{"id":4191,"date":"2023-03-18T11:42:16","date_gmt":"2023-03-18T10:42:16","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=4191"},"modified":"2023-08-22T09:55:59","modified_gmt":"2023-08-22T08:55:59","slug":"optimization-variable-specification","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=4191","title":{"rendered":"Optimization: Variable specification"},"content":{"rendered":"\n<p class=\"has-vivid-red-color has-text-color\"><strong>Mandatory element<\/strong><\/p>\n\n\n<p>The variable specification works the same way as in the simulation. Therefore, general explanations are given <a href=\"http:\/\/mosaic-modeling.de\/?page_id=4179\">elsewhere<\/a>.<\/p>\n<h3>Purpose<\/h3>\n<p>Nevertheless, there are a couple of additional requirements for an optimization. The optimization requires exactly one objective variable. Remember that MOSAICmodeling solves the following optimization problem:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b13f9741744129807d7467d326204cd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" &#92;&#109;&#105;&#110;&#95;&#123;&#117;&#44;&#121;&#125;&#32;&#102;&#40;&#120;&#44;&#117;&#44;&#121;&#41;&#32;&#92;&#92;&#91;&#49;&#101;&#120;&#93;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#46;&#92;&#44;&#116;&#46;&#92;&#44;&#125;&#32;&#103;&#40;&#120;&#44;&#117;&#44;&#121;&#41;&#32;&#61;&#32;&#48;&#44;&#32;&#92;&#92;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#46;&#92;&#44;&#116;&#46;&#92;&#44;&#125;&#125;&#32;&#120;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#76;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#120;&#32;&#92;&#108;&#101;&#113;&#32;&#120;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#85;&#125;&#44;&#32;&#92;&#92;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#46;&#92;&#44;&#116;&#46;&#92;&#44;&#125;&#125;&#32;&#117;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#76;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#117;&#32;&#92;&#108;&#101;&#113;&#32;&#117;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#85;&#125;&#44;&#32;&#92;&#92;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#46;&#92;&#44;&#116;&#46;&#92;&#44;&#125;&#125;&#32;&#121;&#32;&#92;&#105;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#90;&#125;&#94;&#110;&#44;&#32;&#92;&#92;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#115;&#46;&#92;&#44;&#116;&#46;&#92;&#44;&#125;&#125;&#32;&#121;&#94;&#76;&#32;&#92;&#108;&#101;&#113;&#32;&#121;&#32;&#92;&#108;&#101;&#113;&#32;&#121;&#94;&#85;&#46; \" title=\"Rendered by QuickLaTeX.com\" height=\"135\" width=\"149\" style=\"vertical-align: 0px;\"\/><\/p>\n<p>The objective function can thus be formulated as<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-dea210472373f0132ee7788304031727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#101;&#116;&#97;&#32;&#61;&#32;&#102;&#40;&#120;&#44;&#117;&#44;&#121;&#41;&#46;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>Therefore, the simulation must include this additional constraint and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-214bff80bfc7b96ffa7e69b30456634c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/> must be defined as the objective variable in the variable specification.<\/p>\n<p>In addition, the degrees of freedom in the optimization must be assigned optimization variables. It is recommended to also supply reasonable lower and upper bounds &#8211; not only for optimization variables but also for all other variables.<\/p>","protected":false},"excerpt":{"rendered":"<p>Mandatory element The variable specification works the same way as in the simulation. Therefore, general explanations are given elsewhere. Purpose Nevertheless, there are a couple of additional requirements for an optimization. The optimization requires exactly one objective variable. Remember that MOSAICmodeling solves the following optimization problem: The objective function can thus be formulated as Therefore, [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":4187,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4191","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4191","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=4191"}],"version-history":[{"count":4,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4191\/revisions"}],"predecessor-version":[{"id":5691,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4191\/revisions\/5691"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4187"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}