Affiliation:
1. Department of Computer Sciences , Faculty of Exact and Natural Sciences , Iv. Javakhishvili Tbilisi State University , 13 University Str ., Tbilisi 0186 , Georgia
Abstract
Abstract
Route planning problems are among the activities that have the highest impact in emergency logistical planning, goods transportation and facility location-distribution because of their effects on efficiency in resource management, service levels and client satisfaction.
In the extreme conditions, such as disaster-stricken zones, the difficulty of vehicle movement between nearest different affected areas (demand points) on planning routes cause the imprecision of time of movement and the uncertainty of feasibility of movement.
In this paper, the imprecision is presented by triangular fuzzy numbers and the uncertainty is presented by a possibility measure.
A new two-stage, fuzzy bi-criterion optimization approach for the vehicle routing problem (VRP) is considered.
On the first stage, the sample of so-called “promising” closed routes are selected based on a “constructive” approach.
On the second stage, triangular fuzzy valued Choquet aggregation (TFCA) operator is constructed for the selected closed routes.
The evaluation of constructed routes, levels of failure and possibility of vehicle movement on the roads are aggregated by the TFCA operator by the new criterion – minimization of infeasibility of movement.
The new criterion together with the classic criterion – minimization of the total distance traveled – creates a bi-criteria fuzzy VRP.
The constructed VRP is reduced to the bi-criteria fuzzy partitioning problem, and an 𝜀-constraint approach is developed for solving it.
For numerical experiments, a parallel algorithm is created on the basis of D. Knuth’s algorithm of Dancing Links (DLX).
An example is presented with the results of our approach for the VRP, where all Pareto-optimal solutions are found from the set of promising routes.
The optimal solutions tend to avoid roads that are problematic because of extreme situations.
Funder
Shota Rustaveli National Science Foundation
Reference70 articles.
1. M. Allahviranloo, J. Y. J. Chow and W. W. Recker,
Selective vehicle routing problems under uncertainty without recourse,
Transp. Res. Part E 62 (2014), 68–88.
2. J.-F. Bérubé, M. Gendreau and J.-Y. Potvin,
An exact 𝜖-constraint method for bi-objective combinatorial optimization problems: Application to the traveling salesman problem with profits,
European J. Oper. Res. 194 (2009), no. 1, 39–50.
3. L. Bodin, B. Golden, A. Assad and M. Ball,
Routing and scheduling of vehicles and crews. The state of the art,
Comput. Oper. Res. 10 (1983), no. 2, 63–211.
4. J. Brito, C. Campos, J. P. Castro, F. J. Martínez, B. Melián, J. A. Moreno and J. M. Moreno,
Fuzzy vehicle routing problem with time windows,
Proceedings of IPMU’08,
Universidad de Málaga, Málaga (2008), 1266–1273.
5. J. Brito, F. J. Martínez, J. A. Moreno and J. L. Verdegay,
An ACO hybrid metaheuristic for close-open vehicle routing problems with time windows and fuzzy constraints,
Appl. Soft Comput. 32 (2015), 154–163.