimal designs to mis-specification of the nominal values of the parameters. It is shown that misspecifications in the nominal values can influence the model profile, with some parameters having a stronger influence than others. Our numerical results also show that locally multiple-objective optimal designs have different level of sensitivities under different optimality criteria.

Design Issues for the Michaelis–Menten Model

We discuss design issues for the Michaelis–Menten model and use geometrical arguments to find optimal designs for estimating a subset of the model parameters, or a linear combination of the parameters. We propose multiple-objective optimal designs when the parameters have different levels of interest to the researcher. In addition, we compare six commonly used sequence designs in the biological sciences for estimating parameters and, propose optimal choices for the parameters for geometric designs using closed-form efficiency formulas.

Sequential Construction of Multiple-Objective Optimal Designs

We propose a sequential approach for constructing multiple-objective locally optimal designs for nonlinear models. The technique used here is a general one and we demonstrate the added benefits of using a multiple-objective design over a single-objective design with examples from biomedical studies.

Multiple-objective optimal designs

We present illustrative multiple-objective optimal designs for nonlinear models useful in biomedical studies. The aim is to demonstrate the added benefits of using a multiple-objective design over the traditional single-objective design.

Multiple-objective optimal designs for the logit model

The toxicity and efficiency of a drug must be determined before it is approved for general use. Quantal dose-response experiments are routinely conducted to examine the response rates at dose levels of interest, Multiple-objective optimal designs for such studies are found and compared with the popular equal allocation rules.

Robust control design using eigenstructure assignment and multi-objective optimization

This paper develops a new approach to multiple objective optimization design for robust multivariable control systems, based on eigenstructure assignment and genetic algorithms. It considers various performance indices (or cost functions) in the objectives, which are individual eigenvalue sensitivity functions, and the sensitivity and the complementary sensitivity functions in the frequency domain, instead of a single performance index for a control system. Based on these performance indices, the robustness criteria are expressed by a set of inequalities. The paper will make full use of the freedom provided by eigenstructure assignment to find a controller to satisfy the robustness criteria. A numerical algorithm for multi-objective optimization using genetic algorithm approaches is developed and applied to the simulation of a distillation column control system design