{"id":2267,"date":"2025-09-26T11:07:06","date_gmt":"2025-09-26T04:07:06","guid":{"rendered":"https:\/\/www.its.ac.id\/publikasi\/?p=2267"},"modified":"2025-09-26T11:07:06","modified_gmt":"2025-09-26T04:07:06","slug":"solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2","status":"publish","type":"post","link":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/","title":{"rendered":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem"},"content":{"rendered":"
Nadya Sulistia, Irwansyah Irwansyah, Marwan Marwan<\/em><\/div>\n

 <\/p>\n

\n

Abstract<\/h4>\n
Traveling Salesman Problem (TSP) is a method of finding the minimum tour in a graph. In line with the development of TSP theory and its application, TSP Art shows up as the implementation of mathematics in art. TSP Art is an art which represented in a graph. TSP Art consists of a lot of vertice that make the solution more complicated to be found. This problem has been solved using the Parallel Genetic Algorithm with Edge Assembly Crossover algorithm (GA-EAX). However, there are few lacks of this algorithm e.g., the running time is too long, it needs $12$ hours to solve the problem. In addition, GA-EAX required too much amount of RAM to process hundreds thousands of these vertice. While, in this research, one of the TSP variants is used, that is Clustered Traveling Salesman Problem (CTSP). CTSP is a modification of TSP by clustering number of vertice in a cluster, where each cluster must be visited one by one. The purpose of this study is to determine the TSP Art’s solution using the CTSP method and to know the length of the CTSP\u2019s minimum tour on the TSP Art problem. In this study, the Nearest Neighbor Heuristic algorithm is used to find the minimum path of each cluster. Furthermore, Kruskal\u2019s algorithm is used to connect those minimum paths to become CTSP\u2019s minimum tour. Based on this study, the minimum tour of Monalisa, Van Gogh, and Venus are 6.932.014,192594253 distance units, 7.902.043,90173308 distance units, and 8.210.589,60220378 distance units, respectively.<\/div>\n<\/div>\n
\n

Keywords<\/h4>\n
Clustered Traveling Salesman Problem, Kruskal\u2019s Algorithm, Nearest Neighbor Heuristic Algorithm, TSP Art.<\/div>\n
PDF<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Nadya Sulistia, Irwansyah Irwansyah, Marwan Marwan   Abstract Traveling Salesman Problem (TSP) is a method of finding the minimum tour in a graph. In line with the development of TSP theory and its application, TSP Art shows up as the implementation of mathematics in art. TSP Art is an art which represented in a graph. […]<\/p>\n","protected":false},"author":250,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_joinchat":[],"footnotes":""},"categories":[216],"tags":[],"class_list":["post-2267","post","type-post","status-publish","format-standard","hentry","category-ijcsam-journal"],"yoast_head":"\nSolving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )\" \/>\n<meta property=\"og:description\" content=\"Nadya Sulistia, Irwansyah Irwansyah, Marwan Marwan   Abstract Traveling Salesman Problem (TSP) is a method of finding the minimum tour in a graph. In line with the development of TSP theory and its application, TSP Art shows up as the implementation of mathematics in art. TSP Art is an art which represented in a graph. […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\" \/>\n<meta property=\"og:site_name\" content=\"IJC ( ITS Journal Center )\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-26T04:07:06+00:00\" \/>\n<meta name=\"author\" content=\"itspublikasi\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"itspublikasi\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\"},\"author\":{\"name\":\"itspublikasi\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7\"},\"headline\":\"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem\",\"datePublished\":\"2025-09-26T04:07:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\"},\"wordCount\":282,\"commentCount\":0,\"articleSection\":[\"ijcsam journal\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\",\"url\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\",\"name\":\"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )\",\"isPartOf\":{\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#website\"},\"datePublished\":\"2025-09-26T04:07:06+00:00\",\"author\":{\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.its.ac.id\/publikasi\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#website\",\"url\":\"https:\/\/www.its.ac.id\/publikasi\/\",\"name\":\"IJC ( ITS Journal Center )\",\"description\":\"Institut Teknologi Sepuluh Nopember\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.its.ac.id\/publikasi\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7\",\"name\":\"itspublikasi\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/1c672fdec2c22686bbf54db48608a7cbb61f01783efa5776676dd183144eeffd?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/1c672fdec2c22686bbf54db48608a7cbb61f01783efa5776676dd183144eeffd?s=96&d=mm&r=g\",\"caption\":\"itspublikasi\"},\"url\":\"https:\/\/www.its.ac.id\/publikasi\/author\/itspublikasi\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/","og_locale":"en_US","og_type":"article","og_title":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )","og_description":"Nadya Sulistia, Irwansyah Irwansyah, Marwan Marwan   Abstract Traveling Salesman Problem (TSP) is a method of finding the minimum tour in a graph. In line with the development of TSP theory and its application, TSP Art shows up as the implementation of mathematics in art. TSP Art is an art which represented in a graph. […]","og_url":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/","og_site_name":"IJC ( ITS Journal Center )","article_published_time":"2025-09-26T04:07:06+00:00","author":"itspublikasi","twitter_card":"summary_large_image","twitter_misc":{"Written by":"itspublikasi"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#article","isPartOf":{"@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/"},"author":{"name":"itspublikasi","@id":"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7"},"headline":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem","datePublished":"2025-09-26T04:07:06+00:00","mainEntityOfPage":{"@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/"},"wordCount":282,"commentCount":0,"articleSection":["ijcsam journal"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/","url":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/","name":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem - IJC ( ITS Journal Center )","isPartOf":{"@id":"https:\/\/www.its.ac.id\/publikasi\/#website"},"datePublished":"2025-09-26T04:07:06+00:00","author":{"@id":"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7"},"breadcrumb":{"@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.its.ac.id\/publikasi\/en\/2025\/09\/26\/solving-traveling-salesman-problem-art-using-clustered-traveling-salesman-problem-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.its.ac.id\/publikasi\/"},{"@type":"ListItem","position":2,"name":"Solving Traveling Salesman Problem Art Using Clustered Traveling Salesman Problem"}]},{"@type":"WebSite","@id":"https:\/\/www.its.ac.id\/publikasi\/#website","url":"https:\/\/www.its.ac.id\/publikasi\/","name":"IJC ( ITS Journal Center )","description":"Institut Teknologi Sepuluh Nopember","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.its.ac.id\/publikasi\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/cba0179fe82f2c584109af8e270dbfc7","name":"itspublikasi","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.its.ac.id\/publikasi\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/1c672fdec2c22686bbf54db48608a7cbb61f01783efa5776676dd183144eeffd?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/1c672fdec2c22686bbf54db48608a7cbb61f01783efa5776676dd183144eeffd?s=96&d=mm&r=g","caption":"itspublikasi"},"url":"https:\/\/www.its.ac.id\/publikasi\/author\/itspublikasi\/"}]}},"_links":{"self":[{"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/posts\/2267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/users\/250"}],"replies":[{"embeddable":true,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/comments?post=2267"}],"version-history":[{"count":1,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/posts\/2267\/revisions"}],"predecessor-version":[{"id":2268,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/posts\/2267\/revisions\/2268"}],"wp:attachment":[{"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/media?parent=2267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/categories?post=2267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.its.ac.id\/publikasi\/wp-json\/wp\/v2\/tags?post=2267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}