Introduction: Tools and Challenges in Derivative-Free and Blackbox Optimization

Audet, Charles; Hare, Warren

doi:10.1007/978-3-319-68913-5_1

Cited by 20 publications

(16 citation statements)

References 129 publications

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“…Global optimization methods attempt to find the global optimum of an objective function f as opposed to stopping on the discovery at a local optimum. 30 In many cases, the difference between an arbitrary local minimum and the global minimum could mean a considerable performance loss. However, global optimization is significantly more challenging since there is no guaranteed way to find the global optimum without examining the entire search-space (i.e., traversing all combinations on M and D), which is often not feasible.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

Framework for Expediting Discovery of Optimal Solutions with Blackbox Algorithms in Non-Topology Photonic Inverse Design

2022

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Photonic inverse design has emerged as an indispensable engineering tool for complex optical systems. In many instances it is important to optimize for both material and geometry configurations, which results in complex nonsmooth search spaces with multiple local minima. Finding solutions approaching the global optimum may present a computationally intractable task. Here, we develop a framework that allows expediting the search of solutions close to a global optimum on complex optimization spaces with blackbox algorithms for nontopology inverse design problems in photonics. We study the way representative blackbox optimization algorithms work, including a genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and a mesh adaptive direct search (NOMAD). We then propose and utilize a two-step approach that identifies best performance algorithms on highly irregular and nonsmooth search spaces with 60+ optimization parameters. We reveal a connection between the search space complexity and algorithm performance and find that PSO and NOMAD consistently deliver better performance for mixed integer problems encountered in photonic inverse design, particularly with the account of material combinations. Our results differ from a commonly anticipated advantage of GA. Our findings will foster a more efficient design of photonic systems with optimal performance.

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Section: ■ Results and Discussionmentioning

confidence: 99%

Framework for Expediting Discovery of Optimal Solutions with Blackbox Algorithms in Non-Topology Photonic Inverse Design

2022

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“…In the next step, illustrated in Figure 2 , we aimed to identify the optimal value of an additional variable (symbolized by X ) that could be added to improve the regression model’s accuracy. This was formulated as black-box optimization [ 15 ], then solved using the Genetic Algorithm (GA) [ 16 ] due to its capability of providing good solutions in a reasonable time. The objective function of this optimization problem is to maximize the Pearson correlation coefficient (R-value) using a decision variable X that has a lower bound of 0 and an upper bound of 10.…”

Section: Methodsmentioning

confidence: 99%

Remote Learning in Transnational Education: Relationship between Virtual Learning Engagement and Student Academic Performance in BSc Pharmaceutical Biotechnology

et al. 2021

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The 21st century has seen dramatic changes to education delivery which have widened the scope of transnational education and remote learning via various virtual learning environments (VLEs). Efficient remote teaching activities require students to be engaged with taught materials and academic staff, and for educators to be able to track and improve student engagement. This article describes the generation of a predictive mathematical model for students’ exam performance using VLE engagement indicators and coursework marks together to enable the creation of a model with a correlation coefficient of 0.724. This article examines the relationship of each of these variables with final exam marks, as well as the addition of personal related variable X on the generated model’s accuracy. The generated models show that each variable had a different impact on the prediction of the final exam mark. The results’ analysis suggests that coursework marks and total VLE page views were the major attributes, while personal factors were also found to greatly impact model accuracy. Considering the case of outliers, who were students with low VLE engagement achieving high exam marks, it is proposed that personal factors, such as behavioural factors and study style, also have a significant effect on student academic attainment. The generated model can be used by students to improve self-efficacy by adjusting their study style and by educators to provide early interventions to support disengaged students. This model can be replicated in different remote learning settings and transnational education, and the findings might be insightful for courses with remote learning strategies to investigate the key educational, personal and engagement parameters for students’ overall success.

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“…The previous work with data profiles has assumed that the number of simplex evaluations (one dimension) is the dominant performance measure for testing how well a solver performs relative to the other solvers ( More & Wild, 2009 ; Audet & Hare, 2017 ). However, they did not investigate the performance of derivative free optimization solvers if a variety of metrics were used to evaluate the performance.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Such problems arise naturally in almost every branch of modern science and engineering. For example, pediatric cardiologists seek to delay the next operation as much as possible to identify the best shape of a surgical graft ( Audet & Hare, 2017 ). In this particular example, a number of variables can affect the objective function to treat and manage heart problems in children.…”

Section: Introductionmentioning

confidence: 99%

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High-dimensional normalized data profiles for testing derivative-free optimization algorithms

Musafer

Tokgoz

Mahmood

2022

PeerJ Computer Science

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This article provides a new tool for examining the efficiency and robustness of derivative-free optimization algorithms based on high-dimensional normalized data profiles that test a variety of performance metrics. Unlike the traditional data profiles that examine a single dimension, the proposed data profiles require several dimensions in order to analyze the relative performance of different optimization solutions. To design a use case, we utilize five sequences (solvers) of trigonometric simplex designs that extract different features of non-isometric reflections, as an example to show how various metrics (dimensions) are essential to provide a comprehensive evaluation about a particular solver relative to others. In addition, each designed sequence can rotate the starting simplex through an angle to designate the direction of the simplex. This type of features extraction is applied to each sequence of the triangular simplexes to determine a global minimum for a mathematical problem. To allocate an optimal sequence of trigonometric simplex designs, a linear model is used with the proposed data profiles to examine the convergence rate of the five simplexes. Furthermore, we compare the proposed five simplexes to an optimized version of the Nelder–Mead algorithm known as the Genetic Nelder–Mead algorithm. The experimental results demonstrate that the proposed data profiles lead to a better examination of the reliability and robustness for the considered solvers from a more comprehensive perspective than the existing data profiles. Finally, the high-dimensional data profiles reveal that the proposed solvers outperform the genetic solvers for all accuracy tests.

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Introduction: Tools and Challenges in Derivative-Free and Blackbox Optimization

Cited by 20 publications

References 129 publications

Framework for Expediting Discovery of Optimal Solutions with Blackbox Algorithms in Non-Topology Photonic Inverse Design

Framework for Expediting Discovery of Optimal Solutions with Blackbox Algorithms in Non-Topology Photonic Inverse Design

Remote Learning in Transnational Education: Relationship between Virtual Learning Engagement and Student Academic Performance in BSc Pharmaceutical Biotechnology

High-dimensional normalized data profiles for testing derivative-free optimization algorithms

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