A Probabilistic Hill-Climbing Algorithm for the Single-Source Transportation Problem

Pisut Pongchairerks ()
Additional contact information
Pisut Pongchairerks: Digital Engineering Program, Thai-Nichi International College, Thai-Nichi Institute of Technology, Bangkok 10250, Thailand

Sustainability, 2023, vol. 15, issue 5, 1-14

Abstract: This paper proposes a probabilistic hill-climbing algorithm, called PH, for the single-source transportation problem (STP). PH is a tree search algorithm in which each node contains an assignment problem (AP) transformed from the STP being solved. The transformation converts each source’s product units into product lots; a product lot equals multiple product units. The AP aims to find the optimal assignment of product lots to destinations to minimize the total assignment cost. PH uses the Hungarian method to find the optimal solution of the AP in every node, which is a solution of the STP. For the AP of the root node (as the initial current node), the number of each source’s product lots is set to be small enough to guarantee the generation of a feasible solution for the STP. To generate every subsequent level, the current node is branched into multiple child nodes, in which the number of child nodes equals the number of sources in the STP. The AP of each child node is modified from the AP of the current node by adding one more product lot into a specific different source. Consequently, each child node provides a solution that is better than or the same as the current node’s solution; however, some child nodes’ solutions may be infeasible for the STP due to the insufficiency of a source’s capacity. If all of the child nodes cannot find a better feasible solution than the current node’s solution, PH stops its procedure. To diversify the search, PH selects one of the child nodes as the new current node in a probabilistic way, instead of always selecting the best child node. The experiment’s results in this paper reveal the performance of the three variants of PH.

Keywords: single-source transportation problem; assignment problem; hill-climbing algorithm; beam search algorithm; tree search algorithm (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2071-1050/15/5/4289/pdf (application/pdf)
https://www.mdpi.com/2071-1050/15/5/4289/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jsusta:v:15:y:2023:i:5:p:4289-:d:1082866

Access Statistics for this article

Sustainability is currently edited by Ms. Alexandra Wu

More articles in Sustainability from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().