{"id":4280,"date":"2021-02-17T17:07:21","date_gmt":"2021-02-17T17:07:21","guid":{"rendered":"http:\/\/141.23.68.248\/wp\/?page_id=4280"},"modified":"2021-02-25T00:37:47","modified_gmt":"2021-02-25T00:37:47","slug":"5-multi-objective-optimization","status":"publish","type":"page","link":"http:\/\/141.23.68.248\/wp\/?page_id=4280","title":{"rendered":"4. Multi-Objective Optimization"},"content":{"rendered":"<p style=\"text-align: justify;\">The main goal of this Multi-Objective Optimization (MOO) is to combine individual systems with each other by combining their maintenance plans over a lifetime of 50 years. In the course of the <a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4272\"><strong>integration context<\/strong><\/a>\u00a0the optimization will lead to a minimization of costs while causing a maximization of functionality time. In detail, the aim is to <strong>maximize the time between the interventions<\/strong> while <strong>minimizing the total number of interventions<\/strong> as well as their <strong>durations<\/strong>\u00a0(see Fig.1).<\/p>\n<p><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7095 aligncenter\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO-1024x376.png\" alt=\"210224_moo\" width=\"1024\" height=\"376\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO-1024x376.png 1024w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO-300x110.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO-520x191.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO-740x272.png 740w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO.png 1294w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><em>Fig 4.1: Summary of conflicting objectives for the Multi-Objective-Optimization<\/em><\/span><\/p>\n<p style=\"text-align: justify;\">To satisfy these conflicting objectives a <strong>Fitness Function<\/strong> is defined and used as a basis for a genetic algorithm (GA). The GA submits the best set of solutions for the given objectives by using an initial data set provided by the Fitness Function and applies a suitability function to sort out and crossover the data, so that a new data set is generated. These phases are repeated iteratively, until the best data set is found.<\/p>\n<p style=\"text-align: justify;\">The input parameters for the fitness function are defined by a set range of intervention durations for each component as part of the <a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4276\"><strong>maintenance planning<\/strong><\/a>.<\/p>\n<ul>\n<li><span style=\"text-decoration: underline;\">Interventions durations for the Frame<\/span>\n<ul>\n<li>13 \u2264 SFO \u2264 23<\/li>\n<li>3 \u2264 M.F \u2264 9<\/li>\n<li>25 \u2264 F.R \u2264 35<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"text-decoration: underline;\">Intervention durations for the Xpelair<\/span>\n<ul>\n<li>1 \u2264 FR \u2264 3<\/li>\n<li>1 \u2264 FM \u2264 3<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"text-decoration: underline;\">Intervention durations for the Stellio<\/span>\n<ul>\n<li>3 \u2264 M.S \u2264 8<\/li>\n<li>20 \u2264 RM \u2264 30<\/li>\n<li>15 \u2264 RMC \u2264 25<\/li>\n<\/ul>\n<\/li>\n<li><span style=\"text-decoration: underline;\">Intervention durations for the Isolated Footing<\/span>\n<ul>\n<li>5 \u2264 M.I \u2264 11<\/li>\n<li>7 \u2264 G \u2264 17<\/li>\n<li>30 \u2264 RI \u2264 40<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Moreover, the parameters of <strong>width<\/strong> as the integration parameter of the integrated system will be based on a value generated by the genetic algorithm, and thus, also varying within a range.<\/p>\n<p style=\"text-align: justify;\">As the output of the fitness functions the parameters of the total duration, the minimum distance between two consecutive interventions, energy demand as well as the amount of emissions as CO<sub>2<\/sub>, NO<sub>x<\/sub>, SO<sub>2<\/sub> and their related cost will be derived (see Fig.2). These resulting data set is than displayed in a plot using the Pareto Frontier as the optimal solution.<\/p>\n<p><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-7096 aligncenter\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2-1024x545.png\" alt=\"210224_moo_2\" width=\"1024\" height=\"545\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2-1024x545.png 1024w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2-300x160.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2-520x277.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2-740x394.png 740w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_2.png 1219w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><em><span style=\"text-decoration: underline;\">Fig 4.2: Operating Principle of the genetic algorithm applied for the Integrated System<\/span><\/em><\/p>\n<p style=\"text-align: justify;\">Because of the random character of the GA different results are obtained with every new run of the R-Code as its input parameter are set differently every time. But for each set of input parameters the best solution is found. In R the <em>nsg2()-function<\/em> is applied for the GA. During 10 iterations (generation) an initial data set consisting of 13 different input parameters (idim) is processed to generate a new data set containing 7 output parameters (odim) out of 100 alternatives (popsize).<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_KOnsole1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-7388\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_KOnsole1.jpg\" alt=\"210224_moo_konsole\" width=\"474\" height=\"70\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_KOnsole1.jpg 474w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_KOnsole1-300x44.jpg 300w\" sizes=\"auto, (max-width: 474px) 100vw, 474px\" \/><\/a><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/210224_MOO_KOnsole.jpg\"><br \/>\n<\/a><\/p>\n<p style=\"text-align: center;\"><em><span style=\"text-decoration: underline;\">Fig 4.3: Application of the nsg2()-function with defining lower and upper boundaries for the generation of the data se<\/span>t<\/em><\/p>\n<p style=\"text-align: justify;\">Because of the random character of the GA different results are obtained with every new run of the R-Code as its input parameter are set differently every time. But for each set of input parameters the best solution is found. In R the <em>nsg2()-function<\/em> is applied for the GA (see Fig.3). During 10 iterations (generation) an initial data set consisting of 13 different input parameters (idim) is processed to generate a new data set containing 7 output parameters (odim) out of 100 alternatives (popsize).