{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/78688"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/78688","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Deterministic annealing algorithm: tutorial, application to pickup and delivery problem and computational aspects","abstract":"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 $t$.","abstract_html":"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 $T(t)=\\rho T(t-1), 0&lt;\\rho&lt;1$, where $T(t)$ is the temperature at time $t$.","abstract_has_math":true,"creators":["Parekh, Pratik Mayur"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-04-30","date_published":"2015-04-30","updated_at":"2026-07-22T22:26:12Z","subjects":["Deterministic Annealing Algorithm","Computational Aspects"],"languages":["en"],"rights":["Copyright 2015 Pratik Mayur Parekh"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/78688","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Parekh, Pratik Mayur"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-04-30","2015-07-22T22:34:01Z","2017-07-23T09:15:19Z","2015-05","2015-5"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Deterministic Annealing Algorithm","Computational Aspects"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Pratik Mayur Parekh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/78688"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Deterministic annealing algorithm: tutorial, application to pickup and delivery problem and computational aspects"]}]}],"canonical_facts":{"dc:creator":["Parekh, Pratik Mayur"],"dc:date":["2015-04-30","2015-07-22T22:34:01Z","2017-07-23T09:15:19Z","2015-05","2015-5"],"dc:description":["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."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/78688"],"dc:language":["en"],"dc:rights":["Copyright 2015 Pratik Mayur Parekh"],"dc:subject":["Deterministic Annealing Algorithm","Computational Aspects"],"dc:title":["Deterministic annealing algorithm: tutorial, application to pickup and delivery problem and computational aspects"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:12Z"}