{"id":11488,"date":"2023-02-02T15:43:20","date_gmt":"2023-02-02T15:43:20","guid":{"rendered":"http:\/\/141.23.68.248\/wp\/?page_id=11488"},"modified":"2023-02-13T12:23:22","modified_gmt":"2023-02-13T12:23:22","slug":"multi-objective-optimization","status":"publish","type":"page","link":"http:\/\/141.23.68.248\/wp\/?page_id=11488","title":{"rendered":"Multi-Objective Optimization"},"content":{"rendered":"<h2><\/h2>\n<h3 style=\"text-align: justify;\">Goal<\/h3>\n<p>Multi-objective optimization is a problem-solving technique that involves finding the most efficient solution among several possible options that must be optimized simultaneously. For this assignment, the goal is to find an optimal maintenance strategy in order to reduce costs, system downtime, greenhouse gases, etc. Therefore, a genetic algorithm needs to be implemented in order to identify a set of Pareto-optimal solutions.<\/p>\n<h3 style=\"text-align: justify;\">Multi-Objective Optimization<\/h3>\n<p>To implement a\u00a0multi-objective optimization for our system, the nsga2() function, part of the mco package, was used. It was necessary to define the function to be minimized, the number of input variables, the number of output measures, and the lower and upper bounds for the input variables.<\/p>\n<p>To create the function to be minimized, it is important\u00a0to look at the input and output variables. For this purpose, different maintenance strategies had to be analyzed.\u00a0Therefore, the durations of the interventions were considered in a specific range, as defined in the page: <a href=\"http:\/\/141.23.68.248\/wp\/?page_id=11484\">Maintenance Strategies<\/a>.<\/p>\n<p><span style=\"text-decoration: underline;\">Kindergarden interventions<\/span><\/p>\n<ul>\n<li>10 \u2265 M1 \u2264 20<\/li>\n<li>\u00a03 \u2265 M2 \u2264 8<\/li>\n<li>20 \u2265 M3 \u2264 35<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\">Exterior interventions<\/span><\/p>\n<ul>\n<li>12 \u2265 E1 \u2264 25<\/li>\n<li>5 \u2265 E2 \u2264 10<\/li>\n<li>27 \u2265 E3 \u2264 37<\/li>\n<\/ul>\n<p>An additional input variable which was\u00a0varied\u00a0within a range is the depth of the footing. Moreover, the output parameters\u00a0for the multi-objective optimization are\u00a0the total duration of the interventions, the minimum distance between two consecutive interventions, energy, CO2, NOx, SO2, and Costs.<\/p>\n<p>Based on this information, it was possible to define the fitness function, which provided the following results:<\/p>\n<figure id=\"attachment_14009\" aria-describedby=\"caption-attachment-14009\" style=\"width: 368px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-14009 \" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27.png\" alt=\"\" width=\"368\" height=\"70\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27.png 862w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27-300x57.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27-520x99.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Bildschirm\u00adfoto-2023-02-12-um-22.09.27-740x141.png 740w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/a><figcaption id=\"caption-attachment-14009\" class=\"wp-caption-text\">Figure 1 Results of the fitness\u00a0function<\/figcaption><\/figure>\n<h3 style=\"text-align: justify;\">Results<\/h3>\n<p>By\u00a0using the ggplot2 package, it was possible to generate the graphs of\u00a0the Pareto front. In Figure 2 the red dots form the Pareto front, which considers\u00a0the total duration of the interventions and the costs of maintenance. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 With the help of the created Pareto front it is possible to explore the different options. The best options have a short duration of maintenance and low costs.<\/p>\n<figure id=\"attachment_13970\" aria-describedby=\"caption-attachment-13970\" style=\"width: 522px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-13970\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD.png\" alt=\"Figure 2 Pareto front\" width=\"522\" height=\"252\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD.png 882w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD-300x145.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD-520x251.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot1GroupD-740x357.png 740w\" sizes=\"auto, (max-width: 522px) 100vw, 522px\" \/><\/a><figcaption id=\"caption-attachment-13970\" class=\"wp-caption-text\">Figure 2 Pareto front<\/figcaption><\/figure>\n<p>Figure 3 shows the accumulated impact of the input parameters on the performance criteria.\u00a0The red lines show the solutions of the Pareto front, that\u00a0are optimal. Moreover, the blue lines represent the non-optimal solutions. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Overall,\u00a0it can be seen that some options consume more energy or produce more greenhouse gases than others. Accordingly, depending on the scope and objective of a stakeholder, the choice of solution can\u00a0vary.<\/p>\n<figure id=\"attachment_14017\" aria-describedby=\"caption-attachment-14017\" style=\"width: 627px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-14017\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06.png\" alt=\"Figure 3 Solutions\" width=\"627\" height=\"304\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06.png 879w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06-300x145.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06-520x252.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2023\/02\/Rplot06-740x359.png 740w\" sizes=\"auto, (max-width: 627px) 100vw, 627px\" \/><\/a><figcaption id=\"caption-attachment-14017\" class=\"wp-caption-text\">Figure 3 Optimal and Non-Optimal Solutions<\/figcaption><\/figure>\n<p>\u2190 Previous Page: <a href=\"http:\/\/141.23.68.248\/wp\/?page_id=11486\">Life Cycle Analysis<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Goal Multi-objective optimization is a problem-solving technique that involves finding the most efficient solution among several possible options that must be optimized simultaneously. For this assignment, the goal is to find an optimal maintenance strategy<a class=\"read-more\" href=\"http:\/\/141.23.68.248\/wp\/?page_id=11488\">Continue reading<\/a><\/p>\n","protected":false},"author":77,"featured_media":0,"parent":11369,"menu_order":5,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-11488","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/11488","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11488"}],"version-history":[{"count":39,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/11488\/revisions"}],"predecessor-version":[{"id":14496,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/11488\/revisions\/14496"}],"up":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/11369"}],"wp:attachment":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}