{"id":5203,"date":"2023-08-11T14:20:30","date_gmt":"2023-08-11T13:20:30","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=5203"},"modified":"2023-09-20T16:24:25","modified_gmt":"2023-09-20T15:24:25","slug":"examples-opimizations","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=5203","title":{"rendered":"Examples: Optimizations"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Model-description\" >Model description<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Modeling-Workflow\" >Modeling Workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Notation-of-equation-system\" >Notation of equation system<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Base-names\" >Base names<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Indices\" >Indices<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Equations\" >Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Equation-system\" >Equation system<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Simulation-workflow\" >Simulation workflow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\/#Optimization-workflow\" >Optimization workflow<\/a><\/li><\/ul><\/nav><\/div>\n<p>In this section, examples for using MOSAICmodeling&#8217;s optimization capabilities are given. The examples are visible to all users and the examples always note the ID of the respective element. Therefore, you can always consult this solution if you do not know how to proceed.<\/p>\n<ul>\n<li>\u201c<strong>Use of Optimizations I \u2013 MINLP Example<\/strong>\u201d explains how a simple synthesis problem can be set up and solved<\/li>\n<li><strong>\u201cUse of Optimizations II &#8211; Dynamic Optimization via Single Shooting\u201d\u00a0<\/strong>shows how the operation of a CSTR is modeled and optimized in Matlab<\/li>\n<li>\u201c<strong>Use of Optimizations III \u2013 NLP Example<\/strong>\u201d explains how a nonlinear programming problem (NLP) can be formulated and solved<\/li>\n<li>\u201c<strong>Use of Optimizations IV \u2013 MILP Example<\/strong>\u201d explains how a mixed-integer linear programming problem (MILP) can be formulated and solved<\/li>\n<\/ul>\n<div id=\"ccchildpages-1\" class=\"ccchildpages ccflex threecol ccblue ccclearfix\"><div class=\"ccchildpage  ccfirst ccodd ccpage-count-1 ccpage-id-5208 ccpage-use-of-optimizations-minlp-example ccpage-has-parent ccpage-pid-5203 ccpage-parent-examples-opimizations\"><h3 class=\"ccpage_title ccpage_linked_title\" title=\"Use of Optimizations I &#8211; MINLP Example\"><a class=\"ccpage_title_link\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\" title=\"Use of Optimizations I &#8211; MINLP Example\">Use of Optimizations I &#8211; MINLP Example<\/a><\/h3><div class=\"ccpages_excerpt\">This tutorial explains how a simple process synthesis problem can...<\/div><p class=\"ccpages_more\"><a href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\"  title=\"Read more ...\">Read more ...<\/a><\/p><\/div><div class=\"ccchildpage  cceven ccpage-count-2 ccpage-id-5838 ccpage-use-of-optimizations-ii-dynamic-optimization-via-single-shooting ccpage-has-parent ccpage-pid-5203 ccpage-parent-examples-opimizations\"><h3 class=\"ccpage_title ccpage_linked_title\" title=\"Use of Optimizations II &#8211; Dynamic Optimization via Single Shooting\"><a class=\"ccpage_title_link\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\" title=\"Use of Optimizations II &#8211; Dynamic Optimization via Single Shooting\">Use of Optimizations II &#8211; Dynamic Optimization via Single Shooting<\/a><\/h3><div class=\"ccpages_excerpt\">Model description This example shows how to solve a dynamic...<\/div><p class=\"ccpages_more\"><a href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\"  title=\"Read more ...\">Read more ...<\/a><\/p><\/div><div class=\"ccchildpage  cclast ccodd ccpage-count-3 ccpage-id-5939 ccpage-use-of-optimizations-i-nlp-example ccpage-has-parent ccpage-pid-5203 ccpage-parent-examples-opimizations\"><h3 class=\"ccpage_title ccpage_linked_title\" title=\"Use of Optimizations III &#8211; NLP Example\"><a class=\"ccpage_title_link\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5939\" title=\"Use of Optimizations III &#8211; NLP Example\">Use of Optimizations III &#8211; NLP Example<\/a><\/h3><div class=\"ccpages_excerpt\">This tutorial explains how a nonlinear programming problem can be...<\/div><p class=\"ccpages_more\"><a href=\"https:\/\/mosaic-modeling.de\/?page_id=5939\"  title=\"Read more ...\">Read more ...<\/a><\/p><\/div><div class=\"ccchildpage  ccfirst cceven ccpage-count-4 ccpage-id-5954 ccpage-use-of-optimization-iv-milp-example ccpage-has-parent ccpage-pid-5203 ccpage-parent-examples-opimizations\"><h3 class=\"ccpage_title ccpage_linked_title\" title=\"Use of Optimization IV &#8211; MILP Example\"><a class=\"ccpage_title_link\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\" title=\"Use of Optimization IV &#8211; MILP Example\">Use of Optimization IV &#8211; MILP Example<\/a><\/h3><div class=\"ccpages_excerpt\">This tutorial explains how a simple mixed-integer linear programming problem...<\/div><p class=\"ccpages_more\"><a href=\"https:\/\/mosaic-modeling.de\/?page_id=5954\"  title=\"Read more ...\">Read more ...<\/a><\/p><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In this section, examples for using MOSAICmodeling&#8217;s optimization capabilities are given. The examples are visible to all users and the examples always note the ID of the respective element. Therefore, you can always consult this solution if you do not know how to proceed. \u201cUse of Optimizations I \u2013 MINLP Example\u201d explains how a simple [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":4731,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5203","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/252"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5203"}],"version-history":[{"count":8,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5203\/revisions"}],"predecessor-version":[{"id":5957,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5203\/revisions\/5957"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4731"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}