{"id":5838,"date":"2023-09-09T03:19:50","date_gmt":"2023-09-09T02:19:50","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=5838"},"modified":"2025-09-11T16:56:02","modified_gmt":"2025-09-11T15:56:02","slug":"use-of-optimizations-ii-dynamic-optimization-via-single-shooting","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=5838","title":{"rendered":"Use of Optimizations II &#8211; Dynamic Optimization via Single Shooting"},"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=5838\/#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=5838\/#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=5838\/#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=5838\/#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=5838\/#Superscripts\" >Superscripts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Subscripts\" >Subscripts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#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-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Equations\" >Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#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-10\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#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-11\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Optimization-workflow\" >Optimization workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Constraints\" >Constraints<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Variable-specification\" >Variable specification<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5838\/#Code-generation-and-execution\" >Code generation and execution<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Model-description\"><\/span>Model description<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This example shows how to solve a dynamic optimization problem with single shooting via MOSAICmodeling. The case study focuses on a CSTR for which two inputs must be optimally chosen so that the integral of component 1 over a time horizon of one hour is maximized. The example is governed by the following equations:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 283px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2e328291783e9d3aca3fa53d6042269e_l3.png\" height=\"283\" width=\"651\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#99;&#95;&#99;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#86;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#99;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;&#32;&#45;&#32;&#99;&#95;&#99;&#41;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#114;&#61;&#49;&#125;&#94;&#123;&#78;&#82;&#125;&#92;&#110;&#117;&#95;&#123;&#99;&#44;&#114;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#107;&#95;&#114;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#95;&#123;&#99;&#61;&#114;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#101;&#120;&#112;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#69;&#95;&#114;&#125;&#123;&#82;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#84;&#125;&#41;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#84;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#70;&#125;&#123;&#86;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;&#32;&#45;&#32;&#84;&#41;&#32;&#43;&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#114;&#61;&#49;&#125;&#94;&#123;&#78;&#82;&#125;&#32;&#107;&#95;&#114;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#95;&#123;&#99;&#61;&#114;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#101;&#120;&#112;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#69;&#95;&#114;&#125;&#123;&#82;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#84;&#125;&#41;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#104;&#95;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#82;&#125;&#44;&#114;&#125;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#112;&#125;&#32;&#45;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#85;&#65;&#125;&#123;&#92;&#114;&#104;&#111;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#112;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#86;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#84;&#32;&#45;&#32;&#84;&#95;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#106;&#97;&#99;&#107;&#101;&#116;&#125;&#41;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#99;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#116;&#101;&#103;&#114;&#97;&#108;&#125;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#99;&#95;&#123;&#99;&#61;&#49;&#125;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#105;&#110;&#101;&#113;&#32;&#61;&#32;&#84;&#32;&#45;&#32;&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#102;&#32;&#61;&#32;&#45;&#32;&#99;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#116;&#101;&#103;&#114;&#97;&#108;&#125;&#46;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p>The first equation is the generic component balance. The second equation is the energy balance. The third equation determines the integral of the concentration of component 1 numerically. The fourth equation represents an inequality constraint that specifies the upper bound of the reactor temperature. Finally, the last equation calculates the objective value for the optimization. This is the negative integral as we want to minimize the function later on.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Modeling-Workflow\"><\/span>Modeling Workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"Notation-of-equation-system\"><\/span>Notation of equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>For the notation of the equation, we need to set up all base names, superscripts, and indices that appear in the equations, i.e.<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Base-names\"><\/span>Base names<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-42f87252e4007771ae40decd7840509e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: 0px;\"\/>, enthalpy difference in kJ\/mol<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5376f6867c11bfe62d1de72e3207e7cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, stoichiometric coefficient<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e8e197a6f1572ae9b5a16039ea626388_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#114;&#104;&#111;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/>, density in kg\/m\u00b3<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, molar concentration in mol\/m\u00b3<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, activation energy in J\/mol<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/>, objective<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-88df03c55e081c7cd9da4e7d74ba7265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, volume flow in m\u00b3\/s<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00c74495598990338e57656f9ec62f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#110;&#101;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -4px;\"\/>, inequality slack variable in K<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>, pre-exponential factor for kinetics in 1\/s<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d6abdd487c56e5efbb2c9522ed4b9360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, universal gas constant in J\/mol\/K<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>, time in s<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/>, temperature in K<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ae080f27f28c45d7dd64415f54572dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#85;&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\"\/>, product of overall heat transfer coefficient and jacket are in kW\/K<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-54e215a7a583b4f357a5a627420bcf2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, volume in m\u00b3<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Superscripts\"><\/span>Superscripts<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>in, inlet<\/li>\n<li>integral, integral over time horizon<\/li>\n<li>max, maximum<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Subscripts\"><\/span>Subscripts<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>jacket, reactor jacket<\/li>\n<li>R, reaction<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Indices\"><\/span>Indices<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, component index 1..NC<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, reaction index 1..NR<\/li>\n<\/ul>\n<p>The resulting notation has ID 185805.