High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and Applications--Stuttgart 2014, Lecture Notes in Computational Science and Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer International Publishing, 201

Optimization Algorithms in Project Scheduling

Scheduling, or planning in a general perspective, is the backbone of project management; thus, the successful implementation of project scheduling is a key factor to projects’ success. Due to its complexity and challenging nature, scheduling has become one of the most famous research topics within the operational research context, and it has been widely researched in practical applications within various industries, especially manufacturing, construction, and computer engineering. Accordingly, the literature is rich with many implementations of different optimization algorithms and their extensions within the project scheduling problem (PSP) analysis field. This study is intended to exhibit the general modelling of the PSP, and to survey the implementations of various optimization algorithms adopted for solving the different types of the PSP

A study on the robustness of strain optimization algorithms

5th International Conference on Practical Applications of Computational Biology & Bioinformatics (PACBB 2011), ISBN 978-3-642-19913-4In recent years, there have been considerable advances in the use of genome-scale metabolic models to provide accurate phenotype simulation methods, which in turn enabled the development of efficient strain optimization algorithms for Metabolic Engineering. In this work, we address some of the limitations of previous studies regarding strain optimization algorithms, mainly its use of Flux Balance Analysis in the simulation layer.We perform a thorough analysis of previous results by relying on Flux Variability Analysis and on alternative methods for phenotype simulation, such as ROOM. This last method is also used in the simulation layer, as a basis for optimization, and the results obtained are also the target of thorough analysis and comparison with previous ones.Fundação para a Ciência e a Tecnologia (FCT) - project MIT-PT/BS-BB/0082/200

Fixed-Parameter Algorithms For Protein Similarity Search Under mRNA Structure Constraints

International audienceIn the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codon-wise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the so-called mRNA Structure Optimization (MRSO) problem. Since MRSO is known to be APX-hard, Bongartz [10] suggested to attack the problem using the approach of parameterized complexity. In this paper we propose three fixed-parameter algorithms that apply for several interesting parameters of MRSO. We believe these algorithms to be relevant for practical applications today, as well as for possible future applications. Furthermore, our results extend the known tractability borderline of MRSO, and provide new research horizons for further improvements of this sort

Global optimization algorithms for image registration and clustering

Global optimization is a classical problem of finding the minimum or maximum value of an objective function. It has applications in many areas, such as biological image analysis, chemistry, mechanical engineering, financial analysis, deep learning and image processing. For practical applications, it is important to understand the efficiency of global optimization algorithms. This dissertation develops and analyzes some new global optimization algorithms and applies them to practical problems, mainly for image registration and data clustering. First, the dissertation presents a new global optimization algorithm which approximates the optimum using only function values. The basic idea is to use the points at which the function has been evaluated to decompose the domain into a collection of hyper-rectangles. At each step of the algorithm, it chooses a hyper-rectangle according to a certain criterion and the next function evaluation is at the center of the hyper-rectangle. The dissertation includes a proof that the algorithm converges to the global optimum as the number of function evaluations goes to infinity, and also establishes the convergence rate. Standard test functions are used to experimentally evaluate the algorithm. The second part focuses on applying algorithms from the first part to solve some practical problems. Image processing tasks often require optimizing over some set of parameters. In the image registration problem, one attempts to determine the best transformation for aligning similar images. Such problems typically require minimizing a dissimilarity measure with multiple local minima. The dissertation describes a global optimization algorithm and applies it to the problem of identifying the best transformation for aligning two images. Global optimization algorithms can also be applied to the data clustering problem. The basic purpose of clustering is to categorize data into different groups by their similarity. The objective cost functions for clustering usually are non-convex. $k$-means is a popular algorithm which can find local optima quickly but may not obtain global optima. The different starting points for $k$-means can output different local optima. This dissertation describes a global optimization algorithm for approximating the global minimum of the clustering problem. The third part of the dissertation presents variations of the proposed algorithm that work with different assumptions on the available information, including a version that uses derivatives

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity

Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale optimization problems, we are often concerned with the adaptivity complexity of an algorithm, which quantifies the number of sequential rounds where polynomially-many independent function evaluations can be executed in parallel. While low adaptivity is ideal, it is not sufficient for a distributed algorithm to be efficient, since in many practical applications of submodular optimization the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of adaptive submodular optimization. Our main result is a distributed algorithm for maximizing a monotone submodular function with cardinality constraint $k$ that achieves a $(1-1/e-\varepsilon)$-approximation in expectation. This algorithm runs in $O(\log(n))$ adaptive rounds and makes $O(n)$ calls to the function evaluation oracle in expectation. The approximation guarantee and query complexity are optimal, and the adaptivity is nearly optimal. Moreover, the number of queries is substantially less than in previous works. Last, we extend our results to the submodular cover problem to demonstrate the generality of our algorithm and techniques.Comment: 30 pages, Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019