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2015-04-30 2015-07-22T22:34:01Z 2015-07-22T22:34:01Z 2017-07-23T09:15:19Z 2015-05 Parekh, Pratik Mayur The deterministic annealing (DA) method, used for the solution of several nonconvex problems, offers the ability to avoid shallow local minima of a given cost surface and the ability to minimize the cost function even when there are many local minima. The method is established in a probabilistic framework through basic information-theoretic techniques such as maximum entropy and random coding. It arises naturally in the context of statistical mechanics by the emulation of a physical process whereby a solid is slowly cooled and at zero temperature assumes its minimum energy configuration. We start with the introduction to DA method and then present a tutorial to describe the algorithm steps. Also, we discuss the connections of DA method with Statistical Mechanics and Rate-Distortion Theory. Next, we present the application of DA method to pickup and deliver scheduling problem with time windows. Finally, a computational complexity analysis for DA is presented for a given temperature schedule. The case study focuses on the geometric cooling law $T(t)=\rho T(t-1), 0<\rho<1$, where $T(t)$ is the temperature at time $t$. Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-05-01 The student, Pratik Mayur Parekh, accepted the attached license on 2015-04-29 at 11:47. The student, Pratik Mayur Parekh, submitted this Thesis for approval on 2015-04-29 at 11:54. This Thesis was approved for publication on 2015-04-30 at 15:06. DSpace SAF Submission Ingestion Package generated from Vireo submission #8183 on 2015-07-22 at 14:19:02 Made available in DSpace on 2015-07-22T22:34:01Z (GMT). No. of bitstreams: 2 PAREKH-THESIS-2015.pdf: 1206816 bytes, checksum: 55dda3d59a2fd68c519e62a706ce7365 (MD5) LICENSE.txt: 4216 bytes, checksum: 61153f08a4282ff58434bad3e7f8ee9d (MD5) Previous issue date: 2015-04-30 Embargo set by: Seth Robbins for item 79929 Lift date: 2017-07-22T22:34:16Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 79929 on 2017-07-23T09:15:19Z. application/pdf http://hdl.handle.net/2142/78688 en Copyright 2015 Pratik Mayur Parekh Deterministic Annealing Algorithm Computational Aspects Deterministic annealing algorithm: tutorial, application to pickup and delivery problem and computational aspects text text 2015-5 Mechanical Sci & Engineering Mechanical Engineering University of Illinois at Urbana-Champaign Thesis M.S.