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equations\"><\/span>Equations<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Next, we can define the equations of the model. Therefore, we open the equation editor, load the notation we just created, and enter the equations as stated above in the model description. The formulated equations are available with the IDs 185806, 185807, 185819, 185811, and 185812 (5 equations).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equation-system\"><\/span>Equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Now we are able to construct our equation system:<\/p>\n<ol>\n<li>Go to &#8220;Equation System&#8221; and load the notation for the equations<\/li>\n<li>Add the eleven constraints and the objective function to your system in the Connected Elements tab<\/li>\n<li>Save your equation system<\/li>\n<\/ol>\n<p>This equation system is available with ID 185808.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Simulation-workflow\"><\/span>Simulation workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Your model is now complete and you can move on to the &#8220;Simulation&#8221; section of MOSAICmodeling.<\/p>\n<ol>\n<li>Enter a suitable description<\/li>\n<li>Select the tab Equation System and load the system created in the previous steps. Assign the maximum values for the available indices (NC = 3, NR = 2) and click on Confirm Index Data<\/li>\n<li>Select the tab Specifications. In the list ALL VARIABLES, you will find the variables as defined in your model notation.<\/li>\n<li>Classify the variables as design variables and iteration values, respectively, by selecting the category from the dropdown menu in the Type column.<\/li>\n<\/ol>\n<p>The simulation will be specified and initialized with the values given in Table 1. After having assigned the initial guesses and the parameter values, you can save the variable specification and then the simulation. The simulation is available in MOSAICmodeling with ID 185809. The respective variable specification that may serve as initialization for the optimization has ID 185810.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value \/ Initial guess \/ Initial condition<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8446763b6e165b6c68e393bf6604abd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#104;&#95;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#82;&#125;&#44;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Enthalpy of reaction for reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">45000.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5dc5362ea86efcda4687055637fd96ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#104;&#95;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#82;&#125;&#44;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Enthalpy of reaction for reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">-55000.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d89b5ddb293d02ace5d40532ba423b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#44;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 for reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c52a1424f7f8e1e6f79787947dbf3d93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#44;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 for reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2a98f90a77e7bc711f67e8984916ea74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#44;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 for reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e061f78a47b2388e4df367bd4a849e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#44;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 for reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-a81ed638a32e52d00bcf1ba0f1838846_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#44;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 for reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-17b65b7f28576799caaf50a748ee7c4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#44;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 for reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e8e197a6f1572ae9b5a16039ea626388_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#114;&#104;&#111;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Density<\/td><td class=\"has-text-align-left\" data-align=\"left\">800.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-201f9ea0cb2180d726a3ab40a9ffc046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#95;&#123;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Activation energy of reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">69000.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2037e8a73bcbba0d1424a34663d76770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#95;&#123;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"38\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Activation energy of reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">72000.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-88df03c55e081c7cd9da4e7d74ba7265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Volume flow of feed<\/td><td class=\"has-text-align-left\" data-align=\"left\">6.5E-4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d6abdd487c56e5efbb2c9522ed4b9360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Universal gas constant<\/td><td class=\"has-text-align-left\" data-align=\"left\">8.3144598<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4b3ca1e2efa7fb9c4757e3a0006d6297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Inlet temperature<\/td><td class=\"has-text-align-left\" data-align=\"left\">333.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-330dd9f7c2922d73f8f9b69485ea8bda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum temperature<\/td><td class=\"has-text-align-left\" data-align=\"left\">350.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-83183ea2038f80bda605296af2b01653_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#95;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#106;&#97;&#99;&#107;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Temperature of jacket<\/td><td class=\"has-text-align-left\" data-align=\"left\">333.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ae080f27f28c45d7dd64415f54572dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#85;&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Cooling characteristic<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-54e215a7a583b4f357a5a627420bcf2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Volume<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4cde722db99ef5b3e4890285dd6db7ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"31\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Inlet concentration of component 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">5.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cc12f5630ffcf49264b594f292778a92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Inlet concentration of component 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">20.