A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Software for Implementing the Sequential Elimination of Level Combinations Algorithm

Genetic algorithms (GAs) are a popular technology to search for an optimum in a large search space. Using new concepts of forbidden array and weighted mutation, Mandal, Wu, and Johnson (2006) used elements of GAs to introduce a new global optimization technique called sequential elimination of level combinations (SELC), that efficiently finds optimums. A SAS macro, and MATLAB and R functions are developed to implement the SELC algorithm.

Engineering design applications of surrogate-assisted optimization techniques

The construction of models aimed at learning the behaviour of a system whose responses to inputs are expensive to measure is a branch of statistical science that has been around for a very long time. Geostatistics has pioneered a drive over the last half century towards a better understanding of the accuracy of such ‘surrogate’ models of the expensive function. Of particular interest to us here are some of the even more recent advances related to exploiting such formulations in an optimization context. While the classic goal of the modelling process has been to achieve a uniform prediction accuracy across the domain, an economical optimization process may aim to bias the distribution of the learning budget towards promising basins of attraction. This can only happen, of course, at the expense of the global exploration of the space and thus finding the best balance may be viewed as an optimization problem in itself. We examine here a selection of the state of-the-art solutions to this type of balancing exercise through the prism of several simple, illustrative problems, followed by two ‘real world’ applications: the design of a regional airliner wing and the multi-objective search for a low environmental impact hous

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

A multiobjective optimization approach to statistical mechanics

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions involve a compromise between both. The theory of Pareto (or multi objective) optimization provides a general framework to explore these problems and find the space of possible solutions compatible with the underlying tradeoffs, known as the {\em Pareto front}. Conflicts between constraints can lead to complex landscapes of Pareto optimal solutions with interesting implications in economy, engineering, or evolutionary biology. Despite their disparate nature, here we show how the structure of the Pareto front uncovers profound universal features that can be understood in the context of thermodynamics. In particular, our study reveals that different fronts are connected to different classes of phase transitions, which we can define robustly, along with critical points and thermodynamic potentials. These equivalences are illustrated with classic thermodynamic examples.Comment: 14 pages, 8 figure

Revisiting nested group testing procedures: new results, comparisons, and robustness

Group testing has its origin in the identification of syphilis in the US army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this paper, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article is available online.Comment: Submitted for publication on May 3, 2016. Revised versio

Neo-Schumpeterian Simulation Models

The use of simulation modelling techniques by neo-Schumpeterian economists dates back to Nelson and Winter’s 1982 book “An Evolutionary Theory of Economic Change”, and has rapidly expanded ever since. This paper considers the way in which successive generations of models have extended the boundaries of research (both with respect to the range of phenomena considered and the different dimensions of innovation that are considered), and while simultaneously introducing novel modelling techniques. At the same time, the paper will highlight the distinct set of features that have emerged in these neo-Schumpeterian models, and which set them apart from the models developed by other schools. In particular, they share a distinct view about the type of world in which real economic agents operate, and a invariably contain a generic set of algorithms. In addition to reviewing past models, the paper considers a number of pressing issues that remain unresolved and which modellers will need to address in future. Notable amongst these are the methodological relationship between empirical studies and simulation (e.g. ‘history friendly modelling’), the development of common standards for sensitivity analysis, and the need to further extend the boundaries of research in order to consider important aspects of innovation and technical change.macroeconomics ;

Aircraft optimization by a system approach: Achievements and trends

Recently emerging methodology for optimal design of aircraft treated as a system of interacting physical phenomena and parts is examined. The methodology is found to coalesce into methods for hierarchic, non-hierarchic, and hybrid systems all dependent on sensitivity analysis. A separate category of methods has also evolved independent of sensitivity analysis, hence suitable for discrete problems. References and numerical applications are cited. Massively parallel computer processing is seen as enabling technology for practical implementation of the methodology

Implementing the EffTox dose-finding design in the Matchpoint trial

Background: The Matchpoint trial aims to identify the optimal dose of ponatinib to give with conventional chemotherapy consisting of fludarabine, cytarabine and idarubicin to chronic myeloid leukaemia patients in blastic transformation phase. The dose should be both tolerable and efficacious. This paper describes our experience implementing EffTox in the Matchpoint trial. Methods: EffTox is a Bayesian adaptive dose-finding trial design that jointly scrutinises binary efficacy and toxicity outcomes. We describe a nomenclature for succinctly describing outcomes in phase I/II dose-finding trials. We use dose-transition pathways, where doses are calculated for each feasible set of outcomes in future cohorts. We introduce the phenomenon of dose ambivalence, where EffTox can recommend different doses after observing the same outcomes. We also describe our experiences with outcome ambiguity, where the categorical evaluation of some primary outcomes is temporarily delayed. Results: We arrived at an EffTox parameterisation that is simulated to perform well over a range of scenarios. In scenarios where dose ambivalence manifested, we were guided by the dose-transition pathways. This technique facilitates planning, and also helped us overcome short-term outcome ambiguity. Conclusions: EffTox is an efficient and powerful design, but not without its challenges. Joint phase I/II clinical trial designs will likely become increasingly important in coming years as we further investigate non-cytotoxic treatments and streamline the drug approval process. We hope this account of the problems we faced and the solutions we used will help others implement this dose-finding clinical trial design. Trial registration: Matchpoint was added to the European Clinical Trials Database (2012-005629-65) on 2013-12-30

The potential of genetic algorithms for conceptual design of rotor systems

The capabilities of genetic algorithms as a non-calculus based, global search method make them potentially useful in the conceptual design of rotor systems. Coupling reasonably simple analysis tools to the genetic algorithm was accomplished, and the resulting program was used to generate designs for rotor systems to match requirements similar to those of both an existing helicopter and a proposed helicopter design. This provides a comparison with the existing design and also provides insight into the potential of genetic algorithms in design of new rotors