[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-137805-en":3,"doc-seo-137805-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},137805,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",6,"Technology","Applying Ant Colony Optimization to Dynamic Binary-Encoded Problems - Study and Comparison","Ant colony optimization (ACO) adapts to dynamic optimization problems when stagnation is controlled, yet most ACO work targets permutation-encoded formulations such as dynamic traveling salesman problems, while binary-encoded cases like dynamic knapsack are usually handled by evolutionary algorithms. This paper introduces a binary version of ACO to solve binary-encoded dynamic problems and compares it with existing evolutionary approaches. Results indicate that, with suitable pheromone evaporation, the proposed ACO variant outperforms evolutionary algorithms across most dynamic test scenarios.","Applying Ant Colony Optimization to Dynamic Binary-Encoded Problems  \nMichalis Mavrovouniotis and Shengxiang Yang  \nCentre for Computational Intelligence (CCI) School of Computer Science and Informatics, De Montfort University The Gateway, Leicester LE1 9BH, United Kingdom {mmavrovouniotis,[syang](syang}@dmu.ac.uk)[}](syang}@dmu.ac.uk)[@dmu.ac.uk](syang}@dmu.ac.uk)  \nAbstract. Ant colony optimization (ACO) algorithms have proved tobe able to adapt to dynamic optimization problems (DOPs) when stagnation behaviour is addressed. Usually, permutation-encoded DOPs, e.g. , dynamic travelling salesman problems, are addressed using ACO algorithms whereas binary-encoded DOPs, e.g., dynamic knapsack problems, are tackled by evolutionary algorithms (EAs) . This is because of the initial developments of the algorithms. In this paper, a binary version of ACO is introduced to address binary-encoded DOPs and compared with existing EAs. The experimental results show that ACO with an appropriate pheromone evaporation rate outperforms EAs in most dynamic test cases.  \n1 Introduction  \nAnt colony optimization (ACO) algorithms have shown good performance when applied to di􀀎cult optimization problems under static environments [1] . In general, ACO has been initially developed to tackle permutation-encoded problems [1] . There are also a few applications for binary-encoded problems, such as the multidimensional knapsack problem [2–6] . Most of the existing ACO applications assume stationary environments. However, in many real-world applications we have to deal with dynamic environments, where the optimum changes and needs re-optimization.  \nSimilarly to other nature-inspired algorithms [7,8], ACO algorithms can adapt to dynamic changes since they are also inspired from nature, which is a continuous adaptation process. Practically, ACO can adapt to dynamic changes by transferring knowledge from past environments, using the pheromone trails, to speed up re-optimization [9] . The challenge to such algorithms when addressing dynamic optimization problems (DOPs) is that they su􀀋er from the stagnation behaviour, where all ants construct the same solution from early stages of the algorithm execution. The adaptation capabilities of ACO rely on the pheromone evaporation where a constant amount of pheromone is deducted to eliminate pheromone trails that represent bad solutions that may bias ants to search to the non-promising areas of the search space. ACO algorithms have been successfully applied to dynamic extensions of the aforementioned permutation-encoded  \nproblems, e.g., dynamic travelling salesman problems (TSPs) [10,11] and dynamic vehicle routing problems (VRPs) [12,13] .  \nIn this paper, we investigate the performance of ACO for solving dynamic binary-encoded optimization problems. Such problems have been successfully tackled by evolutionary algorithms (EAs) [14,15], but not by ACO. Therefore, the original ACO framework is modi􀀌ed to construct binary-encoded solutions rather than permutation-encoded solutions (e.g., for the TSP) [16,4] . In addition, we study the e􀀋ect of introducing di􀀋erent pheromone evaporation ratesand pheromone update policies into ACO for DOPs. As a result, a binary ACO framework, denoted ACO B , is established and integrated to the exclusive-or (XOR) DOP generator which can generate di􀀋erent dynamic test cases from given stationary binary-encoded problems [17] . Using this generator, an experimental study of comparing the proposed ACOB with an existing genetic algorithm (GA) [14] and a population-based incremental learning (PBIL) algorithm [15] .  \nThe rest of the paper is organized as follows. Section 2 describes in detail the proposed ACOB . Section 3 describes the dynamic test environment for this study, including the details for the integration of ACOB with the XOR DOP. Section 4 describes the experiments carried out on a series of di􀀋erent DOPs including relevant analysis. Finally, Section 5 concludes this paper with d","cbCaim4YO6F5Xhrs","https://ap.wps.com/l/cbCaim4YO6F5Xhrs","pdf",239504,1,12,"English","en",105,"# Introduction\n## Dynamic environments and stagnation in ACO\n# Binary Ant Colony Optimization\n## Initialization and pheromone table design","[{\"question\":\"Why are binary-encoded dynamic problems usually solved by evolutionary algorithms instead of ACO?\",\"answer\":\"ACO was originally developed for permutation-encoded problems, and earlier implementations focused on such representations. Binary-encoded dynamic problems have therefore been tackled more commonly by evolutionary algorithms.\"},{\"question\":\"What modification is proposed for applying ACO to binary-encoded problems?\",\"answer\":\"The original ACO framework is modified so ants construct binary-encoded solutions rather than permutation-encoded ones, and different pheromone evaporation rates and update policies are investigated.\"},{\"question\":\"How does pheromone evaporation affect performance on dynamic test cases?\",\"answer\":\"The experimental findings show that ACO with an appropriate pheromone evaporation rate outperforms evolutionary algorithms in most dynamic scenarios.\"}]","Applying Ant Colony Optimization to Dynamic Binary-Encoded Problems - Study and Comparison | PDF",1787447884,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"applying-ant-colony-optimization-to-dynamic-binary-encoded-problems-study-and-comparison","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/applying-ant-colony-optimization-to-dynamic-binary-encoded-problems-study-and-comparison/137805/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are binary-encoded dynamic problems usually solved by evolutionary algorithms instead of ACO?","Question",{"text":75,"@type":76},"ACO was originally developed for permutation-encoded problems, and earlier implementations focused on such representations. Binary-encoded dynamic problems have therefore been tackled more commonly by evolutionary algorithms.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What modification is proposed for applying ACO to binary-encoded problems?",{"text":80,"@type":76},"The original ACO framework is modified so ants construct binary-encoded solutions rather than permutation-encoded ones, and different pheromone evaporation rates and update policies are investigated.",{"name":82,"@type":73,"acceptedAnswer":83},"How does pheromone evaporation affect performance on dynamic test cases?",{"text":84,"@type":76},"The experimental findings show that ACO with an appropriate pheromone evaporation rate outperforms evolutionary algorithms in most dynamic scenarios.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,113,118,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":111,"slug":112},50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":29,"slug":121},8,"Research & Report","research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]