Least squares splines with free knots: global optimization approach

2004 ◽  
Vol 149 (3) ◽  
pp. 783-798 ◽  
Author(s):  
Gleb Beliakov
Author(s):  
S.P. Wilson ◽  
M.C. Bartholomew-Biggs ◽  
S.C. Parkhurst

This chapter describes the formulation and solution of a multi-aircraft routing problem which is posed as a global optimization calculation. The chapter extends previous work (involving a single aircraft using two dimensions) which established that the algorithm DIRECT is a suitable solution technique. The present work considers a number of ways of dealing with multiple routes using different problem decompositions. A further enhancement is the introduction of altitude to the problems so that full threedimensional routes can be produced. Illustrative numerical results are presented involving up to three aircraft and including examples which feature routes over real-life terrain data.


2021 ◽  
Author(s):  
Li Chen ◽  
Wenyun Lu ◽  
Lin Wang ◽  
Xi Xing ◽  
Xin Teng ◽  
...  

AbstractA primary goal of metabolomics is to identify all biologically important metabolites. One powerful approach is liquid chromatography-high resolution mass spectrometry (LC-MS), yet most LC-MS peaks remain unidentified. Here, we present a global network optimization approach, NetID, to annotate untargeted LC-MS metabolomics data. We consider all experimentally observed ion peaks together, and assign annotations to all of them simultaneously so as to maximize a score that considers properties of peaks (known masses, retention times, MS/MS fragmentation patterns) as well network constraints that arise based on mass difference between peaks. Global optimization results in accurate peak assignment and trackable peak-peak relationships. Applying this approach to yeast and mouse data, we identify a half-dozen novel metabolites, including thiamine and taurine derivatives. Isotope tracer studies indicate active flux through these metabolites. Thus, NetID applies existing metabolomic knowledge and global optimization to annotate untargeted metabolomics data, revealing novel metabolites.


Author(s):  
Deyi Xue

Abstract A global optimization approach for identifying the optimal product configuration and parameters is proposed to improve manufacturability measures including feasibility, cost, and time of production. Different product configurations, including alternative design candidates and production processes, are represented by an AND/OR graph. Product parameters are described by variables including continuous variables, integer variables, Boolean variables, and discrete variables. Two global optimization methods, genetic algorithm and simulated annealing, are employed for identifying the optimal product configuration and parameters. The introduced approach serves as a key component in an integrated concurrent design system. A case study example is given to show how the proposed method is used for solving the engineering problems.


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