Application of graph theory to find optimal paths for the transportation problem

Likaj, Ramë; Shala, Ahmet; Mehmetaj, Merita; Hyseni, Pajazit; Bajrami, Xhevahir

doi:10.3182/20130606-3-xk-4037.00031

Cited by 23 publications

(7 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, researchers have employed a variety of heuristic approaches to solve PDPTW and CVRP. Data mining (Chen et al, 2012), evolutionary algorithms (Lau et al, 2010;Koc et al, 2015;Vidal et al, 2013), integer programming (Toth and Tramontani, 2008;Vidal et al, 2013), tabu searches (Berbotto et al, 2014;Escobar et al, 2014;Cordeau and Maichberger, 2012;Vidal et al, 2013), simulated annealing (Banos et al, 2013;Vidal et al, 2013;Xiao et al, 2014), graph theory (Likaj et al, 2013) and ant colony optimization (Vidal et al, 2013) are techniques that have been explored in the literature to solve these complex transportation problems. All of these approaches seek to find near optimal solutions to address routing problem variants.…”

Section: Literature Reviewmentioning

confidence: 99%

An evolutionary algorithm approach for the constrained multi-depot vehicle routing problem

Lightner-Laws

Agrawal

Lightner

et al. 2016

International Journal of Intelligent Computing and Cybernetics

View full text Add to dashboard Cite

Purpose – The purpose of this paper is to explore a real world vehicle routing problem (VRP) that has multi-depot subcontractors with a heterogeneous fleet of vehicles that are available to pickup/deliver jobs with varying time windows and locations. Both the overall job completion time and number of drivers utilized are analyzed for the automated job allocations and manual job assignments from transportation field experts. Design/methodology/approach – A nested genetic algorithm (GA) is used to automate the job allocation process and minimize the overall time to deliver all jobs, while utilizing the fewest number of drivers – as a secondary objective. Findings – Three different real world data sets were used to compare the results of the GA vs transportation field experts’ manual assignments. The job assignments from the GA improved the overall job completion time in 100 percent (30/30) of the cases and maintained the same or fewer drivers as BS Logistics (BSL) in 47 percent (14/30) of the cases. Originality/value – This paper provides a novel approach to solving a real world VRP that has multiple variants. While there have been numerous models to capture a select number of these variants, the value of this nested GA lies in its ability to incorporate multiple depots, a heterogeneous fleet of vehicles as well as varying pickup times, pickup locations, delivery times and delivery locations for each job into a single model. Existing research does not provide models to collectively address all of these variants.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

An evolutionary algorithm approach for the constrained multi-depot vehicle routing problem

Lightner-Laws

Agrawal

Lightner

et al. 2016

International Journal of Intelligent Computing and Cybernetics

View full text Add to dashboard Cite

show abstract

“…However, as more complex constraints are considered, finding an explicit optimal solution becomes computationally expensive and virtually impossible to ascertain; thus researchers have explored a variety of heuristics such as data mining (Chen et al 2012), evolutionary algorithms (Vidal et al 2011b;Lau et al 2010), tabu searches (Cordeau and Maichberger 2011;Brandao 2011), graph theory (Likaj et al 2013) andsimulated annealing (1993) to solve these complex transportation problems. All of these approaches seek to find near optimal solutions to address routing problem variants.…”

Section: Literature Reviewmentioning

confidence: 99%

A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem

et al. 2016

View full text Add to dashboard Cite

Most research about the vehicle routing problem (VRP) does not collectively address many of the constraints that real-world transportation companies have regarding route assignments. Consequently, our primary objective is to explore solutions for real-world VRPs with a heterogeneous fleet of vehicles, multi-depot subcontractors (drivers), and pickup/delivery time window and location constraints. We use a nested bi-criteria genetic algorithm (GA) to minimize the total time to complete all jobs with the fewest number of route drivers. Our model will explore the issue of weighting the objectives (total time vs. number of drivers) and provide Pareto front solutions that can be used to make decisions on a case-by-case basis. Three different real-world data sets were used to compare the results of our GA vs. transportation field experts' job assignments. For the three data sets, all 21 Pareto efficient solutions yielded improved overall job completion times. In 57 % (12/21) of the cases, the Pareto efficient solu- Keywords Vehicle routing problem · Bi-criteria genetic algorithm · Pareto front · Multi-depot transportation problem · Hard and soft time windows

show abstract

“…Techniques like Kruskal's and Dijkstra's algorithms are instrumental in resolving practical troubles, consisting of cost-effective transportation and shipment [14]. Lastly, the enormous adoption of graph-theoretical techniques across various mathematical regions emphasizes its versatility and growing influence in solving a multitude of current problems [15] in table 1.…”

Section: Introductionmentioning

confidence: 99%

Expanding Horizons: Graph Theory’s Multifaceted Applications

Saxena,

Lalitha

et al. 2024

E3S Web of Conf.

View full text Add to dashboard Cite

A subfield of mathematics called graph theory studies networks of points interconnected by lines. Researchers may model and examine the structure of a network using graph theory. Mostly topological in nature, graph theory supports both qualitative and quantitative methods. Important scientific findings have been made possible by graph theory, including a better understanding of how electrical distribution systems malfunction and how health problems spread through social networks. Although network analysis typically conjures images of graph theory, complex network theory, and network optimisation, geographers employ a variety of techniques to study networks. This study emphasises the foundational significance of graph theory in modelling and analysing complicated networks by methodically exploring the many applications of graph theory throughout several fields. It starts with a review of the fundamental roles that graph theory plays in mathematical information, computational science, and chemistry. The discussion then moves to cutting-edge applications in the fields of social media, means of transport, and the field of neuroscience, demonstrating graph theory’s versatility. The research emphasises its new application in improving traffic flow projections and assessing cultural environmental amenities employing social media data. The present article validates the crucial role of graph theory in addressing contemporary issues through an extensive overview and methodological study.

show abstract

Application of graph theory to find optimal paths for the transportation problem

Cited by 23 publications

References 1 publication

An evolutionary algorithm approach for the constrained multi-depot vehicle routing problem

An evolutionary algorithm approach for the constrained multi-depot vehicle routing problem

A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem

Expanding Horizons: Graph Theory’s Multifaceted Applications

Contact Info

Product

Resources

About