[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83037-en":3,"doc-seo-83037-105":29,"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":20,"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":13,"seo_description":14,"update_tm":27,"read_time":28},83037,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Reward Density Heuristic for Dynamic Multi Vehicle Routing Performance and Computational Efficiency","Vehicle Routing Problem (VRP) variants form key optimization challenges in logistics and urban mobility. The work targets a dynamic online variant that blends VRP with the Orienteering Problem, assigning multiple vehicles to maximize cumulative reward over a fixed horizon while replanning as new tasks arrive. It proposes an Efficiency reward density heuristic for dynamic multi-vehicle assignment, evaluated in autonomous drone task allocation and urban taxi dispatch across multiple fleet sizes. Compared with construction heuristics and ALNS, GA, and SA, the heuristic attains matching reward quality with two to three orders of magnitude less planning time, dominating on the reward–compute frontier.","Reward-Density Heuristic for Dynamic Multi-Vehicle Routing: Performance and Computational Efficiency  \nManish Kolachalam  \nAutonomous Machines Applied Research Center Infosys Center for Imaging Technologies, Infosys Bengaluru, India [manish.k02@infosys.com](manish.k02@infosys.com)  \nRani Malhotra  \nAutonomous Machines Applied Research Center Infosys Center for Imaging Technologies, Infosys Bengaluru, India [rani.malhotra@infosys.com](rani.malhotra@infosys.com)  \narXiv :2607 .06066v 1 [ cs .AI ] 7 Jul 2026  \nAbstract—The Vehicle Routing Problem (VRP) and its variants represent some of the most practically consequential optimization challenges in modern logistics and urban mobility. We address a dynamic, online variant combining elements of the VRP and the Orienteering Problem (OP), in which a fleet of vehicles must maximise cumulative reward within a fixed time horizon while continuously replanning as new tasks arrive. We propose and evaluate a reward-density heuristic for dynamic multi-vehicle assignment (the Efficiency heuristic) across two domains —autonomous drone task allocation and urban taxi dispatch—at multiple fleet sizes. The method is compared with four construction heuristics and three metaheuristic algorithms (ALNS, GA, SA) under identical conditions. Across all tested configurations, the Efficiency heuristic matches the solution quality of the best metaheuristics while requiring two to three orders of magnitude less planning time, establishing Pareto dominance over all competing methods on the reward-versus-compute frontier.  \nIndex Terms—vehicle routing, dynamic dispatch, rewarddensity heuristic, drone task allocation, taxi dispatch, orienteering problem  \nI. INTRODUCTION  \nIn 2018, U.S. businesses spent 10.4% of their revenue on transportation costs alone, while overall logistics expenditure constituted 8% of GDP [1] . The Vehicle Routing Problem (VRP), first formalized by Dantzig and Ramser in 1959 [2], isone of the most extensively studied problems in combinatorial optimization. The VRP and the Travelling Salesman Problem (TSP) [3] are both NP-hard, making exact solutions intractable at scale [4], with broad implications for fuel consumption, delivery times, and carbon emissions [5] .  \nA particularly challenging variant is the dynamic VRP, in which tasks arrive online and vehicles must replan continuously [6], [7] . We focus on a formulation combining the dynamic VRP with the Orienteering Problem (OP) [8], where vehicles maximise cumulative reward within a fixed time horizon. This structure arises in drone task allocation [9],[10] and urban taxi dispatch [11],[12]: in both settings, tasks arrive dynamically, vehicles are allocated based on current location, and the binding constraint is a time budget. This aligns our formulation with the prize-collecting VRP [13] and the OP [8],  \nwhere selective task completion is central, and both domains require assignment decisions within milliseconds.  \nA natural candidate for such settings is a greedy rewarddensity heuristic — scoring each candidate task by reward divided by time cost [14] . Such a rule requires no population, no iteration, and no convergence. Whether this simplicity comes at a meaningful cost in solution quality relative to metaheuristics is an open empirical question with direct practical implications.  \nThis paper evaluates that question across five experimental configurations. The Efficiency heuristic consistently matches ALNS, GA, and SA while requiring two to three orders of magnitude less planning time, across synthetic drone environments and real-world NYC taxi dispatch data [15] . Contributions: (1) a unified dynamic reward-maximising VRP framework; (2) two reward-density instantiations — greedy sequential and optimal Hungarian matching [16]; and (3) systematic demonstration of Pareto-optimal performance across five configurations.  \nII. RELATED WORK  \nA. Construction Heuristics  \nNearest Neighbour (Greedy-Nearest): The nearestneighbour heurist","cbCaieVUkXkYG2of","https://ap.wps.com/l/cbCaieVUkXkYG2of","pdf",890105,1,6,"English","en",105,"# Introduction\n# Related Work\n## Construction Heuristics\n## Hungarian Algorithm\n# Experimental Results","[{\"question\":\"What problem setting does the paper address?\",\"answer\":\"It studies a dynamic online vehicle routing variant combining VRP with the Orienteering Problem, where vehicles continuously replan as new tasks arrive and maximize cumulative reward within a fixed time horizon.\"},{\"question\":\"What is the Efficiency heuristic proposed in the paper?\",\"answer\":\"The paper proposes a reward-density heuristic for dynamic multi-vehicle assignment, including two instantiations: greedy sequential selection and an optimal Hungarian matching approach.\"},{\"question\":\"How does the Efficiency heuristic compare to metaheuristics?\",\"answer\":\"Across tested configurations, it matches the solution quality of ALNS, GA, and SA while requiring two to three orders of magnitude less planning time, yielding Pareto dominance on the reward-versus-compute 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problem setting does the paper address?","Question",{"text":75,"@type":76},"It studies a dynamic online vehicle routing variant combining VRP with the Orienteering Problem, where vehicles continuously replan as new tasks arrive and maximize cumulative reward within a fixed time horizon.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the Efficiency heuristic proposed in the paper?",{"text":80,"@type":76},"The paper proposes a reward-density heuristic for dynamic multi-vehicle assignment, including two instantiations: greedy sequential selection and an optimal Hungarian matching approach.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the Efficiency heuristic compare to metaheuristics?",{"text":84,"@type":76},"Across tested configurations, it matches the solution quality of ALNS, GA, and SA while requiring two to three orders of magnitude less planning time, yielding Pareto dominance on the reward-versus-compute 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