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-929e328f13dbb8ff8162a752a9a9caa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Inlet concentration of component 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">3.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fda390ccc503779a7603e6418e2f97de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Heat capacity<\/td><td class=\"has-text-align-left\" data-align=\"left\">3.5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c79665c5b0e29bd918c389e30ef723e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#114;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Pre-exponential factor of reaction 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">5.0E6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-391ea254018529a8d1ae921ae150b134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#114;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Pre-exponential factor of reaction 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.0E7<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial condition for temperature<\/td><td class=\"has-text-align-left\" data-align=\"left\">333.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d95f5074095fe093670979ae0466b8ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial condition for concentration of component 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">8.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cc3540fc91d4ae127886bd215c8fc6e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"32\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial condition for concentration of component 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">20.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2a69ebca95d1669d7d5e56a95d88c436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"32\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial condition for concentration of component 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-a2433234180b1c03687464146243e50c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#116;&#101;&#103;&#114;&#97;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"53\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial condition for integral of concentration of component 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00c74495598990338e57656f9ec62f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#110;&#101;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial guess for slack variable<\/td><td class=\"has-text-align-left\" data-align=\"left\">-17.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Initial guess for objective<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Overview of design values, initial conditions, and initial guesses.<\/figcaption><\/figure>\n\n\n<h3><span class=\"ez-toc-section\" id=\"Optimization-workflow\"><\/span>Optimization workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now move to the &#8220;Optimization&#8221; section in MOSAICmodeling and go to the Specification tab.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Constraints\"><\/span>Constraints<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Constraints tab and load your simulation from the previous step. Make sure that all constraints and the objective function are loaded successfully.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Variable-specification\"><\/span>Variable specification<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Variable specification. If you saved the simulation after you saved the variable specification, the variable specification from the simulation should be loaded in the optimization as well.<\/p>\n<ol>\n<li>Start by assigning <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> as objective value.<\/li>\n<li>Then assign <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4b3ca1e2efa7fb9c4757e3a0006d6297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-83183ea2038f80bda605296af2b01653_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#95;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#106;&#97;&#99;&#107;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -6px;\"\/> as optimization values and set their lower and upper bounds to 273 and 373, respectively<\/li>\n<li>Set an upper bound of 0 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00c74495598990338e57656f9ec62f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#110;&#101;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -4px;\"\/><\/li>\n<li>You can now save the variable specification &#8211; either by overwriting the one from your simulation or by creating a new one.<\/li>\n<li>Save the optimization<\/li>\n<\/ol>\n<p>The resulting variable specification with the updated type classifications and variable bounds has ID 185817. The optimization has ID 185816.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Code-generation-and-execution\"><\/span>Code generation and execution<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the tab Code Generation &amp; Execution and take a look at the Status window: It should read 1 variable selected for minimization and 2 variables selected for optimization. Load the user-defined language specificator with ID 185804, which is created in the example <a href=\"http:\/\/mosaic-modeling.de\/?page_id=5833\">Use of User-defined Language Specifications II \u2013 Parameter Estimation with Single Shooting<\/a> and click on Generate Code. Copy the export to Matlab and solve this optimization problem sequentially. Note that the algorithm &#8216;SQP&#8217; is chosen as preference because this was the only algorithm that was able to solve this problem. The default algorithm &#8216;Interior-point&#8217; might be able to solve the problem if the algorithm&#8217;s parameters are modified. With the default options, it terminates with an infeasible solution. The optimal solution for the two controls <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4b3ca1e2efa7fb9c4757e3a0006d6297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#105;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"25\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-83183ea2038f80bda605296af2b01653_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;&#95;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#106;&#97;&#99;&#107;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -6px;\"\/> are 327 K and 328 K, respectively. However, the solution depends on the initial guesses for the decisions as the only constraint for the maximum temperature is active and the reactor temperature can either be reduced by a lower inlet temperature or a lower cooling temperature.<\/p>\n<p>Note that the used UDLS is still fairly simple as only one control setpoint is allowed over the full time horizon of one hour. Of course, this could be further refined.<\/p>","protected":false},"excerpt":{"rendered":"<p>Model description This example shows how to solve a dynamic optimization problem with single shooting via MOSAICmodeling. The case study focuses on a CSTR for which two inputs must be optimally chosen so that the integral of component 1 over a time horizon of one hour is maximized. The example is governed by the following [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":5203,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5838","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5838","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=5838"}],"version-history":[{"count":23,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5838\/revisions"}],"predecessor-version":[{"id":6218,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5838\/revisions\/6218"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5203"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}