Probabilistic Traveling Salesman Problem and Harmony Search Algorithms in Pharmacy Supply Optimization

Abstract

<jats:p>This paper demonstrates the utilitarian significance of the Probabilistic Traveling Salesman Problem (PTSP) in planning travel routes by companies which provide distribution services for pharmacies, with a particular consideration of variable customer demand. The optimization problem was solved using the Harmony Search (HS) algorithm, thus verifying its utility based on one real instance of PTSP (representing the problem of pharmacy supply reliability) and three tasks from the public TSPLIB library (adjusted to PTSP). As a result of the conducted research, significant utility of the hybrid approach was identified, assuming the combination of HS with popular 2‑opt method, which enabled achievement of good results within acceptable period (in practical applications).</jats:p>

Multiple probabilistic traveling salesman problem in the coordination of drug transportation—In the context of sustainability goals and Industry 4.0

“…Based on [ 47 ], we chose the following HS parameter values: HMS = 5, HMCR = 0.98, PAR = 0.25, R = 1000 and IT = 1, 000, 000.…”

“…An example of a metaheuristic that has achieved good results in probabilistic TSP (PTSP) instances is HS [ 47 ], which draws inspiration from the process of seeking harmony in music and has been used in the process of solving many optimization problems [ 48 ]. This, indicates that it may have potential for solving MPTSP instances, especially in Industry 4.0.…”

“…If p i for each node i is the same (and amounts to p ), then we have a homogeneous PTSP, which was used to model a problem of drug distribution in [ 47 ] (from the utilitarian point of view, pharmacies are characterized practically with the same probability of supply necessity).…”

“…In [ 47 ], an attempt was made to adjust HS for the efficient solving of PTSP instances (based on an approach intended for the asymmetric TSP proposed in [ 38 ]). The authors assumed that the pitches in the harmony correspond to the number of nodes to be visited by the traveling salesman and that the order of their occurrence indicates the sequence of travel.…”

“…Each cluster created in step 1 is treated as a separate PTSP instance being solved by a new HS instance, according to the approach proposed in [ 47 ] (described in Subsection HS for PTSP ). This approach allows for the use of parallel computing, facilitating shorter computation time.…”