<\/p>\n<p style=\"text-align: justify;\">During the<a title=\"Integrated Maintenance Strategy\" href=\"http:\/\/141.23.68.248\/wp\/?page_id=4276\"> Integrated Mainenance Strategy<\/a> a solution was found for the duration of the maintenance of the integrated system throughout its lifecycle. As a recall, we obtained 2 values, 70.25 days and 72 days, which was already much\u00a0suitable as the initial duration of 185 days. Similarly, we obtained of the<a title=\"Life-Cycle Inventory Analysis\" href=\"http:\/\/141.23.68.248\/wp\/?page_id=4278\">\u00a0Life-Cycle Analysis<\/a> the results for the combined system,\u00a0containing the energy consumed by the individual systems and the emitted greenhouse gases (CO<sub>2<\/sub>, SO<sub>2<\/sub>, NO<sub>X<\/sub>) as well as including repairs till the end of the system&#8217;s lifecycle.<\/p>\n<p>In order to improve the maintenance strategy the maintenance period and\/or the costs involved in the lifecycle will be reduced. For this aim, a pareto front is being expressed graphically to explore these alternatives. A total of 12 alternatives are generated and are shown in the diagram below (see Fig.4.4).<\/p>\n<figure id=\"attachment_7443\" aria-describedby=\"caption-attachment-7443\" style=\"width: 774px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-7443\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart.png\" alt=\"Pareto Chart\" width=\"774\" height=\"717\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart.png 1078w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart-300x278.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart-1024x948.png 1024w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart-520x481.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Pareto_chart-740x685.png 740w\" sizes=\"auto, (max-width: 774px) 100vw, 774px\" \/><\/a><figcaption id=\"caption-attachment-7443\" class=\"wp-caption-text\"><span style=\"text-decoration: underline;\"><em>Fig 4.4 : Pareto Chart<\/em><\/span><\/figcaption><\/figure>\n<p>From these alternatives, it is possible to figure out 2 options: <strong>The least costly<\/strong> (costs in Euros) and the one with the l<strong>east duration of maintenance<\/strong> (duration in days). They are shown in detail on the table below (see Fig.4.5).<\/p>\n<figure id=\"attachment_7453\" aria-describedby=\"caption-attachment-7453\" style=\"width: 887px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7453\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving.png\" alt=\"cost saving vs time saving solution\" width=\"887\" height=\"136\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving.png 887w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving-300x46.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving-520x80.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/cost-saving-vs-Time-saving-740x113.png 740w\" sizes=\"auto, (max-width: 887px) 100vw, 887px\" \/><\/a><figcaption id=\"caption-attachment-7453\" class=\"wp-caption-text\">Fig 4.5 : Cost saving vs. time saving solution<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">By this, it gets obsious,\u00a0that the optimization does reduce the maintenance days by 30%, which is a great improvement. From these options, a conclusion could already be made, if the stakeholders only stick to those two factors (time and money). Still, they are not the only objectives, so that for each of the 12 solutions other factors (emissions, energy and interventions) should be taken into consideration. The values of all factors included in the option are shown in the diagram below (see Fig.4.6).<\/p>\n<figure id=\"attachment_7447\" aria-describedby=\"caption-attachment-7447\" style=\"width: 828px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions.png\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-7447\" src=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions.png\" alt=\"optimized_solutions\" width=\"828\" height=\"767\" srcset=\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions.png 1078w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions-300x278.png 300w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions-1024x948.png 1024w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions-520x481.png 520w, http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2021\/02\/Optimized_Solutions-740x685.png 740w\" sizes=\"auto, (max-width: 828px) 100vw, 828px\" \/><\/a><figcaption id=\"caption-attachment-7447\" class=\"wp-caption-text\"><span style=\"text-decoration: underline;\"><em>Fig 4.6 : optimized_solutions<\/em><\/span><\/figcaption><\/figure>\n<p style=\"text-align: justify;\">Each option is visualized with a color (alice blue, azure, blue, cadet blue, chocolate,\u00a0 cyan, dark grey, dark orchid, dark slate gray, deep sky blue, fire brick and golden rod for option 1 to 12 respectively). It can be noticed, that some options consume more energy than others or produce more greenhouse gases than others. These factors may affect the decision of stakeholders depending on the defined scope and goal.<\/p>\n<p style=\"text-align: justify;\">The Interpretation of these data as well as a recommendation for Decision-Making can be found under <a title=\"Interpretations and Decision making\" href=\"http:\/\/141.23.68.248\/wp\/?page_id=4282\">here<\/a>.<\/p>\n<hr \/>\n<p style=\"text-align: left;\"><span style=\"text-decoration: underline;\"><strong>Page Navigation<\/strong><\/span><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4272\">1. Integration Context<\/a><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4276\">2. Maintenance Strategy\u00a0<\/a><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4278\">3. Life-Cycle Inventory Analysis<\/a><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4280\">4. Multi-Objective Optimization<\/a><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/141.23.68.248\/wp\/?page_id=4282\">5. Interpretations and Decision making<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The main goal of this Multi-Objective Optimization (MOO) is to combine individual systems with each other by combining their maintenance plans over a lifetime of 50 years. In the course of the integration context\u00a0the optimization<a class=\"read-more\" href=\"http:\/\/141.23.68.248\/wp\/?page_id=4280\">Continue reading<\/a><\/p>\n","protected":false},"author":72,"featured_media":0,"parent":4115,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"page-templates\/page_fullwidth.php","meta":{"footnotes":""},"class_list":["post-4280","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/4280","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\/72"}],"replies":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4280"}],"version-history":[{"count":18,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/4280\/revisions"}],"predecessor-version":[{"id":7426,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/4280\/revisions\/7426"}],"up":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/4115"}],"wp:attachment":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}